Which trig function and ratio would you use to solve the following?


tan 30 = x4

sin 30 = 4x

cos 30 = x4

cos 30 = 4x

Answer:

[tex]\frac{\sqrt{11} }{6}[/tex]

Step-by-step explanation:

Using the Pythagorean identity

sin²x + cos²x = 1, then

cosx = [tex]\sqrt{1-sin^2x}[/tex]

cosΘ = [tex]\sqrt{1-(5/6)^2}[/tex]

         = [tex]\sqrt{1-\frac{25}{36} }[/tex] = [tex]\sqrt{\frac{11}{36} }[/tex] = [tex]\frac{\sqrt{11} }{6}[/tex]

Answer: 4

Step-by-step explanation:

Answer:

[tex]2^{\frac{5}{2}}[/tex]

Step-by-step explanation:

We have to solve the given expression [tex][(2)^{\frac{1}{2}}(2)^{\frac{3}{4}}]^{2}[/tex]

As we know [[tex]x^{a}.x^{b}=x^{a+b}[/tex]]

Now by solving the given expression by this identity

[tex][2^{\frac{1}{2}+\frac{3}{4}}]^{2}[/tex]

= [tex][2^{\frac{5}{4}}]^{2}[/tex]

= [tex]2^{\frac{(5)(2)}{4}}[/tex]

= [tex]2^{\frac{10}{4} }[/tex]

= [tex]2^{\frac{5}{2}}[/tex]

Therefore, the given expression can be represented by [tex]2^{\frac{5}{2}}[/tex].

Keep at x on one side so 7x+21x=180+11-23

Move everything that is not the x to the other side

7x+21x=180-23+11

28x=168

x=6

Answer:

D. :)

Step-by-step explanation:

The total cost of materials is $1658

How to find the total cost?

Total cost is defined as the addition of the cost of individual material.

Cost of material=Cost*Number of pieces

Cost of:

Adding them up: 20*16.69+2*20.78+2*15.58+6*21.38+118*6.60+500*0.22+10*8.44+1*150

=$1658

Therefore, The subtotal of costs of material is $1658.

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ANSWER

EXPLANATION

We want to simplify:

[tex](2\sqrt{5}+3)(\sqrt{5}-1)[/tex]

Recall the distributive property;

(a+b)(c+d)=a(c+d)+b(c+d)

We apply this property to get,

[tex]2\sqrt{5}(\sqrt{5}-1) + 3(\sqrt{5}-1)[/tex]

We expand to get,

[tex]2 \times 5-2 \sqrt{5} + 3\sqrt{5}-3[/tex]

This simplifies to,

[tex]10 + \sqrt{5}-3[/tex]

The simplest form of the given expression is:

[tex]7 + \sqrt{5}[/tex]

Answer:

Trapezoid

Step-by-step explanation:

Given quadrilateral has vertices at points A(-2,-1), B(3,13), C(15,5) and D(13,-11).

Find slopes of lines AD and BC:

[tex]\text{Slope}_{AD}=\dfrac{y_D-y_A}{x_D-x_A}=\dfrac{-11-(-1)}{13-(-2)}=\dfrac{-11+1}{13+2}=\dfrac{-10}{15}=-\dfrac{2}{3}\\ \\\text{Slope}_{BC}=\dfrac{y_C-y_B}{x_C-x_B}=\dfrac{5-13}{15-3}=\dfrac{-8}{12}=-\dfrac{2}{3}[/tex]

Since the slopes are the same, lines AD and BC are parallel.

Find slopes of lines ABD and CD:

[tex]\text{Slope}_{AB}=\dfrac{y_B-y_A}{x_B-x_A}=\dfrac{13-(-1)}{3-(-2)}=\dfrac{14}{5}\\ \\\text{Slope}_{CD}=\dfrac{y_D-y_C}{x_D-x_C}=\dfrac{-11-5}{13-15}=\dfrac{-16}{-2}=8[/tex]

Since the slopes are different, lines AB and CD are not parallel.

This means quadrilateral ABCD is trapezoid (two opposite sides - parallel and two another opposite sides - not parallel)

Answer:

The answer is the graph in the image.

Give brainliest if you please.  :)

A logarithmic graph that can be used to approximate the value of y in the equation [tex]3^y = 8[/tex] is =: B. graph B.

