How does the Pythagorean Theorem relate to trigonometric ratios? What is important to remember about coterminal angles and their trigonometric function values?

Answers

Answer 1

Answer:

How Pythagoras theorem relates to Trigonometry ratios

For a right angled triangle ∆ABC,

Let a = hypothenus

b = opposite

c = adjacent

Sin²θ + Cos²θ = 1

Provided that a² + b² = c²

To prove this divide through by c²

Tongive

a²/c² + b²/c² = c²/c²

Sinθ = a/c , Cosθ = b/c

So, the above equation becomes

(Sinθ)² + (Cosθ)² = 1

Sin²θ + Cos²θ = 1

Coterminal Angles

Coterminal Angles are angles who share the same initial side and terminal sides.

Finding coterminal angles is as simple as adding or subtracting 360° or 2π to each angle, depending on whether the given angle is in degrees or radians.

Answer 2

Final answer:

The Pythagorean Theorem and trigonometric ratios are related through the relationships between the sides of a right triangle. The theorem helps to calculate the sides involved in defining the sine, cosine, and tangent functions. Coterminal angles share the same trigonometric values despite having different measurements.

Explanation:

The Pythagorean Theorem is intimately related to trigonometric ratios, as it provides the fundamental relationship between the sides of a right-angled triangle. In trigonometry, the ratios of these sides define sine, cosine, and tangent functions. The Pythagorean theorem states that a² + b² = c², where 'a' and 'b' are the lengths of the legs and 'c' is the length of the hypotenuse of a right triangle. For example, given an angle θ within the right triangle, the cosine of θ is the adjacent side over the hypotenuse (cos(θ) = a/c), which implicitly uses the Pythagorean relationship when solving for the hypotenuse 'c'.

It's also important to remember coterminal angles in trigonometry, which are angles that share the same terminal side. Coterminal angles can be found by adding or subtracting whole multiples of 360° (or 2π radians). Although coterminal angles are different in measure, they have the same sine, cosine, and tangent values because these trigonometric functions are based on the position of the terminal side, not the actual angle measurement. Hence, coterminal angles have identical trigonometric function values.


Related Questions

Determine if the side lengths could form a triangle use an inquality to prove your answer

16m.. 21m.. 39m

Answers

Answer:

With side lengths 16 m, 21 m and 39 m a triangle cannot be formed.

Step-by-step explanation:

Given:

Sides of the triangle are given.

First side = 16 m

Second Side = 21 m

Third side = 39 m

We need to find whether the side length can form the triangle.

Solution:

Now we know that;

By Triangle In equality property which states that;

"The sum of length of any two side of triangle is greater than the length of the thirds side."

By applying the same in given data we get;

First Side + second side > Third side

[tex]16+21>39\\\\37>39[/tex]

which is false.

The first condition has failed itself.

So we can say that;

With side lengths 16 m, 21 m and 39 m a triangle cannot be formed.

Final answer:

The side lengths 16m, 21m, and 39m do not form a triangle as they do not satisfy the triangle inequality theorem, which states that for any three lengths to form a triangle, the sum of any two lengths must be greater than the third length.

Explanation:

In mathematics, specifically in triangle geometry, the triangle inequality theorem states that for any given three sides, the lengths to form a triangle, the sum of the lengths of any two sides must be greater than the length of the third side. In other words, if a, b, and c are the lengths of the sides:

 

a + b > c

a + c > b

b + c > a

Our given side lengths are 16m, 21m, and 39m. Let's check if they satisfy the triangle inequality:

 

16m + 21m > 39m (Is 37m > 39m? No, 37m is less than 39m, thus the inequality is not satisfied)

 

Therefore, the given side lengths do not form a triangle.

Learn more about Triangle Inequality here:

https://brainly.com/question/24078586

#SPJ11

The population of Greenville is currently 50,000 and declines at a rate of 1.2% every year. This models:

Answers

Answer:

Every year they are losing 600 people a year.

Step-by-step explanation:

You take 50,000/100= 500 x 1.2=600

Compare the light gathering power of an 8" primary mirror with a 6" primary mirror. The 8" mirror has how much light gathering power?

Answers

Answer:

1.778 times more or 16/9 times more

Step-by-step explanation:

Given:

- Mirror 1: D_1 = 8''

- Mirror 2: D_2 = 6"

Find:

Compare the light gathering power of an 8" primary mirror with a 6" primary mirror. The 8" mirror has how much light gathering power?

