Drag the tiles to the correct boxes to complete the pairs.
Determine whether each pair of lines is perpendicular, parallel, or neither.
2y = 4x + 4
y=-2x-2
4y= 2x - 4
y=-2x+9
Perpendicular
Parallel
y = 2x+4
2y = 4x - 7
Neither

The measure of the angle in line y = 3x/2 is 56.31 degrees

Comparing the given equation y = 3x/2 with equation of a line in the slope intercept form  form as

y = mx + c

where

m = slope

c = intercept

x = input variables

y = output variables

This shows the y = 3x/2 is a line with c = 0 and slope as 3/2

calculation of slope

m = (y₂ - y₁) / (x₂ - x₁)

the formula is similar to definition of tan, assuming the angle is x

tan x = 3/2 (positive x and y axis)

x = arc tan 3/2

x = 56.3099

x = 56.31 degrees (to the nearest tenth of a degree)

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A and B are mutually exclusive events

The correct answer is yes

What are mutually exclusive events?

Two events are mutually exclusive in statistics and probability theory if they cannot happen simultaneously. A coin toss is the most basic illustration of two events that cannot coexist. The result of tossing a coin can be either heads or tails, but neither outcome can happen at the same time.

We are given that Amanda has 5 office assistants.

Events A is the event that at least 4 of them are men. this means that there is at most 1 female assistant

Events B is the event that at least 4 of them are women. this means that there is at most 1 male assistant.

Now one of the conditions is possible but both at the same time is not possible

Hence the both events are mutually exclusive.

The correct answer is yes

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Part 1

[tex]\frac{x}{3.2}=\frac{4}{2} \implies x=6.4 \\ \\ \frac{y}{2.4}=\frac{2}{4} \implies y=1.2[/tex]

Part 2

[tex]\frac{x}{3.6}=\frac{10.8}{5.4} \implies x=7.2 \\ \\ \frac{y}{5.4}=\frac{15.2}{10.8} \implies y=7.6[/tex]

Regarding the given matrix, it is found that:

1. a. The matrix has three rows.

1. b. The matrix has five columns.

1. c. The matrix has two dimensions.

2. The entry is 2.

3. The entry is 7.

4. The entry is -2.

5. The entry is 0.

6. The entries are: m21 and m33.

The matrix is composed by three lines of elements, and each line has five elements, hence:

The number of dimensions of the matrix are:

2, which are the rows and the columns.

The entries are symbolized as follows:

mrc.

In which:

Hence the entry m11, for example, is the element at the first row and at the first column, which is of 2.

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The answer to the inequality is  -55 < 49. That is -55 is less than 49.

What is inequality?

This refers to the relationship between two values that are not equal. It can be represented with the following symbols; < less than,> greater than, ≥ greater than or equal to,≤ less than or equal to, and  ≠ not equal to.

The given equation States that;

5(11 − ) < + 49

5*11- < +  49

-55  < +49

Therefore, -55 is less than 49.

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Answer:

Yes

Step-by-step explanation:

It depends on the questions before hand but this seems to answer the previous two questions.

The statement that can represent P = Q is If x = 5, then 2x = 10. That is option B.

An equivalent value is defined as the value or an equation that can be used to replace another value in an expression.

From the question, the expression P--> Q means that P = Q.

The statement that shows that a value is equivalent to the other;

x = 5, then 2x = 10

That is, X = 5 can also be written as follows;

2x = 10.

This is because, when 2x = 10 is simplified, X = 10/2 =5

Therefore, P =Q because both shears the same value and can be said to be equivalents.

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Answer:

[tex]-9,-18,-27,-36[/tex]

Step-by-step explanation:

If the first term of a sequence is [tex]-9[/tex] and the common difference is [tex]-9[/tex], then each successive term in the sequence is [tex]9[/tex] less than the previous term:

[tex]a_n=-9n[/tex]

Therefore, the first term is [tex]-9[/tex], followed by [tex]-18[/tex], [tex]-27[/tex], and [tex]-36[/tex].

Answer:

25

Step-by-step explanation:

Let the age of Thomas be x.

Huilan is 11 years older than Thomas,

Huilan = x + 11

The sum of their ages is 61.

x + x + 11 = 61

2x + 11 = 61

2x = 61 - 11

2x = 50

x = 50/2

x = 25

Hence,

Thomas's age is 25.