In Mathematics and Geometry, an exponential function can be modeled by using this mathematical equation:

[tex]y = a(b)^x[/tex]

Where:

Based on the information provided above, we can logically deduce the following equation;

[tex]3^y = 8[/tex]

By applying base 3 logarithm to boths sides of the equation, we have;

[tex]log_{3}(3^y)=log_{3}(8)\\\\ylog_{3}3=log_{3}8\\\\y=log_{3}8\\\\y\approx 1.89\\\\\\\\y=log_{3}x[/tex]

In conclusion, we can reasonably infer and logically deduce that only graph B is a logarithmic graph that can be used to approximate the value of y in the equation [tex]3^y = 8[/tex], which is approximately equal to 1.89.

Missing information:

Which logarithmic graph can be used to approximate the value of y in the equation [tex]3^y = 8[/tex]?

Answer:

B

Step-by-step explanation:

The president's company makes money from almonds, so he wants people to believe that almonds are good for one's teeth so that they buy more almonds.

Answer:

B. The president wants people to believe that almonds are good for one's teeth so that they buy more almonds.

Step-by-step explanation:

The report shows that people who eat a handful of almonds each day have 10% fewer cavities.

The most likely reason the president releases such report is - B. The president wants people to believe that almonds are good for one's teeth so that they buy more almonds.

The report is a way to emphasize that consuming almonds will help in reducing cavities. This is a great marketing skill by the President as making people believe the effects of almonds, will help in more sales of almonds.

Answer:

[tex]27cm^{2}[/tex]

Step-by-step explanation:

You would use the equation, [tex]area = r^{2} sin(\frac{360}{n})/2[/tex]

r= radius, n = number of sides

Answer:

The number of pennies doubles each time, so the count grows exponentially.

The number of pennies on Rows 5-8 will be much greater than on Rows 1-4.

Answer:

The number of pennies doubles each time, so the count grows exponentially.

The number of pennies on Rows 5-8 will be much greater than on Rows 1-4.

Step-by-step explanation:

Answer:

C

Step-by-step explanation:

Using sum/difference to product identity

• sin x - sin y = 2 cos([tex]\frac{x+y}{2}[/tex]) sin ([tex]\frac{x-y}{2}[/tex])

with x = 4Θ and y = 2Θ

Then

sin(4Θ) - sin(2Θ)

= 2 cos([tex]\frac{4o+2o}{2}[/tex]) sin([tex]\frac{4o-2o}{2}[/tex])

= 2cos(3Θ)sinΘ → C

Answer:

$4706.81

Step-by-step explanation:

The value each year is multiplied by 100% -12% = 88% = 0.88. After 13 years, the value is 0.88^13 ≈ 0.1897906 times what it was originally: ≈ 4,706.81 dollars.

Answer:

4706.81

Step-by-step explanation:

Answer:

  -2x^7 + ...

Step-by-step explanation:

When the end behaviors are different, the function is one of odd degree. When the slope is downward to the right, the leading coefficient (the coefficient of the highest-degree term) is negative.

The one function shown with an odd degree and a negative leading coefficient is the one that starts ...

  -2x^7 + ...

Step-by-step explanation:

A geometric series is:

an = a₁ (r)^(n-1)

Here:

an = 2/5 (5)^(n-1)

So a₁ = 2/5, and r = 5.  So an = 5an-1.

Your answer is correct, well done!

Answer:

Greatest common factor = 1

Step-by-step explanation:

given algebraic expressions are 7w and [tex]4m^3[/tex].

Now we need to find about what is the greatest common factor that is GCF of given algebraic expressions 7w and [tex]4m^3[/tex].

7 is a prime number so that can't be factored more.

There is no common factor of 7 and 4 except 1.

there is no common factor of w and [tex]m^3[/tex].

Hence required greatest common factor of given algebraic expressions 7w and [tex]4m^3[/tex] is 1.

Answer:

A line.

Step-by-step explanation:

This is a line passing through the origin and rising to the right. The angle betwee the line and the x axis = pi/3 radians.

Answer:

C. Line.

Step-by-step explanation:

We are asked to find the name of shape that is graphed by the function [tex]\theta =\frac{\pi}{3}[/tex].

We can see that the measure of theta is constant [tex]\frac{\pi}{3}[/tex]. This means that slope of function is also constant.

We know that slope of a straight line is always constant for all values in its domain.

Therefore, the shape of our given function is a line and option C is the correct choice.

Answer:

93.66 but you can’t use only .66 of a container so I would say round up so 94

Step-by-step explanation:

The number of containers that Casey used will be 94 containers.

The analysis of mathematical representations is algebra, and the handling of those symbols is logic.

Division means the separation of something into different parts, sharing of something among different people, places, etc.

Casey has 281 tennis balls. She will put them in containers that hold 3 tennis balls.

Then the number of containers that Casey used will be given by the division of the numbers 281 and 3.

⇒ 281 / 3

⇒ (279 + 2) / 3

⇒ 279 / 3 + 2 / 3

⇒ 93 + 2/3

⇒ 93 + 0.667

⇒ 93.667 or 94

The number of containers that Casey used will be 94 containers.

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Answer:

a cone

Step-by-step explanation:

If the base is circular, then the cone is said to be a "regular" or "circular" cone, much like an ice cream cone.

If the base is elliptical, then it becomes an "elliptical" cone.  

Both shapes can be right (where the perpendicular line dropping from the vertex lands on the exact center of the base) or oblique (when the line dropping from the vertex doesn't land on the center of the base)

Answer: 48.75$

Step-by-step explanation:

just took it

Answer:48.75

Step-by-step explanation:

Answer:

Step-by-step explanation:

the x coordinate is to the right so your choices are J A K G and C. You know this because 1 is positive and that moves to the right.

The -3 moves 3 units below the x axis. That limits your answer to KCG

We have to assume that each square is worth one, so the answer must be C.

Answer:

b. an = 2 • (-3)^(n - 1)

Step-by-step explanation:

Before we test a solution or two, we can easily discard most of them.

We see the values alternate of signs (-5 for the 2nd term and +162 for the 5th term)... so the progression factor has to be negative (in order to alternate sign).  That already excludes answers A and C.

Normally, a geometric progression has the (n-1) exponent, not (n+1), so our chances seem to be better with B.

We can test both D and B with n = 2, to obtain -6

Let's test answer D before:

[tex]a_{2} = 2 * (-3)^{2+1} =  2 * (-3)^{3} = 2 * -27 = -54[/tex]

The result is -54, not -6... so it's not the right result.

Let's test answer B then:

[tex]a_{2} = 2 * (-3)^{2-1} =  2 * (-3)^{1} = 2 * -3 = -6[/tex]

Right!  Let's verify with n=5 to get 162:

[tex]a_{5} = 2 * (-3)^{5-1} =  2 * (-3)^{4} = 2 * 81 = 162[/tex]

Confirmed, answer is B. an = 2 • (-3)^(n - 1)

Answer:

  D.  (x - 2)(x - 2)

Step-by-step explanation:

x² - 4x + 4 = (x -2)(x -2)

___

The expression matches the form ...

  (a +b)² + a² +2ab +b²

where a = x and b = -2

Good luck to Jonathan. I hope he gets his sport set soon.

The answer will be 3.33

Hope this Help:)

Answer:

6.22

Step-by-step explanation:

First find the mean:

μ = (105+104+110+112+114+108+108+109) / 8

μ = 108.75

The standard deviation is then:

σ² = [(105-108.75)²+(104-108.75)²+(110-108.75)²+(112-108.75)²+(114-108.75)²+(108-108.75)²+(108-108.75)²+(109-108.75)²] / 8

σ² = 77.5 / 8

σ = 3.11

Margin of error is ±2σ, so ME = ±6.22.

Answer:

x = 14

Step-by-step explanation:

Chords equidistant from the centre of a circle are equal.

Both chords are 9 units from the centre, thus equidistant and equal, so

x = 7 + 7 = 14

Answer:

[tex]k=110[/tex]

Step-by-step explanation:

Part 15) we know that

[tex]n=klog(A)[/tex]

Solve for k

That means ----> isolate the variable k

[tex]k=n/log(A)[/tex]

we have

[tex]n=440\ wolves[/tex]

[tex]A=10,000\ mi^{2}[/tex]

substitute

[tex]k=440/log(10,000)[/tex]

[tex]k=110[/tex]

Answer:

1. 6w+6=48

2. n = 9

3. 2x+2 = 5.64

4. 2x-3 = 7.80

5. 2x+6 = 30

6. 3x+3 = 153

7. 2x - 6 = 14

8. 3x + 6 = 54

9. 1424 = 356*t

Step-by-step explanation:

1.

Let the width be w, then twice the width is 2w. But our length is 3 more than twice the width, implying that our length will be 2w+3.

The perimeter of a rectangle is given by the formula;

p = 2(length + width)

2(2w+3+w) = 48

6w+6=48 is our required equation.

2.

Fifteen more than four times a number is 6 more than five times the number. Use "n" for the number.

We first evaluate, Fifteen more than four times a number;

since our number is n, the above statement can be written mathematically as,

4n + 15

The next step we evaluate; five times the number,

5n

In the final step we compare these two expression and solve for n;

we have been told that; Fifteen more than four times a number is 6 more than five times the number. This implies;

4n + 15 - 5n = 6

-n = -9

n = 9

3.

