Question 9 of 10
Which pairs of angles in the figure below are vertical angles?
Check all that apply.

The simplified form of the given expression is tan(r) + cot(r) - 2

From the question, we are to simplify the given trigonometric function

The given trigonometric function is

[tex]\frac{(1-cot(r))^{2} }{cot(r)}[/tex]

Expanding, we get

[tex]\frac{(1-cot(r))(1-cot(r)) }{cot(r)}[/tex]

Simplifying

[tex]\frac{1 - 2cot(r) +cot^{2}(r) }{cot(r)}[/tex]

[tex]\frac{1}{cot(r)} -\frac{2cot(r)}{cot(r)}+\frac{cot^{2}(r) }{cot(r)}[/tex]

[tex]\frac{1}{cot(r)} -2+cot(r)[/tex]

Recall: [tex]tan(x) = \frac{1}{cot(x)}[/tex]

Therefore, we get

[tex]tan(r) -2 + cot(r)[/tex]

[tex]tan(r) + cot(r)-2[/tex]

Hence, the simplified form of the given expression is tan(r) + cot(r) - 2.

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Answer:

They use collected data to recognize trends, predict outcomes, and plan for the future.

Step-by-step explanation:

Answer:

a. {(0, 7), (-1, 6)}

Step-by-step explanation:

[tex]y = x^{2} +2x+7\\y=x+7[/tex]

subtract the equations

[tex]y = x^{2} +2x+7 \\- \ \ \ \ \ y=x+7\\y - y =x^{2} +2x+7-(x+7)\\0=x^{2} +x\\x = 0 \ and \ x= -1[/tex]

for [tex]y = x^{2} +2x+7[/tex], substitute x = 0

[tex]y = (0)^{2} +2(0)+7\\y = 0 +0+7\\y=7[/tex]

for [tex]y = x^{2} +2x+7[/tex], substitute x = 0

[tex]y = (-1)^{2} +2(-1)+7\\y = 1 -2+7\\y=6[/tex]

Answer:

A

Step-by-step explanation:

Answer:

Step-by-step explanation:

x² - 3x - 28

What factors multiply to -28 and add to -3?

-7 and 4.

(x - 7) (x + 4)

Answer:

(x - 7)(x + 4)

Step-by-step explanation:

To find the factors, you just need to ask yourself the question: Which two numbers multiply to -28 but add to -3?

Simple guess-and-check will lead you to the numbers -7 and 4.

-7 x 4 = -28

-7 + 4 = -3

These numbers will make up the factored equation.

x² - 3x - 28

(x - 7)(x + 4)

You can check your answer by re-expanding the factored expression. This is done by multiplying each term in the first parentheses by each term in the second parentheses.

(x - 7)(x + 4)  ---->  x² - 7x + 4x - 28  ---->  x² - 3x - 28

The attached graph represent the points in the domain -6 < x ≤ -2

The function is given as:

[tex]f(x) = \left[\begin{array}{ccc}-2&-6 < x \le -1\\1&-1 < x \le 2 & \\5 & 2 < x \le 4\end{array}\right[/tex]

The question says that we plot two points in the domain -6 < x ≤ -2

The domain -6 < x ≤ -2 means that the values of x are greater than -6, but they do not exceed -1

The function at this interval means that all values of x have an output value of -2

So, the two points to plot could be (-5,-2) and (-1,-2)

See attachment for the graph of the points

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Answer:

1/12

Step-by-step explanation:

Answer:

Ann bought 32 ounces of cheese.

Step-by-step explanation:

First of all, that is a lot of cheese, I hope she is not lactose intolerant.

Second of all, one pound is equivalent to 16 ounces. Given this, we can multiply the pounds of cheese by 16.

That would look like 2×16=32.

I hope this answer helped you and also made you laugh. It is correct though, despite the comedy.

The number of the cups of honey has she collected will be 52 and 2/3 cups.

A ratio is a collection of ordered integers a and b represented as a/b, with b never equaling zero. A proportionate expression is one in which two items are equal.

Gerrie collects honey from a few beehives.

She scoops out the honey with a small jar that holds 1/3 of a cup.

Over the last two weeks, Gerrie has filled this jar 158 times.

1 small jar = 1/3 cup

But we have done this for 158 times. Then we have

158 small jar = 158 x 1/3 cups

158 small jar = 52 and 2/3 cups

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Answer: A compass.

Step-by-step explanation: an instrument for drawing circles and arcs and measuring distances between points, consisting of two arms linked by a movable joint, one arm ending in a point and the other usually carrying a pencil or pen.

Answer:

29.44

Step-by-step explanation:

Since we know the both the measure of the angle and the adjacent line of the angle, we can use tan to find x.

tan is (Opposite/Adjacent Line)

[tex] \tan(31) = \frac{x}{49} \\ 49 \tan(31) = x \\ 29.44 = x[/tex]

That is the answer

- Kan Academy Advance

Answer:

BC ≈ 11.8 m

Step-by-step explanation:

using the tangent ratio in the right triangle

tanΘ = [tex]\frac{opposite}{adjacent}[/tex] = [tex]\frac{AB}{BC}[/tex] , that is

tan32° = [tex]\frac{x}{BC}[/tex] = [tex]\frac{7.4}{BC}[/tex] ( multiply both sides by BC )

BC × tan32° = 7.4 ( divide both sides by tan32° )

BC = [tex]\frac{7.4}{tan32}[/tex] ≈ 11.8 m ( to 3 sf )

Answer: No the expressions are not equal

Work Shown:

3² = 3*3 = 9

3³ = 3*3*3 = 27

3²+3³ = 9+27 = 36

3⁵ = 3*3*3*3*3 = 243

The 3²+3³ = 36 doesn't match up with 3⁵ = 243

Therefore, the two expressions are not equal.

Answer:

Step-by-step explanation:

No, the expressions are not equal.

3^2 + 3^3 = 9 + 27 = 36

3^2 * 3^3 = 3^5

keep the base the same and add the exponents

Answer:

1:19

2:20

3:21

4:22

Step-by-step explanation:

I think that's the answer

By identifying the largest exponent in each expression, we see that the answers are:

a) D = 3.

b) D = 5.

c) D = 0.

The degree is just the largest exponent of the variable in an expression.

First, we have:

a) √3xyz - 5

The largest exponent is on the term √3*xyz is 3 (because we add the 3 exponents 1 of x, y, and z) so this expression has a degree of 3.

b)  y² - 3y⁵ -y + 2y³ - 4

Here the largest exponent is on the second term, so we can see that the degree is 5.

c) -10³

Here we don't have a variable, so this is a constant, which means that the degree is zero, because we could write:

-10³*x⁰

Where we use the fact that x⁰ = 1

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Answer: 5 levels

Step-by-step explanation:

      We will set up a system of equations and solve. Let x be the number of levels beaten, and let y be the number of total points.

          Miguel's version:

              y = 1x + 25

          Lauren's version:

              y = 2x + 20

      Now, we will graph both equations. The x-coordinate of the point-of-intersection is the answer to our question.

          See attached.

             The lines intersect at (5, 30) meaning they will have the same number of points after 5 levels, with 30 points.

Use distributive law

a(b+c)=ab+ac

Using the combination formula, it is found that 15,876 teams would include Julia.

The order in which the people are chosen to the team is not important, hence the combination formula is used to solve this question.

[tex]C_{n,x}[/tex] is the number of different combinations of x objects from a set of n elements, given by:

[tex]C_{n,x} = \frac{n!}{x!(n-x)!}[/tex]

In this problem:

Hence the number of teams is given by:

[tex]C_{9,5} \times C_{9,4} = \frac{9!}{5!4!} \times \frac{9!}{5!4!} = 15876[/tex]

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By critically observing the scatter plot (see attachment), the type of relationship that would best model this data is positive nonlinear.

In Statistics, there are four (4) main types of relationship (association) in a scatter plot and these include the following:

By critically observing the scatter plot shown in the image attached below, we can logically deduce that the type of relationship that would best model this data is positive nonlinear because the change in one of the variables doesn't result in a constant change in other variables.

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Answer:

300,000

Step-by-step explanation:

423 x 764 = 323,172

Hi student, let me help you out! :)

. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

We are asked to find which expression represents the description "twice the quantity m plus n".

[tex]\triangle~\fbox{\bf{KEY:}}[/tex]

First, add m and n:

[tex]\star~\large\pmb{m+n}[/tex]

Now, multiply two times this sum:

[tex]\star~\large\pmb{2(m+n)}[/tex]

See, the parentheses around the sum show that we multiply two times both m and n.

Hope it helps you out! :D

Ask in comments if any queries arise.

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~Just a smiley person helping fellow students :)

Answer:

2(m + n)

Step-by-step explanation:

The words describe a quantity. "Twice" means two-times the previous amount. m and n are the unknown numbers that are being added, so you must put them in parentheses to indicate that they should be added first.

Based on the information provided, the statement which is a valid conclusion is only: option A.

A valid conclusion can be defined as a statement that is essentially based on empirical data, formulated hypotheses, facts, and prudent experimental design, which entails that relationship between data variables are reasonable, credible and valid.

Based on the information provided, the statement which is a valid conclusion is that the botanist can make inferences for all plants, and he can draw his conclusion that the fertilizer would help all plants grow taller.

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Answer: C

Step-by-step explanation:

Inferences can be made for these types of plants, and the conclusion can be drawn that the fertilizer will help these types of plants grow taller

The result of the expressionn 1/5 - 3/4 will be negative 11/20. Then the correct option is C.

A fraction number is a number that represents the part of the whole, where the whole can be any number. It is in the form of numerator and denominator.

The expression is given below.

⇒ 1/5 - 3/4

⇒ (4 - 15) / 20

⇒ -11 / 20

Then the correct option is C.

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Answer:

c

Step-by-step explanation:

The measure of angle A  is 17.8

The correct  option is (A)

A figure which is formed by two rays or lines that shares a common endpoint is called an angle.

As,  perpendicular from B to side AC

In triangle BDC,

its angles are 30°, 60° and 90°

So, the sides ratio be 1 :√3 : 2

Now,

BD : DC : BC = 1 :√3 : 2

= 11√3/2 : 11/2 : 11

Now, using trigonometry

Sin A = P /H

Sin A = BD/AB

=(11/2)/18

= 11/36

= 0.3055

m<A = 17.79 ≈ 17.8°

hence, the measure of A  is 17.8°.

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Answer:

Step-by-step explanation:

Simplify in steps, using below properties of exponents:

Correct choice is D

Answer:

[tex]4x^2y^3\sqrt[3]{x^2y}[/tex]

Step-by-step explanation:

Given expression:

[tex]\left(8x^4y^5\right)^{\frac{2}{3}}[/tex]

Rewrite 4 as (3 + 1) and 5 as (3 + 2):

[tex]\implies \left(8x^{(3+1)}y^{(3+2)}\right)^{\frac{2}{3}}[/tex]

[tex]\textsf{Apply exponent rule} \quad a^{b+c}=a^b \cdot a^c:[/tex]

[tex]\implies \left(8x^3xy^3y^2}\right)^{\frac{2}{3}}[/tex]

[tex]\textsf{Apply exponent rule} \quad (a^b)^c=a^{bc}:[/tex]

[tex]\implies 8^{\left(\frac{2}{3}\right)}x^{\left(3 \times\frac{2}{3}\right)}x^{\left(\frac{2}{3}\right)}y^{\left(3 \times \frac{2}{3}\right)}y^{\left(2 \times \frac{2}{3}\right)}}[/tex]

[tex]\implies 4x^2x^{\frac{2}{3}}y^2y^{\frac{4}{3}}[/tex]