Answer:

Step-by-step explanation:

1) sixty-seventh and nine hundred and twenty-five thousands

2)one-eighty two and fifty-one thousands

3)thirty-nine and thousand four thirty two thousands

4) eighty five and two sixty seven thousands

5) ninety seven and seven thousand and three-fifty two thousands

An ordered pair which is a solution to the given system of linear equations is: (1, 4).

In order to determine which ordered pairs are valid and true solutions based on the given system of linear equations, we would have to test the given ordered pairs by substituting their values into the linear equations as follows;

For ordered pair (0, -4), we have:

-3x + 2y = 5

-3(0) + 2(-4) = 5

0 - 8 = 5

-8 = 5 (No)

For ordered pair (-3, 5), we have:

-3x + 2y = 5

-3(-3) + 2(5) = 5

9 + 10 = 5

19 = 5 (No)

For ordered pair (1, 4), we have:

-3x + 2y = 5

-3(1) + 2(4) = 5

-3 + 8 = 5

5 = 5 (Yes)

For ordered pair (1, 4), we have:

y = 8x - 4

4 = 8(1) - 4

4 = 4 (Yes).

For ordered pair (-7, -8), we have:

-3x + 2y = 5

-3(-7) + 2(-8) = 5

21 - 16 = 5

5 = 5 (Yes)

For ordered pair (-7, -8), we have:

y = 8x - 4

-8 = 8(-7) - 4

-8 = -58 (No).

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Answer:

  no change

Step-by-step explanation:

Given a temperature rise of 3.85 °F over 4 hours after noon, when the temperature is 85.4 °F, you want to know the change between 4 pm and 5 pm if the temperature at 5 pm is 89.25 °F.

The temperature at 4 pm is the sum of the noon temperature and the change in the 4 hours after noon:

  85.4 °F + 3.85 °F = 89.25 °F

The change from 4 pm to 5 pm is the difference between the 5 pm temperature and the 4 pm temperature:

  82.25 °F -89.25 °F = 0 °F

There is no change in the temperature between 4 pm and 5 pm.

Answer:

please write it more clearly or take a pic

The function y = 4 is a straight line and not an exponential function.

Given, a function y = 4

now, we have to test the function is exponential or not

As, the function is a straight line graph i.e. y = 4.

Now, the function y = 4 is a straight line graph which is parallel to the x-axis.

So, the function y = 4 is not an exponential function

Hence, the function y = 4 is a straight line and not an exponential function.

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Answer:

20 mph

Step-by-step explanation:

If it took the car originally 12 minutes to travel the road with an average speed of 60 mph. Than you would just divide the average speed by three because it is taking 3 times the amount of time than it would originally.
36/12=3
60/3=20
20 mph

The rectangular equation for the plane curve defined by the parametric equation x = t + 4, y = t² is; y = x² - 8x + 16

We are given the parametric equations as;

x = t + 4

y = t²

Now, for us to convert parametric equations to a rectangular equation (cartesian equation) means that we are solving for t in terms of x and then plugging it back into the y equation.  Therefore, we have;

x = t + 4

t = x - 4

Thus;

y = (x - 4)²

Expanding this gives;

y = x² -4x - 4x + 16

y = x² - 8x + 16

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The expression used to find the width using division is:

W = A/L

We know that for a rectangle of width W and length L, we know that the area is given by the product between these two dimensions, then:

A = L*W

We want a expression using division that can be used to find the width, so, suppose we know the values of the area and the length, the we can divide both sides by L to get:

A/L = W

This expression gives the width.

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Answer:

John's rate is faster than Paul's Step-by-step explanation: John, 64 push-ups/4min = 16 push-ups per minute Paul,

:

The value of  x is 26.125°

The measures of each angle are as shown below:

∠P  = 115.625°

∠Q =21.125°

∠R=43.25°

What is an equation?

An equation is a mathematical statement that proves two mathematical expressions are equal in algebra, and this is how it is most commonly used. In the equation 3x + 5 = 14, for instance, the two expressions 3x + 5 and 14 are separated.