Solution:

- The light gathering power of a mirror (LGP) is proportional to the Area of the objects:

                                           LGP ∝ A

- Whereas, Area is proportional to the squared of the diameter i.e an area of a circle:

                                           A ∝ D^2

- Hence,                              LGP ∝ D^2

- Now compare the two diameters given:

                                           LGP_1 ∝ (D_1)^2

                                           LGP ∝ (D_2)^2

- Take a ratio of both:

                           LGP_1/LGP_2 ∝ (D_1)^2 / (D_2)^2

- Plug in the values:

                               LGP_1/LGP_2 ∝ (8)^2 / (6)^2

- Compute:             LGP_1/LGP_2 ∝ 16/9 ≅ 1.778 times more

Consider U = {x|x is a real number}.
A = {x|x ∈ U and x + 2 > 10}
B = {x|x ∈ U and 2x > 10}
Which pair of statements is true?
a. 5 ∉ A; 5 ∈ B
b. 6 ∈ A; 6 ∉ B
c. 8 ∉ A; 8 ∈ B
d. 9 ∈ A; 9 ∉ B

Answers

Answer:

Option c.

Step-by-step explanation:

We have the set of real numbers greater than 8 and B the set of real numbers greater than 5 here:

A: x+2>10 ⇒ x>8

B: 2x > 10 ⇒ x>5

8∉A ; 8∈B

Note: We can see (graph) that the intervals are open, so the corresponding points do not belong to their respective sets.

Find the interest in dollars and the proceeds for the following problem. Remember to use a 360 day year. (Enter a $ along with your answer in $0.00 format.) Chris Shopper received a $1,500.00 discount loan to purchase a washer and dryer. The loan was offered at 15% for 120 days. Find the interest in dollars and the proceeds for the following problem.

Answers

Answer:

Therefore the interest = $ 75.

Step-by-step explanation:

Given , Chris shopper received a loan $1,500 discount to purchase a washer and dryer. The loan was offered at 15%for 120 day.

P = $ 1500

r = 15%

t= [tex]\frac{120}{360} = \frac{1}{3}[/tex] year

[tex]\textrm{intrest} =\frac{Pr t}{100}[/tex]

          [tex]=\$\frac{1500\times 15 \times \frac{1}{3} }{100}[/tex]

         [tex]=\$ 75[/tex]

Therefore the interest = $ 75.

It is estimated that the average college student drinks 10 cups of coffee a week. During final exam week this is projected to grow by 72%. How many cups of coffee will the average college student drink during final exam week?

Answers

7.2 I hope it’s right

Multiple Choice Question The first cash flow at the end of Week 1 is $100, the second cash flow at the end of Month 2 is $100, and the third cash flow at the end of Year 3 is $100. This cash flow pattern is a(n) ______ type of cash flow.

Answers

This cash flow pattern is an uneven type of cash flow.

The R-value of insulation is a measure of its ability to resist heat transfer. For fiber-glass insulation, 3½ inches is rated at R-11 and 6 inches is rated at R-19. Assuming this relationship is linear, write the equation that gives the R-value of fiberglass insulation as a function of its thickness t (in inches).
R =

Answers

Answer:

[tex]R = \dfrac{16}{5}t + \dfrac{1}{5}[/tex]

where R is the R-value and t is the thickness in inches.

Step-by-step explanation:

We are given the following in the question:

The  R-value of fiberglass insulation and f its thickness have a linear relation.

Let R be the R-value and t be the thickness. Then, the equation can be written as:

[tex]R = at + b[/tex]

where a and b are constants.

When t = 3.5, R = 11

[tex]11 = 3.5a + b[/tex]

When t = 6, R = 19

[tex]19 = 6a + b[/tex]

Solving the two equation, using the elimination method, we have,

[tex]19-11 = 6a + b-(3.5a + b)\\8 = 2.5a\\\\\Rightarrow a = \dfrac{16}{5}\\\\11 = 6(\dfrac{16}{5}) + b\\\\\Rightarrow b = \dfrac{1}{5}[/tex]

Thus, the linear relationship is given by:

[tex]R = \dfrac{16}{5}t + \dfrac{1}{5}[/tex]

where R is the R-value and t is the thickness in inches.

Final answer:

To find a linear equation (R = mt + b) that represents the R-value of fiberglass insulation as a function of its thickness, we calculate a slope (m) of 3.2 using two known measurements. We then solve for a y-intercept (b), which is -0.5. Therefore, the equation is R = 3.2t - 0.5.

Explanation:

In order to derive the equation that gives the R-value as a function of the thickness, we need to use the concept of linear equations, specifically slope-intercept form (y = mx + b). First, we need to find the slope (m). Since we know two points on the line (3 ½ , 11) and (6 , 19), we calculate the slope as: m = (19-11) / (6 - 3½) = 8 / 2½ = 3.2. The y-intercept (b) is the R-value when the thickness (t) is 0. To find it, we use one of our points and the slope in the equation y = mx + b, substituting to solve for b: 11 = 3.2 * 3½ + b, hence, b = -0.5. The equation is therefore: R = 3.2t - 0.5.

Learn more about Linear Equations here:

https://brainly.com/question/32634451

#SPJ3

Can u guys PLEASE answer this questions ASAP.

a) A dental patient was billed for two fillings and an X-ray. She paid $107.80 for each of the fillings. $74 for the X-ray and 10% GST on the total bill. How much was she charged altogether?

Answers

107,80+107,80=215,60+74=289,60
289,60 : 100 x 110= your answer

Figure the standard deviation of the distribution of means for a population with a standard deviation of 20 and sample size of 10

Answers

Answer:

standard deviation of the distribution = 6.325.

Step-by-step explanation:

i) standard deviation of the population σ = 20

ii) size of sample n = 10.

iii) standard deviation of the distribution = [tex]\frac{\sigma}{\sqrt{n}} = \frac{20}{\sqrt{10}} = \frac{20}{3.162} = 6.325[/tex]

Final answer:

To find the standard deviation of the distribution of means for a population with a standard deviation of 20 and sample size of 10, use the formula: Standard Deviation of the Distribution of Means = Population Standard Deviation / Square Root of Sample Size. By substituting the values, you get the standard deviation of 6.32.

Explanation:

The standard deviation of the distribution of means for a population with a standard deviation of 20 and sample size of 10 is calculated using the formula:

Standard Deviation of the Distribution of Means = Population Standard Deviation / Square Root of Sample Size

Substitute the values: 20 / √10 = 6.32. Therefore, the standard deviation of the distribution of means is 6.32 for this scenario.

if the slope of a line is -3/7 then its perpendicular line will have the following slope

Answers

Answer:

The slope of the line is:    [tex]$ \frac{\textbf{7}}{\textbf{3}} $[/tex]

Step-by-step explanation:

The product of the slope of two perpendicular slopes = - 1.

Given the slope of one of the perpendicular lines, say, [tex]$ m_{1} $[/tex] = [tex]$ -\frac{3}{7} $[/tex].

We have to determine the slope of the line perpendicular to the first line, We call this slope - [tex]$ m_{2} $[/tex].

We know that the product of the slopes [tex]$ m_{1}. m_{2} = - 1 $[/tex]

[tex]$ \implies -\frac{3}{7} . m_2 = - 1 $[/tex]

[tex]$ \implis m_{2} = - 1 \times - \frac{7}{3} $[/tex]

[tex]$ \therefore m_{2} = \frac{\textbf{7}}{\textbf{3}} $[/tex]

Hence, the answer.

3 rectangular prisms have combined volume of 518 ft³ prism a has 1/3 of the volume of prism B and prisms B &C have equal volume what is the volume of each prism

Answers

Answer:

The answer to your question is  A = 74 ft³, B = 222 ft³, C = 222ft³

Step-by-step explanation:

Data

Total volume = 518 ft³

Prism A volume = Prism B volume / 3

Prism B volume = Prism C volume

Process

Write an equation in terms of volume of B

          Volume A + Volume B + Volume C = 518

Substitution

                B/3 + B + B = 518

                (B + 3B + 3B)/3 = 518

                               7B = 3(518)

                               7B = 1554

                                 B = 1554/7

                                 B = 222

Get the volumes

Volume A = 222/3

                 = 74

Volume B = 222

Volume C = 222

Sam is having a problem with rabbits getting into his vegetable garden, so he decides to fence it in. The length of the garden is 9 feet more than 6 times the width. He needs 74 feet of fencing to do the job. How many feet is the length of the garden?

Answers

Answer:

The length of the garden is 33 feet and the width of the garden is 4 feet.                                        

Step-by-step explanation:

We are given the following in he question:

Perimeter of rectangular garden = 74 feet

Let l be the length of the garden and w be the width.

The length of the garden is 9 feet more than 6 times the width.

Thus, we can write

[tex]l = 9 + 6w\\\Rightarrow l-6w = 9[/tex]

Perimeter of rectangular garden =

[tex]2(l + w) = 74\\\Rightarrow l+w = 37[/tex]

Solving the two equation by elimination method, we get,

[tex]l-6w-(l+w) = 9 -37\\-7w = -28\\w = 4\\l = 9 + 6(4) = 33[/tex]

Thus, the length of the garden is 33 feet and the width of the garden is 4 feet.

Harper picked 3.5 baskets of apples. Cooper picked 4 1/4 baskets of apples did Harper and cooper pick together? Express your answer as a decimal number and as a mixed number

Answers

Answer:

The number of basket of apples picked by Harper and Cooper together is  [tex]5\frac{1}{4} \ \ Or \ \ 5.25[/tex].

Step-by-step explanation:

Given:

Number of basket picked by Harper = 3.5

Number of basket picked by cooper = [tex]4\frac{1}{4}[/tex]

We need to find the number of basket of apples picked by Harper and Cooper together.

Solution:

Now we can see that one number is in decimal form and other number is in mixed fraction form so we will convert both the number in simplest fraction form and then solve the same.

Number of basket picked by Harper = 3.5

Now if we divide 7 from from 2 we get the answer as 3.5 so we can say that;

3.5 can be rewritten as [tex]\frac{7}{2}[/tex]

Number of basket picked by Harper = [tex]\frac{7}{2}[/tex]

Number of basket picked by cooper = [tex]4\frac{1}{4}[/tex]

[tex]4\frac{1}{4}[/tex] can be rewritten as [tex]\frac{17}{4}[/tex]

Number of basket picked by cooper = [tex]\frac{17}{4}[/tex]

Now we can say that;

to find the number of basket of apples picked by Harper and Cooper together we will add Number of basket picked by Harper and Number of basket picked by cooper.

framing in equation form we get;

number of basket of apples picked by Harper and Cooper together = [tex]\frac{7}{2}+\frac{17}{4}[/tex]

now we will use LCM to make the denominator common we get;

number of basket of apples picked by Harper and Cooper together = [tex]\frac{7\times2}{2\times2}+\frac{17\times1}{4\times1}=\frac{14}{4}+\frac{17}{4}[/tex]

Now denominators are common so we will solve the numerators we get;

number of basket of apples picked by Harper and Cooper together = [tex]\frac{14+7}{4} = \frac{21}{4} \ \ Or\ \ 5\frac{1}{4} \ \ Or \ \ 5.25[/tex]

Hence the number of basket of apples picked by Harper and Cooper together is  [tex]5\frac{1}{4} \ \ Or \ \ 5.25[/tex].

Needing help with getting the slope

Answers

Answer:

The answer is 2/5

Step-by-step explanation:

I found 2 points and did y2-y1/ x2-x1 and got 2/5. And then I tested it and it worked.

Answer: the slope is 2/5

Step-by-step explanation:

The formula for determining slope is expressed as

Slope = change in value of y on the vertical axis / change in value of x on the horizontal axis

change in the value of y = y2 - y1

Change in value of x = x2 -x1

y2 = final value of y

y 1 = initial value of y

x2 = final value of x

x1 = initial value of x

Looking at the graph given,

y2 = 0

y1 = - 2

x2 = 5

x1 = 0

Slope = (0 - -2)/(0 - 0) = 2/5

The mean value of land and building per acre from a sample of farms if 1400 with a standard deviation of 100. the data set has a bell shaped distribution. Assume thenumber of farms in the sample 80.
A. Use the empirical rule to estimate the number of farms whose land and buildings values per acre between 1200 and 1600
B. If 24 additional farms were sampled, about how many of these additional farms would you expect to have land and building values between 1200 per acre and 1600 per acre?

Answers

Answer:A)54 farms

B) 16 farms

Step-by-step explanation:

Y(1200) = (1200-1400)/100 = -200/100

Y(1200) = -2

Y(1600) = 1600-1400)/100

Y(1600) = 200/100 = 2

P(1200-1600) = (2y<-2)

2 standard deviation from the range = 68%=0.68

80 farms × 0.68 = 54 .4 approximately 54

B) 24× 0.68= 16.32 approximately 16

Final answer:

By using the empirical rule, it is expected that around 54 farms among the sample of 80 farms, as well as approximately 71 of 104 farms (after addition of 24 farms) will have land and building values per acre between 1300 and 1500.

Explanation:

The question deals with the concept of mean, standard deviation, and the empirical rule, specifically in the context of data relating to the values of land and buildings per acre on various farms.

A. Using the empirical rule, we know that approximately 68% of the population of a bell-curve distribution lies within one standard deviation from the mean. In this case, the mean is 1400 and the standard deviation is 100. So, one standard deviation above and below the mean is between 1300 and 1500. Therefore, approximately 68% of the 80 farms, or roughly 54 farms, have land and building values per acre between 1300 and 1500.

B. If we add 24 more farms to the sample, the total number of farms will be 104. Applying the same empirical rule, we'd expect approximately 68% of these, roughly 71 farms, to have land and building values per acre between 1300 and 1500.

Learn more about Empirical Rule here:

https://brainly.com/question/35669892

#SPJ3

20 POINTS!!!

What is the sum of the first six terms of the series?
48−12+3−0.75+...

Answers

The difference between terms is the previous term divided by 4:

48/4 = 12

12/4 =3

3/4 = 0.75

Find the next two terms:

0.75/4 = 0.1875

0.1875/4 = 0.046875

Now you have 48 - 12 + 3 - 0.75 + 0.1875 - 0.046875

Answer: 38.390625

Find the circumference, perimeter, and area.

Answers

For a semi-circle with diameter 10, the circumference is 5π, perimeter is 5π + 10, and area is 25/2π. For a circle with radius 6 and a 90-degree cut, remaining circumference is 9π, perimeter is 12π, and remaining area is 27π.

Semi-circle with Diameter 10:

a. Circumference:

The circumference of a circle is given by the formula C = π × d, where d is the diameter. For a semi-circle, it's half of the circumference of a full circle. Thus, C(semi-circle) = π × 10/2 = 5π.

b. Perimeter:

The perimeter of a shape is the sum of all its sides. For a semi-circle, it includes the curved boundary and the diameter. Therefore, P(semi-circle) = 5π + 10.

c. Area:

The area of a semi-circle is given by A(semi-circle) = 1/2 × π × r^2, where r is the radius. Substituting the given diameter, A(semi-circle) = 1/2 × π × (10/2)^2 = 25/2 × π.

Circle with Radius 6 and a 90-Degree Cut:

a. Circumference:

For the full circle, C(circle) = 2π × r = 2 × π × 6 = 12π. Since a 90-degree cut removes a quarter of the circle, the remaining circumference is C(remaining) = 3/4 × 12π = 9π.

b. Perimeter:

The perimeter includes the cut portion, so P(circle) = 12π.

c. Area:

The area of the circle is A(circle) = π × r^2 = π × 6^2 = 36π. With the cut, A(remaining) = 3/4 × 36π = 27π.

Leif knows that the land area of the United States is approximately 9 x 10^6 square kilometers. He is traveling to Norway to visit her grandfather. He knows the land area of Norway is approximately 3 x 10^4 square kilometers. About how many times greater is the land area of the United States than that of Norway
A.3
B.30
C.300
D.3000
Work must be shown

Answers

Answer:

Option C.300

Step-by-step explanation:

we know that

To find out how many times greater is the land area of the United States than that of Norway, divide the area of the United States by the area of the Norway

so

[tex]\frac{9\times10^6}{3\times10^4}[/tex]

Remember that

To divide exponents (or powers) with the same base, subtract the exponents

so

[tex]\frac{9\times10^6}{3\times10^4}=(\frac{9}{3})\times(10^{6-4} )=3\times10^2=300[/tex]

Tires sell for $150 each and rims sell for $200. Three times as many tires were sold than rims. Total sales were $3,250. How many of each were sold? What were the total sales in dollars for each?

Answers

Number of tires that were sold is 15 and number of rims that were sold is 5. Total sales for tires is $2250 and total sales for rims is $1000

Step-by-step explanation:

Step 1:

Given details are selling price of tires = $150, selling price of rims = $200 and total dales = $3250

Step 2:

Form equation out of the given data. Let the number of rims that were sold be x. Then number of tires that were sold is 3x.

⇒ x × 200 + 3x × 150 = 3250

⇒ 200x + 450x = 3250

⇒ 650x = 3250

x = 5

Step 3:

Find number of tires and rims that were sold.

⇒ Number of rims that were sold = x = 5

⇒ Number of tires that were sold = 3x = 15

Step 4:

Find the total sales for each.

⇒ Total sales for rims = 5 × 200 = $1000

⇒ Total sales for tires = 15 × 150 = $2250

5 rims and 15 tires were sold with total sales of $1,000 for rims and $2,250 for tires.

Let x be the number of rims sold and 3x be the number of tires sold, since three times as many tires were sold as rims.

Now, we can create equations based on the given information.

The total sales for rims and tires are $3,250.

x = $3,250 / $650

3x = 3 * 5 = 15 (the number of tires sold)

Total sales for rims were $200 * 5 = $1,000, and total sales for tires were $150 * 15 = $2,250.

The table shows the values of a function f(x).

What is the average rate of change of f(x) from −2 to 2?

Answers

Answer:

-4

Step-by-step explanation:

The average rate of change of a function f(x) between two points x = a and x=b is given by,

[tex]f(x)=\frac{f(b)-f(a)}{b-a}[/tex]

This can be understood with a simpler example, the straight line.

In this case, the rate of change of the 'function' is given by the slope,

[tex]m=\frac{f(x_{2})-f(x_{1})}{x_{2}-x_{1}}[/tex];                

[tex](x_{1},f(x_{1})),(x_{2},f(x_{2}))[/tex] being two points on the straight line.

So, for the given problem,

a = -2

b = 2

Hence, average rate of change of [tex]f(x)=\frac{f(2)-f(-2)}{2-(-2)} =\frac{9-25}{2+2} =\frac{-16}{4} =-4[/tex]

A number was subtracted from 3. After which , that result was multiplied by 3. This result was then divided by 3 for a result of-5 . Given this information, what was the initial number ?

Answers

Answer:

8

Step-by-step explanation:

The violent-crime rate in a certain state of the country in that year was 1,496. Would this be an outlier? O A. No, because it is less than the upper fence OB. Yes, because it is less than the upper fence. OC. Yes, because it is greater than the upper fence. OD. No, because it is greater than the upper fence (d) Do you believe that the distribution of violent-crime rates is skewed or symmetric?

Answers

Answer:

The violent-crime rate in a certain state of the country in that year was 1,496

Would this be an outlier?

C. Yes, because it is greater than the upper fence.

(d) Do you believe that the distribution of violent-crime rates is skewed or symmetric?

C. The distribution of violent-crime rates is skewed right.

Step-by-step explanation:

The violent-crime rate in a certain state of the country in that year was 1,496

The lower fence is 272.8 - 1.5 x 255.5 = -110.45 crimes per​ 100,000 population.

The upper fence is 528.3 + 1.5 x 255.5 = 911.55 crimes per​ 100,000 population.