Let the amount paid by Martha be x. Therefore, the amount paid by Sally would be x+2 since she paid 2 more than Martha. The total amount paid by both is;

x+x+2 = 2x+2

The required equation is thus;

2x+2 = 5.64

4.

We let the amount spent by Tim be x. This would mean that Bob spent x-3 since we are told that Bob paid $3 less than Tim. Therefore, the total amount spent by Bob and Tim in terms of x is;

x+x-3 = 2x-3

Therefore, the required equation would be;

2x-3 = 7.80

5.

We let the number of men be x, then the number of women would be x+6 since we are told that there were six more women on the committee than men. The total number of people on the committee in terms of x is thus;

x+x+6 = 2x+6

Therefore, our required equation would be;

2x+6 = 30

6.

Three consecutive integers have the sum of 153.

We let the three consecutive integers be;

x, x+1, and x+2

The difference between consecutive integers is usually 1.

The sum of the above integers in terms of x would be;

x+x+1+x+2 = 3x+3

Therefore, our required equation would be;

3x+3 = 153

7. Five times the first of three consecutive even integers is fourteen more than three times the second.  

We let the first even integer be x. The second even integer would be x+2 while the third one would be x+4. The difference between two consecutive even integers is always 2. Now Five times the first of three consecutive even integers would be;

5*x = 5x

On the other hand, three times the second even integer would be;

3*(x+2) = 3x + 6

Now, we are told that 5x exceeds 3x + 6 by 14. Therefore, we can write;

5x - (3x +6) = 14

2x - 6 = 14

Which is the required equation

8. The sum of three consecutive even integers is fifty-four.

We let the first even integer be x. The second even integer would be x+2 while the third one would be x+4. The difference between two consecutive even integers is always 2. The sum of the three consecutive even integers in terms of x would be;

x+x+2+x+4 = 3x+6

The required equation would thus be;

3x + 6 = 54

9. An airplane flies at a rate of 356 km/h. The plane travels a total distance of 1424 km. (Use Distance = Rate * Time for your equation.)

The distance traveled by the plane is given as 1424 while its      rate or speed is 356. We let t denote the time it took the plane to travel the given distance at the given rate. Using the equation Distance = Rate * Time, we can write the following equation in t;

1424 = 356*t

Which is our required equation.

Answer:

1. 6w+6=48

2. n = 9

3. 2x+2 = 5.64

4. 2x-3 = 7.80

5. 2x+6 = 30

6. 3x+3 = 153

7. 2x - 6 = 14

8. 3x + 6 = 54

9. 1424 = 356*t

Step-by-step explanation:

Answer:

b. $286,525

Step-by-step explanation:

Mr. and Mrs. Donahue want to buy a home valued at $365,000.

They have 21.5% of this amount saved for a down payment, means they have saved [tex]0.215\times365000=78475[/tex] dollars

So, their home loan will be of [tex]365000-78475=286525[/tex] dollars

Therefore, the answer is $286,525.

Answer:

b.

$286,525

Step-by-step explanation:

Got all correct on edge 2020

Answer:

It changes negative numbers to positive.

Step-by-step explanation:

Absolute value is the measure of a numbers distance from 0. You can't have negative distance, so absolute value of negative numbers is positive and absolute value of positive numbers is always positive. The absolute values of 5 and -5 are both 5 because they are both 5 units away from 0 on a number line, just in opposite directions.

Final answer:

The absolute value of a number measures its distance from zero, ignoring direction. For vectors, it describes the magnitude without considering direction, remaining positive even when multiplied by a negative scalar. The concept is vital in many areas of math and science, such as physics in calculating displacement and in sound when determining beat frequency.

Explanation:

The absolute value of a number or an expression essentially measures its distance from zero on a number line, without considering direction. For vectors, the concept is similar; the magnitude of the vector becomes the absolute value of cA, which indicates its size irrespective of its direction. If the scalar c is positive, the vector maintains its direction. In contrast, if c is negative, the direction is reversed. However, the magnitude, given by the absolute value, remains positive.

For instance, in physics, the concept of absolute value is important when dealing with displacements since displacement is a vector. If the total displacement is a negative value, like -2 m, its magnitude is the absolute value, which is 2 m; thereby indicating that the actual 'size' or length of displacement is 2 m. Likewise, in the context of statistics, the absolute value of a z-score (deviation from the mean) indicates how far a score is from the mean, regardless of whether it's above or below it.

In the field of sound, the concept of absolute value becomes important when calculating beat frequencies, because frequencies cannot be negative. Hence, the beat frequency is the absolute value of the difference between two frequencies, ensuring that the result is always a positive number, indicative of a real-world, physical attribute.