[tex]\implies 4x^2y^2x^{\frac{2}{3}}y^{\frac{4}{3}}[/tex]

Rewrite 4/3 as 1 + 1/3:

[tex]\implies 4x^2y^2x^{\frac{2}{3}}y^{\left(1+\frac{1}{3}\right)}[/tex]

[tex]\textsf{Apply exponent rule} \quad a^{b+c}=a^b \cdot a^c:[/tex]

[tex]\implies 4x^2y^2x^{\frac{2}{3}}y^1y^{\frac{1}{3}}[/tex]

[tex]\implies 4x^2y^2y^1x^{\frac{2}{3}}y^{\frac{1}{3}}[/tex]

[tex]\textsf{Apply exponent rule} \quad a^b \cdot a^c=a^{b+c}[/tex]

[tex]\implies 4x^2y^{(2+1)}x^{\frac{2}{3}}y^{\frac{1}{3}}[/tex]

[tex]\implies 4x^2y^3x^{\frac{2}{3}}y^{\frac{1}{3}}[/tex]

[tex]\textsf{Apply exponent rule} \quad a^{bc}=(a^b)^c:[/tex]

[tex]\implies 4x^2y^3\left(x^2\right)^{\frac{1}{3}}y^{\frac{1}{3}[/tex]

[tex]\textsf{Apply exponent rule} \quad a^b \cdot c^b=ac^b:[/tex]

[tex]\implies 4x^2y^3\left(x^2y\right)^{\frac{1}{3}[/tex]

[tex]\textsf{Apply exponent rule} \quad a^{\frac{1}{n}}=\sqrt[n]{a}:[/tex]

[tex]\implies 4x^2y^3\sqrt[3]{x^2y}[/tex]

Answer:

Mean = 48.5, Median = 53, Mode = nothing, Outlier = 17

Step-by-step explanation:

Mean: Add all the numbers (388) then divide by how many numbers (8) are there. (= 48.5)

Median: Is the middle number () so you have to order them from least to greatest (17, 42, 45, 52, 54, 57, 58, 63) and then just keep marking them off left, right, left, right... until you get to the middle. But since there are two numbers (52, 54) you have to add them (106) then you divide by 2 (53).

Mode: Is the number that shows up the most. In this case none of them do.

Outlier: The number that is farthest from the other numbers (17).

Answer:

65, 65, 115

Step-by-step explanation:

Attached image

The weight of the spherical sculpture in pounds is approximately 251607 pounds

The sculpture is spherical and its made of solid bronze.

Therefore,

density  =  mass   /   volume

where

density  =  7700  kg  / m³

volume  = 4 / 3πr³

volume = 4/ 3  × 3.14  × 1.524³

volume  =  44.4574491494 / 3

volume = 14.8191497165 m³

Therefore,

mass = 7700 × 14.8191497165

mass = 114107.452817 kg

1 kg = 2.205 pounds

114107.452817 = ?

cross multiply

mass in pounds = 114107.452817 × 2.205

mass in pounds = 251606.933461

mass in pounds = 251607 pounds

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Answer:

First, break the shape into smaller shapes.

Bigger rectangle: 5m, 8m

Thin rectangle: 7m, 3m

Thinner rectangle: 8m, 2m

We will call the bigger rectangle B, the thin rectangle R, and the thinner rectangle r.

Step-by-step explanation:

B = 8 • 5 = 40

R = 7 • 3 = 21

r = 2 • 8 = 16

Add the areas together:

40 + 21 + 16 = 77

Therefore, the area is 77 meters.

Answer:

$40 average

Step-by-step explanation:

500-300=200

200/5=40

Monetary policy is the actions taken by the reserve banks to influence the real GDP and the inflation rate in the economy.

These are actions done by the central bank of a country and involves adjusting money supply so as to achieve economic growth.

This influences the real gross domestic product and inflation rate of the country .

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Answer: Monetary and Reserve Bank

Step-by-step explanation:

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