Since violent-crime rate in this certain state of the country in that year is greater than the upper fence (1496>911.55), then it is an outlier.

(d) Do you believe that the distribution of violent-crime rates is skewed or symmetric?

The distribution of violent-crime rates is not symmetric, as there are extreme values in the​ tail, which tend to pull the mean in the direction of the tail to have data are either skewed left or skewed​ right, in this case it is skewed​ right, as there are large observations in the right tail that tend to increase the value of the​ mean, while having little effect on the median.

An architect wants to do a rectangle with the diagonal of 25 inches the length of the rectangle is to be 3 inches more than triple the width. What is the dimensions she should make the rectangle

Answers

Answer: The length is 24 inches. The width is 7 inches.

Step-by-step explanation:

Let L represent the length of the rectangle.

Let W represent the width of the rectangle.

The length of the rectangle is to be 3 inches more than triple the width. This means that

L = 3W + 3

The diagonal of the rectangle divides it into two right angle triangles and the diagonal represents the hypotenuse. The length and width represents the opposite and adjacent side. Applying Pythagoras theorem,

Hypotenuse² = opposite side² + adjacent side²

Therefore,

25² = L² + W²

625 = L² + W² - - - - - - - - - -1

Substituting L = 3W into equation 1, it becomes

625 = (3W + 3)² + W²

625 = 9W² + 9W + 9W + 9 + W²

10W² + 18W - 625 + 9 = 0

10W² + 18W - 616 = 0

Dividing through by 2, it becomes

5W² + 9W - 308= 0

5W² + 44W - 35W - 308 = 0

W(5W + 44) - 7(5W + 44) = 0

W - 7 = 0 or 5W + 44 = 0

W = 7 or W = - 44/5

Since the width cannot be negative, then W = 7

L = 3W + 3 = 7 × 3 + 3

L = 24

Stan and Ollie each earned the same amount last week Stan work 20 hours and earned $13.50 per hour Ollie worked 30 hours. How much did Ollie earn per hour?

Answers

Answer: Ollie earned $9 per hour.

Step-by-step explanation:

Let x represent the amount that Ollie earned per hour.

Stan and Ollie each earned the same amount last week Stan work 20 hours and earned $13.50 per hour. This means that the total amount that Stan earned would be

20 × 13.5 = $270

Ollie worked 30 hours. This means that the total amount that Ollie earned would be

30 × x = $30x

Since they earned the same amount, then

30x = 270

x = 270/30 = $9 per hour

Answer:

$9 per hour

Step-by-step explanation:

The price of an mp3 player is $149.99. The mp3 player was on sale for 20% off. Matt bought the mp3 player at the sale price and also had a rebate of $50. How much did Matt pay for the mp3 player?

Answers

Matt paid $70 for mp3 player.

Step-by-step explanation:

Given,

Cost of mp3 player = $149.99

Discount = 20%

Amount of discount = 20% of 149.99

Amount of discount = [tex]\frac{20}{100}*149.99[/tex]

Amount of discount = 0.2*149.99

Amount of discount = $29.99

Sale price = Cost of mp3 - Amount of discount

Sale price = [tex]149.99 - 29.99 = \$120[/tex]

Rebate = $50

Amount paid by Matt = sale price - rebate

Amount paid by Matt = 120-50 =$70

Matt paid $70 for mp3 player.

Keywords: subtraction, percentage

Learn more about subtraction at:

brainly.com/question/2821386brainly.com/question/2860697

#LearnwithBrainly

Architect Brian Peters spent 60% of a week's time working on drawings for a new apartment building. If Brian spent 18 hours working on projects other than the apartment building, compute the total hours worked

Answers

Answer:

Brian Peters worked for total of 45 hours.

Step-by-step explanation:

Let the total number of hours worked be 'x'.

Now Given:

Hours spent on other projects = 18 hours.

Also Given:

60% of a week's time working on drawings for a new apartment building.

Hours spent on new apartment building = [tex]60\%\times x = \frac{60}{100}x=0.6x[/tex]

We need to find the total hours worked.

Solution:

Now we can say that;

total number of hours worked is equal to sum of Hours spent on new apartment building and Hours spent on other projects.

framing in equation form we get;

[tex]x=0.6x+18[/tex]

Combining like terms we get;

[tex]x-0.6x=18\\\\x(1-0.6)=18\\\\0.4x=18[/tex]

Now Dividing both side by 0.4 we get;

[tex]\frac{0.4x}{0.4}=\frac{18}{0.4}\\\\x=45\ hrs[/tex]

Hence Brian Peters worked for total of 45 hours.

Final answer:

In the question, architect Brian Peters spent 60% of his total work time on a new apartment building and 40% on other projects. If those 40% equates to 18 hours, we can calculate his total work week as 45 hours by dividing 18 by 0.4.

Explanation:

The problem can be solved by identifying that architect Brian Peters spent 65% of his time working on other projects than the new apartment building. This implies that he spent 40% of his time on the apartment building project. Understanding that a week consists of 168 hours, we could conduct a calculation to determine his total work hours. If we take that 60% was spent on the apartment building and 40% was spent on other projects, then those 18 hours represent 40% of his total work time. Therefore, to find his total work time, we can divide 18 (hours spent on other projects) by 40%, or 0.4.

So, the calculation will be: 18/0.4 = 45 hours. This shows that Brian Peters worked a total of 45 hours within the week for all his projects. These 45 hours involve the 18 hours he spent on other projects and the remaining time he dedicated to the new apartment building drawings.

Learn more about Percentage Calculation here:

https://brainly.com/question/32197511

#SPJ3

3:
At the zoo, the aquarium is 36 feet north of the gift shop. The monkey habitat is 323 feet east of the gift shop. What is the distance, in feet, from the aquarium to the monkey habitat?

Answers

The distance between the aquarium and the monkey habitat is 325 feet.

To find the distance between the aquarium and the monkey habitat, we can use the Pythagorean theorem because the aquarium and the monkey habitat form a right triangle with the gift shop.

Let's denote the distance between the aquarium and the gift shop as  a (36 feet) and the distance between the monkey habitat and the gift shop as b (323 feet). The distance between the aquarium and the monkey habitat, which we'll call c, is the hypotenuse of the right triangle.

The Pythagorean theorem states that in a right triangle, the square of the length of the hypotenuse  c  is equal to the sum of the squares of the lengths of the other two sides a and b.

[tex]\[ c^2 = a^2 + b^2 \][/tex]

Substitute the given values:

[tex]\[ c^2 = (36)^2 + (323)^2 \][/tex]

[tex]\[ c^2 = 1296 + 104329 \][/tex]

[tex]\[ c^2 = 105625 \][/tex]

Take the square root of both sides to solve for  c:

[tex]\[ c = \sqrt{105625} \][/tex]

[tex]\[ c = 325 \][/tex]

Orange juice, a raisin bagel, and a cup of coffee from kelly's koffee kart cost a total of $2.40. Kelly posts a notice announcing that, effective the following week, the price of orange juice will increase 50% and the price of bagels will increase 20%. After the increase, the same purchase will cost a total of $3.00, and the orange juice will cost twice as much as coffee. find the price of each.
A. What was the cost of a glass of orange juice before the increase?
B. what was the cost of a raisin bagel before the increase?
C. what was the cost of a cup of coffee before the increase?

Answers

Answer:

Juice $0.6

Bagel $1.5

Coffee $0.3

Step-by-step explanation:

The original price is $2.40 for an orange juice (x), raisin bagel (y) and a cup of coffee(z).

The prices of the orange juice will increase by 50%:

[tex]=x+0.5x=1.5x[/tex]

The price of bagels will increase by 20%:

[tex]=y+0.2x=1.2x[/tex]

The total price of everything is $3.00.

The orange juice will cost twice as much as coffee:

[tex]x=2z[/tex]

We have the following equations:

[tex]x+y+z=2.40[/tex]

[tex]1.5x+1.2y+z=3[/tex]

[tex]x=2z[/tex]

We have 3 equations and 3 unknowns:

Solve through substitution of x=2z into both equations:

[tex]1.5x+y=2.40[/tex]

[tex]2x+1.2y=3[/tex]

Therefore before increase. Use equation before increase to solve z and not x=2z because this is after the increase.

[tex]x=0.6[/tex]

[tex]y=1.5[/tex]

[tex]z=0.3[/tex]

Final answer:

The original prices were $1.00 for orange juice, $0.60 for a raisin bagel, and $0.80 for coffee.

Explanation:

Let's denote the price of orange juice as O, the price of a raisin bagel as B, and the price of coffee as C.

Initially, we know that O + B + C = $2.40.

After the price increase, we know that (1.5O) + (1.2B) + C = $3.00 and also that 1.5O = 2C.

From the equation 1.5O = 2C, we deduce that O = 1.33C. We substitute this in the first equation to get the initial prices:

Orange juice (O) was $1.00 before the increaseRaisin bagel (B) was $0.60 before the increaseCoffee (C) was $0.80 before the increase

Learn more about Price Increase here:

https://brainly.com/question/31571622

#SPJ3

PLEASE HELP ASAP!!! I NEED CORRECT ANSWERS ONLY PLEASE!!!

Find m∠D.

Write your answer as an integer or as a decimal rounded to the nearest tenth.


m∠D = °

Answers

Answer:

26.57 degrees

Step-by-step explanation:

So we need to find the angle of D in your triangle.

Since this is a right triangle we can use trigonometric functions (sin, cos, tan etc)

For this we need to use tangent since wanna do opposite over adjacent.

But since we want the angle we use tan^-1

So plug into your calculator(make sure your calculator is in degrees): tan^-1 (4/8)

We get 26.565 degrees

Answer:

Step-by-step explanation:

Triangle BCD is a right angle triangle.

From the given right angle triangle,

BD represents the hypotenuse of the right angle triangle.