In ∆PQR

∠P is 14 less than five times x = 5x-15

∠Q is five less than x=x-5

∠R is nine less than twice x=2x-9

Angle sum property of triangle : The sum of all angles of triangle is 180°

So,5x-15+x-5+2x-9=180

8x-29=180

8x=180+29

x=( 180+29 )/8

x=26.125

So,∠P  = 5x-15 =5(26.125)-15=115.625°

  ∠Q =x-5=26.125-5=21.125°

 ∠R=2x-9=2(26.125)-9=43.25°

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At an 85% confidence interval, the mean per capita income in thousands of dollars for the major city in Texas is $20.5 ± 0.459.

The confidence interval estimates the mean estimate by adding or subtracting the margin of error.

In random sampling, the margin of error represents the difference between the actual and projected results.

Mean income = $20.5

Sample size, n = 1,190

Standard deviation = $11

Confidence interval = 85%

Z-score for 85% confidence interval = 1.440

The margin of error = z-score x standard deviation/√n

= 1.440 x 11/√1,190

= 1.440 x 11/34.50

= 1.440 x 0.3188

= 0.459

= $459 (0.459 x $1,000)

Lower Limit = Mean - Margin of Error

= $20,500 - $459

= $20,041

= $20.041

Upper Limit = Mean + Margin of Error

= $20,500 + $459

= $20,959

= $20.959

Thus, for the Texas city, the mean per capita income is $20.5 ± 0.459.

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Answer:

Step-by-step explanation:

this is very complicated and i suggest you to go to einstin

By using a trigonometric relation we will see that FD = 32, the correct option is C.

We can see a right triangle, such that FD is the hypotenuse.

We also know one angle of this triangle, and the adjacent cathetus to that angle.

Now remember the relation:

cos(a) = (adjacent cathetus)/(hypotenuse)

Replacing the values we know we get:

cos(30°) = 28/hypotenuse

Solving the equation for the hypotenuse we get:

hypotenuse = 28/cos(30°) = 32.3

Rounding to the next whole number we get FD = 32

The correct option is C.

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The y-intercept of the equation y = (x - 4) is -4

From the question, we have the following equation that can be used in our computation:

y --(x - 4)

Rewrite the equation properly

So, we have the following representation

y = (x - 4)

To calculate the y-intercept, we set x to 0

So, we have the following representation

y = 0 - 4

Evaluate the difference

y = -4

Hence, the y-intercept is -4

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Answer: The answer is D ( 2/5 < 1/2

Step-by-step explanation:

Jarrod needs to walk 1 mile to reach the swimming pool

Given that: He lives 2 3/4 miles from the swimming pool

He walked 7/8 mile to the library

Then he walked 7/8 mile to the museum

The concept we need here is the addition or subtraction of fractions

To determine the miles left, we need to subtract the miles he walked from the miles 2 3/4 miles (since that is the distance from where he lives to the swimming pool)

Thus:

Miles left = 2 3/4 - 7/8 - 7/8

              = 11/4 - 7/8 -7/8              (Note:   2 3/4 = 11/4)

              =  8/8 = 1

Therefore,  he needs to walk 1 mile to reach the swimming pool

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Answer:

  -8, -5

Step-by-step explanation:

You want the second column of matrix B given matrices A and AB.

Matrix B can be found by left-multiplying AB by A^-1, as shown in the attachment.

The second column of matrix B is ...

  [tex]\left[\begin{array}{c}-8\\-5\end{array}\right][/tex]

The measure of angle ∠U = 73.5° in triangle UVW.

A polygon having three vertices and three sides are called a triangle.

Triangles are closed, two-dimensional shapes with three sides, three angles, and three vertices. A triangle is a part of a polygon. In the picture above, Triangle ABC is visible. examples of triangles. Many commonplace items, including sandwiches, traffic signs, clothing hangers, and pool table racks, have triangles.

The line segment VW ≅ UV. That implies ∠U = ∠W.

Given that a triangle's angle measurements add up to 180,

∠U + ∠W + ∠V = 180°

∠U + ∠U + 159° = 180°

2 ∠U = 21°

∠U = 10.5°

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Answer:

12*(1/4+1/3)(1/4+1/3)+2/3= 12*(1/16+1/12+1/12+1/9)+2/3=12*(9/144+12/144+12/144+16/144)+2/3= 12*(49/144)+2/3=12*49/144+2/3= 49/12+2/3=49/12+8/12=57/12= 4*9/12=4* 3/4

Step-by-step explanation: