Module 13 area and polygons answer key please help.

Answer:

53.1°

Step-by-step explanation:

Look at the right triangle formed. You are given the Hypotenuse and an adjacent side to the angle needed to calculate the measure of the arc.

To find measure of angle use Cosine

Once you find measure of angle (central angle), you'll have the measure of the arc because they are the same.

cos -1 (9/15)  = 53.13

[tex]-5x-3 = 2\\-5x=5\\x = -1[/tex]

Now plug the x value into 9x + 2

[tex]9(-1)+2) = -7[/tex]

Hope that helps!

A sample is a group of persons or items collected or selected from a statistical population. The sample is 1127 households that owned a television.

A sample is a group of persons or items collected or selected from a statistical population by a predetermined approach in statistics and quantitative research methods. Sample points, sampling units, and observations are terms used to describe the components of a sample.

We know that sample is a group of people selected from the population, since there are 1565 state households, while there are 1127 households that owned television and who are surveyed. Therefore, the sample is 1127 households that owned a television.

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Answer:56m^2

Step-by-step explanation:

Answer:

[tex](4a)^{-3}*^{-4}[/tex]

[tex]x^m*x^n=x^{m+n}[/tex]

[tex](4a)^{-3}*a^{-4}[/tex]

[tex](-4)^{-3}\: a^{-3}*a^{-4}[/tex]

[tex]4^{-3}\:a^{-3-4}[/tex]

[tex]\cfrac{1}{4^3} \:a^{-7}[/tex]

[tex]\boxed{\frac{1}{64a^{7}} }[/tex]

~

[tex](3xy)^2*(-4x^3y^2)^3[/tex]

[tex]9x^2y^2*(64x^9y^6)[/tex]

[tex]\boxed{-576x^{11}y^8}[/tex]

~

[tex](4a^{-1}b^5c^{-3})^3[/tex]

[tex](4)^3(a^{-1})^3(b^5)^3(c^{-3})^3[/tex]

[tex](4*4*4)\:a^{-1*3}\:b^{5*3}\:c^{-3*3}[/tex]

[tex]64\:a^{-3}b^{15}c^{-9}[/tex]

[tex]\boxed{\frac{64b^{15}}{a^3c^9}}[/tex]

Answer:

11.8° and 78.2°

Step-by-step explanation:

let the angles be x and x + 66.4

complementary angles sum to 90° , then

x + x + 66.4 = 90

2x + 66.4 = 90 ( subtract 66.4 from both sides )

2x = 23.6 ( divide both sides by 2 )

x = 11.8 and

x + 66.4 = 11.8 + 66.4 = 78.2

The 2 angles are 11.8° and 78.2°

Answer:

corresponding angles . the answer

Answer:

corresponding angles

Step-by-step explanation:

its called the corresponding angles and are equal value

Credit is the money you borrow from the bank. and you need to pay in time with interest.

Answer:

no solution

Step-by-step explanation:

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

6x + 12 = 6x + 9

0 = -3

no solution when there are different numbers on either side of the equal sign

infinite is when there is the same number on either side of the equal sign like 0 = 0

Answer:

83 degrees

Step-by-step explanation:

The angles 56 and 41 plus the one in between should add up to 180 degrees. So you do 180 - 56 - 41 = 83.

83 and x are vertical angles so they are the same measure.

<x = 83 degrees

hope this helps! :)

Answer:

(9, - 9 )

Step-by-step explanation:

P (2, 3 ) → P' (5, - 4 )

2 → 5 in the x- direction is + 3

3 → - 4 in the y- direction is - 7

translation rule is then (x, y ) → (x + 3, y - 7 ) , so

(6, - 2 ) → (6 + 3, - 2 - 7 ) → (9, - 9 )

Answer:

  1/3

Step-by-step explanation:

The simulation will say that Jeffrey collected three different toys if the numbers in a group of three are either 0 or 1, a number more than 1 and less than 6, and a number 6 or more.

The groups {3, 7, 1}, {5, 1, 7}, {9, 2, 0}, {3, 0, 6} and {4, 6, 0} all simulate collection of all three toys from three boxes of cereal. Of the 15 simulated sets of three boxes, that is a probability of 5/15, or 1/3.

_____

Additional comment

The simulated toy numbers can be grouped in different ways. For example, we could take a vertical column of numbers as representing the purchase of 3 boxes of cereal. Doing that, we find 3 different toys only for the simulated values {4, 0, 6}, the last digits in the 4th column. The probability from considering the simulation that way is 1/15.

From this group of 45 numbers, one could calculate P(car) = 10/45, P(bus) = 19/45, and P(airplane) = 16/45. These vary a little from the theoretical values. Overall, with these values, the probability of 3 different toys from 3 boxes is about 0.200, only slightly different from the theoretical probability of 0.192.

Answer:

5

Step-by-step explanation:

The whole number obtained as the result of the ratio (10²⁰⁰⁰⁰+10²⁰⁰²) : (10²⁰⁰¹+10²⁰⁰¹) is 5.

It is described as the comparison of two quantities to determine how many times one obtains the other. The proportion can be expressed as a fraction or as a sign: between two integers. Comparing two numbers by dividing them is how ratios work. Your formula would be A/B if you were contrasting one data point (A) with another data point (B).

It is given that the ratio is,

(10²⁰⁰⁰⁰+10²⁰⁰²) : (10²⁰⁰¹+10²⁰⁰¹)

We have to apply the arithmetic operation for the given ratio in which we do the addition of numbers, subtraction, multiplication, and division. It has basic four operators that are +, -, ×, and ÷.

[tex]=\frac{10^{2000}+10^{2002}}{10^{2001}+10^{2001}} \\\\ =\frac{10^{2000}(1+100)}{10^{2000}(10+10)} \\\\ =\frac{101}{20} \\\\=5[/tex]

Thus, the whole number obtained as the result of the ratio (10²⁰⁰⁰⁰+10²⁰⁰²) : (10²⁰⁰¹+10²⁰⁰¹) is 5.

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The equation that represents the amount of soil, s in cubic centimeters the ferret can dig from the burrow in m minute is as follows:

s = 93m

One of the ferrets digs 465 cubic centimeters of soil from a burrow in 5 minutes.

The digging rate can be calculated as follows;

A rate is a ratio between two related quantities in different units. Therefore,

rate = 465 / 5 = 93 cubic centimetres per minutes.

Therefore, the equation that represents the amount of soil, s in cubic centimeters the ferret can dig from the burrow in m minute is as follows:

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Answer:

C&E

Step-by-step explanation:

Answer:

C and E

Step-by-step explanation:

given a quadratic in standard form

y = ax² + bx + c ( a ≠ 0 ) , then

• if a > 0 then the graph opens upward

• if a < 0 then the graph opens downward

----------------------------------------------------------------

A y = - x² + 9x with a < 0 then opens downward

B y = 10x - 5x² with a < 0 then opens downward

C y = (2x - 1)² = 4x² - 4x + 1 with a > 0 then opens upward

D y = (1 - x)(2 + x) = 2 - x - x² with a < 0 then opens downward

E y = x² - 8x - 7 with a > 0 then opens upward

Answer:

120 miles

Step-by-step explanation:

15 x 8 = 120 miles

The Highest Common Factor (HCF) of 18, 36 and 120 is 6.

A factor is a number that divides another number, leaving no remainder.

Given that, we need to find HCF of 18, 36 and 120.

Finding Factors :-

18 = 2 × 3 × 3

36 = 2 × 2 × 3 × 3

120 = 2 × 2 × 2 × 3 × 5

Common factors = 2 and 3

Therefore,

Highest Common Factor = 2 × 3 = 6

Hence, the Highest Common Factor (HCF) of 18, 36 and 120 is 6.

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Answer:

1

Step-by-step explanation:

Answer:

A, x < 12

Step-by-step explanation:

edge

Step-by-step explanation:

given : ABCD is a rhombus; AC and BD intersect at E to prove AC and BD in rhombus , ABCD, AC and BD intersect each other at E . given angle ABE and angle ADE

Answer:

[tex]\textsf{c)} \quad |3x+12|=\begin{cases}3x+12 \; &\text{if}\;x > -4\\0 \; &\text{if} \; x=-4\\-3x-12\; &\text{if}\;x < -4\end{cases}[/tex]

[tex]\textsf{d)} \quad |(x-19)+11|=\begin{cases}x-8\; &\text{if}\;x > 8\\0 \; &\text{if} \; x=8\\8-x \; &\text{if}\;x < 8\end{cases}[/tex]

[tex]\textsf{e)} \quad |14-(x-6)|=\begin{cases}x-20 \; &\text{if}\;x > 20\\0 \; &\text{if} \; x=20\\20-x \; &\text{if}\;x < 20\end{cases}[/tex]

[tex]\textsf{f)} \quad |14-(6-x)|=\begin{cases}x+8 \; &\text{if}\;x > -8\\0 \; &\text{if} \; x=-8\\-x-8 \; &\text{if}\;x < -8\end{cases}[/tex]

Step-by-step explanation:

The absolute value parent function, f(x) = | x |, is defined as:

[tex]f(x)=\begin{cases}x \; &\text{if}\;x > 0\\0 \; &\text{if} \; x=0\\-x\; &\text{if}\;x < 0\end{cases}[/tex]

Therefore:

Its graph is V-shaped and has the following properties:

Given absolute value expression:

[tex]|3x+12|[/tex]

Simplify the given expression:

[tex]\implies |3x+12|=|3(x+4)|=3|x+4|[/tex]

Set the simplified absolute value expression to zero and solve for x:

[tex]\begin{aligned}\implies 3|x+4|&=0\\|x+4|&=0\\x+4&=0\\x&=-4\end{aligned}[/tex]

Therefore, the vertex of the graph of the given absolute expression is (-4, 0).

Therefore, the slope of the expression will be positive for values of x greater than -4, and negative for values of x less than -4.  Set the expression inside the absolute value sign to positive and negative to find the two expressions with positive and negative slopes:

[tex]|3x+12|=\begin{cases}3x+12 \; &\text{if}\;x > -4\\0 \; &\text{if} \; x=-4\\-3x-12\; &\text{if}\;x < -4\end{cases}[/tex]

Given absolute value expression:

[tex]|(x-19)+11|[/tex]

Simplify the given expression:

[tex]|(x-19)+11|=|x-19+11|=|x-8|[/tex]

Set the simplified absolute value expression to zero and solve for x:

[tex]\begin{aligned}\implies |x-8|&=0\\x-8&=0\\x&=8\end{aligned}[/tex]

Therefore, the vertex of the graph of the given absolute expression is (-8, 0).

Therefore, the slope of the expression will be positive for values of x greater than 8, and negative for values of x less than 8. Set the expression inside the absolute value sign to positive and negative to find the two expressions with positive and negative slopes:

[tex]|(x-19)+11|=\begin{cases}x-8\; &\text{if}\;x > 8\\0 \; &\text{if} \; x=8\\8-x \; &\text{if}\;x < 8\end{cases}[/tex]

Given absolute value expression:

[tex]|14-(x-6)|[/tex]

Simplify the given expression:

[tex]|14-(x-6)|=|14-x+6|=|20-x|[/tex]

Set the simplified absolute value expression to zero and solve for x:

[tex]\begin{aligned}\implies |20-x|&=0\\20-x&=0\\x&=20\end{aligned}[/tex]

Therefore, the vertex of the graph of the given absolute expression is (20, 0).

Therefore, the slope of expression will be positive for values of x greater than 20, and negative for values of x less than 20. Set the expression inside the absolute value sign to negative and positive to find the two expressions with positive and negative slopes:

[tex]|14-(x-6)|=\begin{cases}x-20 \; &\text{if}\;x > 20\\0 \; &\text{if} \; x=20\\20-x \; &\text{if}\;x < 20\end{cases}[/tex]

Given absolute value expression:

[tex]|14-(6-x)|[/tex]

Simplify the given expression:

[tex]|14-(6-x)|=|14-6+x|=|x+8|[/tex]

Set the simplified absolute value expression to zero and solve for x:

[tex]\begin{aligned}\implies |x+8|&=0\\x+8&=0\\x&=-8\end{aligned}[/tex]

Therefore, the vertex of the graph of the given absolute expression is (-8, 0).

Therefore, the slope of expression will be positive for values of x greater than -8, and negative for values of x less than -8.  Set the expression inside the absolute value sign to positive and negative to find the two expressions with positive and negative slopes:

[tex]|14-(6-x)|=\begin{cases}x+8 \; &\text{if}\;x > -8\\0 \; &\text{if} \; x=-8\\-x-8 \; &\text{if}\;x < -8\end{cases}[/tex]

Answer:

B

Step-by-step explanation:

if angle A. and angle B are supplementary

the sum of 2angles ,

angle A + angle B =180 ,

if angle A is less than the angle B

in mathematics form,

let's angle A=X and angle B =X-40

then

angle A+ angle B =180

or, X+ (X - 40)=180

or, 2X=220

or, X=110

Answer:

x = 6

Step-by-step explanation:

20x + 11 + 9x - 5 = 180 ( linear pair)

29x + 6 = 180

29x = 180-6

29x = 174

x = 6

hence angles are:

20(6) + 11 = 131

9(6) - 5 = 49

Answer:

Solution,

Step-by-step explanation:

20x+11+9x-5=180° (being linear pair)

or, 29x+6=180

or, 29x=180-6

or, 29x=174

or, x=174 ÷29

Therefore x=6°

Answer:

to solve for k we will put y=6

Answer: y=-4x+2

Step-by-step explanation:

Answer:

Ok, so for this, you just need to multiply
The final answer: It costs $75,000 for the rent per year.

Step-by-step explanation:

1,500 x 50 = 75,000
(it says per square foot, look carefully, so multiplying would be correct)

Step-by-step explanation:

remember the definitions of these 2 types of numbers ?

rational numbers are all numbers that can be written as

a/b

where a and b are integers, and b <> 0.

this includes all real fractions, but also all whole or integer numbers, as they can be written as a/1.

if they have digits after the decimal point, they are either finite, or they have a repeating pattern for all eternity.

irrational numbers are all numbers with an infinite series of digits after the decimal point without any repeating patterns.

that includes all squares roots of non-squared numbers or any other roots of numbers that are not the product of correspondingly many multiplications with themselves. and trigonometric function and logarithm results, and the special numbers in math and physics : pi and e.

so,

4/7 is rational

sqrt(30) is irrational

21/sqrt(4) is a trick question, as sqrt(4) = 2.

so, this is actually

21/2 is rational

pi is irrational

-27 = -27/1 is rational

Answer:

145°

Step-by-step explanation:

180° - 35°