With m∠D as the reference angle,

CD represents the adjacent side of the right angle triangle.

BC represents the opposite side of the right angle triangle.

To determine m∠D, we would apply

the tangent trigonometric ratio.

Tan θ = opposite side/adjacent side. Therefore,

Tan D = 4/8 = 0.5

m∠D = Tan^-1(0.5)

m∠D = 26.6° to the nearest tenth.

Other Questions
Which of the following is among the beliefs by Hindus? a. belief in the three central Gods: Brahma, Vishnu, and Shiva (along with the great female goddess Devi) b. belief in Shiva as Destroyer and the Lord of the Dance c. belief in a nearly endless round of rebirths called 'reincarnation' d. all of the above At the instant the traffic light turns green, an automobile that has been waiting at an intersection starts ahead with a constant acceleration of 2.40 m/s^2. At the same instant, a truck, traveling with a constant speed of 15.5 m/s, overtakes and passes the automobile.How far beyond its starting point does the automobile overtake the truck?How fast is the automobile traveling when it overtakes the truck? how did the blockade of savannah impact the confederacy In a laboratory experiment, students synthesized a new compound and found that when 12.37 grams of the compound were dissolved to make 167.6 mL of a benzene solution, the osmotic pressure generated was 6.26 atm at 298 K. The compound was also found to be nonvolatile and a non-electrolyte. What is the molecular weight they determined for this compound? When a firm produces one unit, the variable cost is $3. When the firm produces two units, the variable cost is $6. What is the marginal cost associated with two units of production? A) $0.5 B) $2 C) $6 D) $3 what happens to a circuit's resistance as more resistors are added in series? I WILL GIVE BRAINLIEST, THANKS AND 5 STARS IF YOU ARE CORRECT!!!Read Sonnet 91 by William Shakespeare:Some glory in their birth, some in their skill,Some in their wealth, some in their bodies' force,Some in their garments, though new-fangled ill,Some in their hawks and hounds, some in their horse;And every humour hath his adjunct pleasure,Wherein it finds a joy above the rest:But these particulars are not my measure;All these I better in one general best.Thy love is better than high birth to me,Richer than wealth, prouder than garments' cost,Of more delight than hawks or horses be;And having thee, of all men's pride I boast: Wretched in this alone, that thou mayst take All this away and me most wretched make. Which lines contain a rhyming couplet?A. lines 12B. lines 1314C. lines 34D. line 2 and line 4 Hotels, restaurants, shops, public restrooms, and drinking fountains are all examples of which trait is most likely a result of artificial selection Youve recently learned that the company where you work is being sold for $300,000. The companys income statement indicates current profits of $11,000, which have yet to be paid out as dividends. Assuming the company will remain a "going concern" indefinitely and that the interest rate will remain constant at 9 percent, at what constant rate does the owner believe that profits will grow? nstruction: Enter your response rounded to one decimal place. Growth rate of: ___ percent. Read the statement:When Mendel crossed a purple-flowered pea plant with a white-flowered pea plant, the offspring were always X. When Mendel crossed the offspring with each other, the distribution was about Y purple and Z white. The more experiments Mendel did with pea plants, the closer they approached these percentages.Which option correctly replaces X, Y, and Z in the statement?a. X: purple Y: 25% Z: 75%b. X: white Y: 25% Z: 75%c. X: white Y: 75% Z: 25%d. X: purple Y: 75% Z: 25% What do you think Tennyson is saying about the role of the artist and the connection of the artist to his or her society? Cite evidence from the poem to support your view. Your answer should be at least one hundred words. (The Lady of Shalott) Mini Mart suspects that Junior is stealing candy. The next time Junior comes into the store, the manager at Mini Mart detains Junior in the stores office until the police can come to investigate. What will happen to the Mini Mart manager? I NEED HELP Write a mathematical equation showing that pressure (P) multiplied by volume (V) remains equal to a constant (k). Complexity theory is an offshoot of the _____ viewpoint because it is the study of how multiple chaotic processes arise into pattern and order1. To build teamwork - trust - and mutual respect - Tqm companies see that every employee is involved in the continuous improvement process. This requires that workers must be trained and empowered to find and solve problems.2. Managing the production and delivery of an organization's products or services more effectively.3. Systems4. Outputs Find f(100) and show how to solve Juana looked at her September issue of O magazine and did not see anything of interest. However, after her mother was diagnosed with bipolar disorder, Juana found the issue extremely interesting because it offered advice on how to help people who are suffering from this problem. The fact that the boring issue became quite interesting is most directly due to a change in ________. An oscillator with angular frequency of 1.00 s-1has initial displacement of 1.00 m and initial velocity of 1.72 m/s. What is the amplitude of oscillation? Which group appointed the committee in charge of drafting the Declaration of Independence and eventually adopted it? A. First Continental Congress B. Executive Branch of the Colonies C. United States Supreme Court D. Second Continental Congress What was unique about world war 1