Part A
What is the area of triangle i? Show your calculation.

Part B
Triangles i and ii are congruent (of the same size and shape). What is the total area of triangles i and ii? Show your calculation.

Part C
What is the area of rectangle i? Show your calculation.

Part D
What is the area of rectangle ii? Show your calculation.

Part E
Rectangles i and iii have the same size and shape. What is the total area of rectangles i and iii? Show your calculation.

Part F
What is the total area of all the rectangles? Show your calculation.

Part G
What areas do you need to know to find the surface area of the prism?

Part H
What is the surface area of the prism? Show your calculation.

Part I
Read this statement: “If you multiply the area of one rectangle in the figure by 3, you’ll get the total area of the rectangles.” Is this statement true or false? Why?

Part J
Read this statement: “If you multiply the area of one triangle in the figure by 2, you’ll get the total area of the triangles.” Is this statement true or false? Why?

Answer:

C. 1.12

Step-by-step explanation:

There are 60' (minutes) in a degree and 60" in a minute meaning that we have (60×60) seconds in a degree.

Therefore to convert seconds to degrees we divide by 3600. and minutes to degrees we divide by 60.

The angle 48°19'23'' can be converted into a decimal as follows

48°+(19/60+23/3600)°

=48.323°

Tan 48.323= 1.12

Answer:

  cos(B) = a/c

Step-by-step explanation:

The mnemonic SOH CAH TOA reminds you that ...

  Cos = Adjacent/Hypotenuse

The leg adjacent to angle B is "a". The hypotenuse is "c", so the desired cosine is ...

  cos(B) = adjacent/hypotenuse = a/c

Answer:

x=45

Step-by-step explanation:

Since AB is a straight line, it is 180 degrees

AOE + EOF + FOD + DOB = 180

15+x+2x+120-2x = 180

Combine like terms

135 +x = 180

Subtract 135 from each side

135-135 +x = 180 -135

x = 45

To find x, use the concept of similar triangles and set up a proportion. Cross multiply and simplify the equation to solve for x.

To find x, we need to use trigonometry. Given that AB and CD are straight lines and the figures are not to scale, we can use the concept of similar triangles. We need to find the relationship between the corresponding sides of the triangles to find x.

Let's assume that the length of AB is a and the length of CD is b. From the given information, we can form a proportion:

a/b = (a+x)/a

Cross multiplying and simplifying the equation, we get:

a^2 = b(a+x)

Now we can substitute the given values to solve for x.

https://brainly.com/question/14926756

#SPJ12

Answer:

you would divide 25 by 5.

Step-by-step explanation:

each of the 5 officers would patrol 5 streets with a final of 5 x 5 = 25.

Answer:

5 streets

Step-by-step explanation:

Data:

The number of streets = 25

Number of officers = 5

Each officer will patrol = [tex]\frac{25}{5}[/tex]

                                      = 5 streets

Combine (or subtract) like terms.

a + b – c + 3a – 2c

4a + b – 3c <-------------------Answer

So, Choice B.

For this case we have the following expression:

[tex](a + b + c) + 3a-2c[/tex]

We eliminate parentheses:

[tex]a + b-c + 3a-2c =[/tex]

We add similar terms:

[tex]a + 3a + b-c-2c =[/tex]

We have that equal signs are added and the same sign is placed, while different signs are subtracted and the sign of the major is placed, then:

[tex]4a + b-3c[/tex]

Answer:

[tex]4a + b-3c[/tex]

Option B

Answer:

  b = 2√22 ≈ 9.381

Step-by-step explanation:

The Pythagorean theorem tells you ...

  a^2 + b^2 = c^2

Filling in the given numbers, we can solve for b.

  9^2 +b^2 = 13^2

  b^2 = 169 -81 = 88

  b = 2√22 . . . . . . . . take the square root and simplify

Answer:

Step-by-step explanation:

Your calculator knows all. You just have to know how to unlock it.

A graphing calculator is not necessary. A simple scientific one will work. The calculator on your computer will work (a PC) and my phone has one that will solve this as well.

2nd Function

Tan-1(

2

)

=

You should get 63.43

Make sure your calculator says degrees (DEG) at the top. Good luck.

Answer: $726 in interest is accumulated over a period of 6 months

Answer:

  $60.50

Step-by-step explanation:

Put the given numbers into the formula and do the arithmetic. 6 months is 1/2 year.

  i = Prt . . . . i is interest earned, P is principal amount, r is annual rate, t is number of years

  i = $2200×0.055×0.5 = $60.50

The amount of simple interest earned in 6 months is $60.50.

Answer:

Step-by-step explanation:

The range is 6 to 10 inches per month; 6 is the least amount of rain, whereas 10 is the most, for these four months.

Find the median by rearranging these four measurements in ascending order:  6 6 8 10.  Since four is an even number (of measurements), we find the median by averaging the middle two measurements:  (6 + 8) /2 = 7 in.

The mean is found by summing up the four measurements and dividing the result by 4:

6+6+8+10

-------------- = 30/4 = 7.5

       4

Draw a histogram as two vertical bars, one of which is 3 units higher than the other.  We don't yet know the total number of cats that each boy has, so your markings of your histogram have to be algebraic expressions, for example:

x + 0 for the first vertical bar and x + 3 for the second.  Then, clearly, one boy has 3 more cats than does the other.

Corey has 3 more cats than Taylor.  Let t represent the number of cats owned by Taylor and c the number by Corey.

Then t = c + 3 (general relationship), and so

        6 = c + 3

We must isolate c to determine how many cats corey has.

Subtract 3 from both sides, which results in c = 3.  Corey has 3 cats and Taylor has 6.

ANSWER

[tex]y = 8x - 26 [/tex]

EXPLANATION

The given points are (3,-2) (4,6).

The slope formula is given by:

[tex] m= \frac{y_2-y_1}{x_2-x_1} [/tex]

We use the slope formula to get:

[tex]m = \frac{6 - - 2}{4 - 3} [/tex]

The slope is

[tex]m = 8[/tex]

We use the point-slope formula to get;

[tex]y-y_1=m(x-x_1)[/tex]

[tex]y + 2 = 8(x - 3)[/tex]

We expand to get;

[tex]y = 8x - 24 - 2[/tex]

The slope-intercept form of the equation is:

[tex]y = 8x - 26[/tex]

Answer:

240

Step-by-step explanation:

Profit = revenue - cost

p(x) = 3^x - 1.25^x

5 seasons would be x = 5

p(5) = 3^5-1.25^5

p(5) = 239.948

It would be around 240

Answer: The profit after 5 seasons is $239.94.

Step-by-step explanation:

Since we have given that

Revenue function is given by

[tex]t(x)=3^x[/tex]

Cost function is given by

[tex]r(x)=1.25^x[/tex]

So, We need to find the total profit:

As we know the formula for profit:

Profit = Revenue - Cost

[tex]P(x)=t(x)-r(x)\\\\P(x)=3^x-1.25^x[/tex]

We need to evaluate the profit after five seasons:

[tex]P(5)=3^5-1.25^5\\\\P(5)=\$239.94[/tex]

Hence, the profit after 5 seasons is $239.94.

Answer:

B. 7/18

Step-by-step explanation:

(-1/6)/(-3/7)

= -1/6 * -7/3

= -1*-7/6*3

= 7/18

(pls give brainliest)

For this case we must find the quotient of the following expression:

[tex]\frac {\frac {-1} {6}} {\frac {-3} {7}} =[/tex]

Applying double C we have:

[tex]\frac {-1 * 7} {6 * -3} =[/tex]

We have by law of signs of multiplication that:

[tex]- * + = -[/tex]

So:

[tex]\frac {-7} {- 18} =\\\frac {7} {18}[/tex]

Answer:

Option B

Answer:

  $3930.56

Step-by-step explanation:

The sum of her required payments is ...

  $950 +238 +149 +78 = $1415

In order for that to be 36% of her income, she must have income that matches ...

  1415 = 0.36 × income . . . . . . . to solve, we divide this equation by 0.36

  1415/0.36 = income ≈ 3930.56

Gina's gross monthly income would need to be $3930.56 to get approved.

_____

Comment on this answer

Often the DTI calculation will include the proposed loan payment. If that is the case, we would need to know the amount of the payment on the loan Gina is applying for. That amount would be added to her existing debt before dividing by 0.36.

Answer:

(x, y) = (10, 18)

Step-by-step explanation:

In a parallelogram, adjacent angles are supplementary, and opposite angles are congruent.

∠A = ∠D

54 = 3y

18 = y . . . . . divide by 3

___

∠B = ∠C

12x +6 = 6x +66

6x = 60 . . . . . . . . . subtract 6x+6

x = 10 . . . . . divide by 6

The values of x and y are 10 and 18, respectively.

Answer:

  3 runners

Step-by-step explanation:

The number of runners needed is the length of the race divided by the length each runner can run:

  (1/3 mi)/(1/9 mi/runner) = 9/3 runner = 3 runners

_____

There are a couple of ways you can divide fractions:

  → "invert and multiply." That is, multiply the numerator by the reciprocal of the denominator. Here, that is (1/3)(9/1) = 9/3 = 3

  → make the denominators the same and use the ratio of the numerators. Here that is (1/3)/(1/9) = (3/9)/(1/9) = 3/1 = 3

  → use a calculator (see attached)

Step-by-step explanation:

Find the miles per hour. Divide 130 with 2

130/2 = 65

Mrs.Rosso travels 65 miles per hour. She has 7 hours to travel. Multiply 7 with 65:

65 x 7 = 455

455 > 390 ∴ If everything stays constant, Mrs.Rosso will arrive to her destination on time.

~

Answer: yes

Step-by-step explanation:

If she travels at that rate she gets 65 miles per hour. 65 multiplied by 7 is 455, so she will get there before the 7 hours is up.

Hello There!

The slope of a function is always in the form of "y=mx"

The slope for this function would be [tex]\frac{1}{6}[/tex] and the y intercept would be positive 7

Answer:

2nd answer

Step-by-step explanation:

For a linear equation in the form

f(x) or y = mx + b

m = slope

b = y - intercept

By observation, f(x) = [tex]\frac{1}{6}[/tex]x + 7

m = slope = [tex]\frac{1}{6}[/tex] (Answer)

b = y-intercept = 7 (answer)

Answer:

the answer is D

Step-by-step explanation: so you know that he can do 9 topics in 45 minutes. which is 1 topic every 5 minutes when you divide 45/9. if there is 60 minutes in an hour, and he does 1 topic every 5 minutes, he would do 12. hope this helps xd

A teacher can cover 12 topics in a 1-hour period. It is given that the number of topics he can cover is directly proportional to the length of the time he has to review. So, option D is correct.

Two variables are said to be directly proportional if one variable increases/decreases with respect to the increase/decrease in the other variable. They are related to each other by proportionality.

A ∝ B (A and B are two variables)

⇒ A2/A1 = B2/B1

The given variables are 'N - number of topics' and 'T - time period'.

It is given that they are directly proportional to each other.

So, we can write

N ∝ T

⇒ N2/N1 = T2/T1

Given that,

A teacher can cover 9 topics in a single 45-minute period.

So, N1 = 9 topics and T1 = 45 minutes

And T2 = 1 hour

We need to find N2 =?

Thus, from the above equation

N2/N1 = T2/T1

⇒ N2/9 = (1 hour)/45 minute

1 hour = 60 minutes

⇒ N2/9 = (60/45)

⇒ N2 = 9 × 4/3

∴ N2 = 12 topics

So, he can cover 12 topics in 1 hour. Thus, option D is correct.

Learn more about proportionality here:

https://brainly.com/question/13354953

#SPJ2

Answer:

D.  

1,068 square feet

Step-by-step explanation:

Split the figure into 2 shapes: triangle and rectangle

Area of rectangle = 36 x 25 = 900 ft^2

Area of triangle = 1/2 (39-25)(36-12) = 1/2 (14)(24) = 168 ft^2

Area of the figure PQRSTU = 900 + 168 = 1068 ft^2

Answer

D.  

1,068 square feet

Answer:

D. 1,068

Step-by-step explanation:

Area of rectangle PQRU = 25 x 36 = 900 sq-ft

Consider triangle RST,

Base of triangle = TR = 36 - 12 = 24 feet

Height if triangle = 39 - 25 = 14 feet

Hence area of triangle = [tex]\frac{1}{2}[/tex] x 24 x 14 = 168 sq-ft

Total area = 900 + 168 = 1068 sq-ft

Answer:

65.4% to 74.6%

Step-by-step explanation:

68% is approximately plus minus 1 standard deviations.

sigma=sqrt(n*p*(1-p))=sqrt(100*.7*.3)=4.58

so we're looking at  70+4.6 and 70-4.6.

Answer: [tex](65.4\%,\ 74.6\%)[/tex]

Step-by-step explanation:

Given : Out of 100 students sampled, 70 of them said that they hoped to get married someday.

i.e. Sample size : n= 100 and Sample proportion:[tex]\hat{p}=\dfrac{70}{100}=0.7[/tex]

Using standard normal table for z,

Critical z-value(two-tailed) for 68% confidence = [tex]z_{\alpha/2}=0.9945[/tex]

Now, confidence interval for population proportion:-

[tex]\hat{p}\pm z_{\alpha/2}\sqrt{\dfrac{\hat{p}(1-\hat{p})}{n}}\\\\=0.7\pm(0.9945)\sqrt{\dfrac{(0.7)(0.3)}{100}}\\\\=0.7\pm0.0455737152863\\\\\approx0.7\pm0.046\\\\=(0.7-0.046,\ 0.7+0.046)=(0.654,\ 0.746)\\\\=(65.4\%,\ 74.6\%)[/tex]

Hence, the approximate percentage of the students in the population who hope to get married someday = [tex](65.4\%,\ 74.6\%)[/tex]

Answer:

  1.05 g/cm³

Step-by-step explanation:

The mass of the child is ...

  (50 lb)(454 g/lb) = 22,700 g

The volume displaced is ...

  (40 cm)(30 cm)(18 cm) = 21,600 cm³

Then the density of the child is ...

  mass/volume = 22700 g/(21600 cm³) ≈ 1.05 g/cm³

The answer is:

The correct option is:

[tex]D.22\°[/tex]

We can calculate the angle of elevation of the rescue ladder (formed triangle) using the following trigonometric formula:

[tex]Sin(\alpha)=\frac{y}{hypothenuse}[/tex]

Where,

y, is represented by the height where the person is located (50 feet) less the height of the top of the fire truck (10 feet)

hypothenuse, is represented by the length of the ladder (105 feet)

So, substituting and calculating we have:

[tex]Sin(\alpha)=\frac{y}{Hypothenuse}\\\\\alpha =Sin(\frac{Height}{LadderLength})^{-1}\\\\\alpha =Sin(\frac{50feet-10feet}{105feet})^{-1}=Sin(\frac{40feet}{105feet})^{-1}\\\\\alpha=Sin(\frac{40feet}{105feet})^{-1}=Sin(0.38)^{-1}=22.33\°=22\°[/tex]

Hence, we have that the correct option is:

[tex]D.22\°[/tex]

Have a nice day!

Answer:

A. lw = (x+6)(x -6); 133 square feet

Step-by-step explanation:

If x is the original length (in feet), when the length is increased by 6 feet, it can be represented by (x+6).

If x is the original width, when it is decreased by 6 feet, it can be represented by (x-6).

The area is the product of length and width, so the new area is ...

lw = (x+6)(x-6)

___

Since the original side is 13 ft, the new length is 13+6 = 19 ft, and the new width is 13-6=7 ft. The area is ...

(19 ft)(7 ft) = 133 ft²

To find the new dimensions of the brick patio, subtract 6 feet from the width and add 6 feet to the length.

To find the new dimensions of Ezra's brick patio, we need to subtract 6 feet from the width and add 6 feet to the length. Let's say the original width of the square brick patio is x feet. The new width would be (x - 6) feet. Similarly, if the original length is y feet, the new length would be (y + 6) feet. Therefore, the new dimensions of the patio would be (x - 6) feet by (y + 6) feet.

https://brainly.com/question/27628940

#SPJ11

Answer:

12

Step-by-step explanation:

For a cube of side length, L

The following formulas apply:

Area = 6L²

Volume = L³

Area / Volume = 6L² ÷ L³ = 6/L

Try L = 12

Area / Volume = 6/12 = 1/2

Hence 12 is the answer.

Answer:

Step-by-step explanation:

Part A: 2(L + W) = P

Part B: 2L + 2W = P

Part C: 2(10 + 5) = 30

Part D: 2(10) + 2(5) = 30

Part E: The reason both strategies work is because of the distributive property (attached)

Both Zack and Rachel's methods for computing the perimeter of a rectangle lead to the same formula: Perimeter = 2 * (Length + Width).

To find the perimeter of a rectangle using Zack's method, he first adds the length (L) and the width (W) together, obtaining the sum (L + W). Next, he doubles this sum by multiplying it by 2, giving him the perimeter of the rectangle.

Perimeter (Zack) = 2 * (L + W)

On the other hand, Rachel takes a slightly different approach. She doubles the length (2 * L) and doubles the width (2 * W) separately, getting two new values. Then, she adds these doubled amounts together, resulting in the perimeter of the rectangle.

Perimeter (Rachel) = 2 * L + 2 * W

Let's analyze the two methods and see if they yield the same result.

We can start by simplifying Rachel's method:

Perimeter (Rachel) = 2 * L + 2 * W

= 2 * (L + W)

Now we can see that both Zack and Rachel's methods end up with the same expression: 2 * (L + W). This means that, despite their different approaches, they arrive at the same formula for calculating the perimeter of a rectangle.

To know more about perimeter here

https://brainly.com/question/6465134

#SPJ2

Answer:

B, D, E

Step-by-step explanation:

A. The vertex is (1, -9).

False.  The vertex is at (-1, -9).

B. The graph opens upward.

True.  The leading coefficient 6 is positive.

C. The graph is obtained by shifting the graph of f(x) = 6(x + 1)² up 9 units.

False.  It is shifted down 9 units.

D. The graph is steeper than the graph of f(x) = x².

True.  The absolute value of the leading coefficient |6| is greater than 1.

E. The graph is the same as the graph of f(x) = 6x² + 12x - 3.

f(x) = 6(x² + 2x + 1) - 9

f(x) = 6x² + 12x + 6 - 9

f(x) = 6x² + 12x - 3

True.

The graph of f(x) = 6(x + 1)² -9 has its vertex at (-1,-9), opens upwards, is steeper than f(x) = x² and is not equal to f(x) = 6x² + 12x - 3. The graph is also shifted downwards by 9 units, not upwards.

The graph of f(x) = 6(x + 1)² -9 is a parabolic function. Let's check each of the given statements:

https://brainly.com/question/35698982

#SPJ3

Answer:

-120 degrees.

Step-by-step explanation:

This triangle has a rotational symmetry of 3  (it repeats its  orientation 3 times as it makes a complete circle around the center),  so the angle of rotation is 360 / 3 = 120 degrees.

As the rotation is counter clockwise  strictly speaking the answer is -120 degrees.

Answer:

its A on egd

Step-by-step explanation:

i just took the test

1. Find how much gas can be obtained: $10 goes into $2.50 4 times, so you can get 4 gallons.

2. Find how much gas is in the car: 1/4 of the maximum 13 gallons is 3.25 gallons, so there is already 3.25 gallons in your car.

3. Find how many gallons you have total: 4 gallons + 3.25 gallons =

7.25 gallons

The total gallons you have in your car after you put $10 worth of gas is 7.25 gallons.

It is required to find out how many total gallons you have in your car after you put $10 worth of gas.

Arithmetic is the branch of mathematics that deals with the study of numbers using various operations on them. Basic operations of math are addition, subtraction, multiplication and division. These operations are denoted by the given symbols.

Given:

Best way to start this is to figure out how much gas you can get for that $10.  

Since gas is $2.50/gallon and you buy $10 worth, that says you'll get 4 gallons of gas ($2.50 * 4 = $10).  Now figure out how many gallons you have left in your car.  If you car holds 13 gallons, 1/4 of that is 3.25 gallons. Add the 3.25 gallons left to the 4 gallons you bought and you get 7.25 gallons in your car.

Therefore, the total gallons you have in your car after you put $10 worth of gas is 7.25 gallons.

Learn more details about  arithmetic here:

https://brainly.com/question/11559160

#SPJ2

Answer: [tex]\bold{N=40e^{\bigg(\dfrac{ln2}{3}\bigg)T}}[/tex]

Step-by-step explanation:

The exponential growth formula is:

[tex]A=Pe^{rt}\\\bullet A=final\ amount\\\bullet P=initial\ amount\\\bullet r=rate\ of\ growth\\\bullet t=time[/tex]

NOTE: This problem is asking to use N instead of A and T instead of t

Step 1: find the rate  

[tex]N=Pe^{rT}\\2P=Pe^{r\cdot 3}\quad \leftarrow(Initial\ population\ doubled\ N=2P, T=3\ days)\\2=e^{3r}\quad \qquad \leftarrow (divided\ both\ sides\ by\ P)\\ln\ 2=ln\ e^{3r}\quad \leftarrow(applied\ ln\ to\ both\ sides)\\ln\ 2=3r\quad \qquad \leftarrow (ln\ e\ cancelled\ out)\\\boxed{\dfrac{ln2}{3}=r}\quad \qquad \leftarrow (divided\ both\ sides\ by\ 3)[/tex]

Step 2: input the rate to find N

[tex]N=Pe^{rT}\\\\\bullet P=40\\\\\bullet r=\dfrac{ln2}{3}\\\qquad \implies \qquad \boxed{N=40e^{\bigg(\dfrac{ln2}{3}\bigg)T}}[/tex]

Answer:

[tex]\boxed{N = 40(2)^{\frac{T}{3}}}[/tex]

Step-by-step explanation:

The growth of bacteria is an exponential function. The equation has the general form

[tex]f(x) = ab^{x}[/tex]

Using the variables N and T, we can rewrite the equation as

[tex]N = ab^{T}[/tex]

We have two conditions:

(1) There are 40 bacteria at T = 0

(2) There are 80 bacteria at T = 3.

Insert these values into the equation.

[tex]\begin{array}{rrcll}(1)&40& = & a(b)^{0} & \\(2)&80 & = & a(b)^{3} & \\(3)& a & = & 40 & \text{Simplified (1)}\\ &80 & = & 40(b)^{3} & \text{Substituted (3) into (2)}\\ & b^{3} & = & 2 & \text{Divided each side by 40}\\ & b & = & (2)^{\frac{1}{3}} &\text{Took the cube root of each side}\\\end{array}\\\\\text{Thus, the explicit equation is } N = 40 \left (2^{\frac{1}{3}\right )^{T}}} \text{ or}\\\\\boxed{\mathbf{N = 40(2)^{\frac{T}{3}}}}[/tex]

Answer: Option C

49°

Step-by-step explanation:

By definition, the cosine of an angle is defined as:

[tex]cos(\theta) = \frac{adjacent}{hypotenuse}[/tex].

The hypotenuse is always the opposite side to the 90 ° angle

The adjacent side is the one that contains the angle theta and the angles of 90 °.

In this case note that:

[tex]adjacent = n = 44\ mm\\\\hypotenuse = p = 67\ mm[/tex]

So:

[tex]cos(\theta) = \frac{44}{67}[/tex]

[tex]\theta = arcos(\frac{44}{67})[/tex]

[tex]\theta =49\°[/tex]

The answer is:

The correct option is:

C. 49°

To calculate the measure of the angle, we can use the following trigonometric relation:

[tex]Cos\theta =\frac{Adjacent}{Hypothenuse}[/tex]

We are given the following information:

[tex]adjacent=n=44mm\\hypothenuse=p=44mm[/tex]

So, substituting and calculating we have:

[tex]Cos(Cos\theta)^{-1} =Cos(\frac{Adjacent}{Hypothenuse})^{-1}\\\\\theta=Cos(\frac{Adjacent}{Hypothenuse})^{-1}\\\\\theta=Cos(\frac{Adjacent}{Hypothenuse})^{-1}[/tex]

[tex]\theta=Cos(\frac{Adjacent}{Hypothenuse})^{-1}=Cos(\frac{44}{67})^{-1}=48.95\°=49\°[/tex]

Hence, the correct option:

C. 49°

Have a nice day!