the **bisectors** of two supplementary angles are perpendicular to each other is proved along with the given diagram.

In Plane Geometry, a figure which is formed by two rays or lines that shares a common endpoint is called an** angle**. The two rays are called the sides of an angle, and the common endpoint is called the vertex.

Here, we have,

from the given diagram we get,

∠BOP=x & ∠AOP=180-x

and, ∠NOP=x/2 & ∠MOP=(90-x/2)

Now,

∠MON=∠MOP+∠NOP

=90-x/2 + x/2

=90

Hence, it is proved that the** bisectors** of two supplementary angles are perpendicular to each other.

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Find the equation of the line passing through the point (–1, 5) and perpendicular to the line y = – 3x + 4.

A) 3y = –x + 16

B) y = –3x + 8

C) y = –3x + 2

D) 3y = x + 16

**Answer:**

D

**Step-by-step explanation:**

the equation of a line in slope- intercept form is

y = mx + c ( m is the slope and c the y- intercept )

y = - 3x + 4 ← is in slope- intercept form

with slope m = - 3

given a line with slope m then the slope of a line perpendicular to it is

[tex]m_{perpendicular}[/tex] = - [tex]\frac{1}{m}[/tex] = - [tex]\frac{1}{-3}[/tex] = [tex]\frac{1}{3}[/tex] , then

y = [tex]\frac{1}{3}[/tex] x + c ← is the partial equation

to find c substitute (- 1, 5 ) into the partial equation

5 = - [tex]\frac{1}{3}[/tex] + c ( add [tex]\frac{1}{3}[/tex] to both sides )

5 [tex]\frac{1}{3}[/tex] = c ⇒ c = [tex]\frac{16}{3}[/tex]

y = [tex]\frac{1}{3}[/tex] x + [tex]\frac{16}{3}[/tex] ( multiply through by 3 to clear the fractions )

3y = x + 16

Va rog!! Cineva rapid

**Answer:18**

**Step-by-step explanation:**

find the expected value of the given variable with the following probability distribution

The **expected value **of the given variable with the **probability distribution **is 7

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

The probability distribution on the **table of values**

The **expected value **of the **variable** is calculated as

Expected value = ∑x * P(x)

Using the above as a guide, we have the following:

Expected value = 2 * 1/36 + 3 * 1/18 + 4 * 1/12 + 5 * 1/9 + 6 * 5/36 + 7 * 1/6 + 8 * 5/36 + 9 * 1/9 + 10 * 1/12 + 11 * 1/18 + 12 * 1/36

Evaluate

Expected value = 7

Hence, the **expected value **of the variable is 7

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top question only fast pls

The **volume **of the **triangular prism** is V = 18ft³

The **volume **of the prism is equal to the **area **of the triangular face, times the length of the prism, which is 9ft.

Remember that the area of a triangle of base B and height H is:

A = B*H/2

Here we can see that the base is 2ft and the height is 2ft, then the area of the triangular face is:

A = 2ft*2ft/2 = 2ft²

And thus, the volume of the prism is:

V = 2ft²*9ft

V = 18ft³

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Aaron kicked a soccer ball with an initial velocity of 39 feet per second at an angle of 44° with the horizontal. After 0.9 seconds, how far has the ball traveled horizontally? A. 11.4 ft B. 24.4 ft C. 12.3 ft D. 25.2 ft

The ball has traveled approximately 25.24 feet **Horizontally**.The correct answer is D. 25.2 ft.

The horizontal **distance **traveled by the soccer ball after 0.9 seconds, we can use the equation:

horizontal distance = initial **velocity *** time * cos(angle)

Substituting the given values:

initial velocity = 39 ft/s

time = 0.9 s

**angle **= 44°

horizontal distance = 39 ft/s * 0.9 s * cos(44°)

Calculating:

horizontal distance ≈ 39 ft/s * 0.9 s * 0.71934 ≈ 25.24 ft

Therefore, after 0.9 seconds, the ball has traveled approximately 25.24 feet horizontally.

The correct answer is D. 25.2 ft.

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Adam’s prepaid card charges a one-time opening fee and a monthly fee. The table below shows his total fees after x months.

x # of months y total fees ($)

2 27

3

4

5 60

a. How much is the initial opening fee?

b. How much is the monthly maintenance fee?

c. Write an equation to model Adam’s fees over time.

Based on a **system of equaitons**, the initial opening fee (one-time payment) is $5.00, the monthly maintenance fee is $11.00, while an **equation** that models Adam's fees over time in months, x is y = 11x + 5.

A **system of equations** or simultaneous equations are two or more equations solved concurrently or at the same time.

An **equation** is a mathematical statement showing the equality or equivalence of two or more algebraic expressions.

While **algebraic expressions** combine variables with numbers and **mathematical operands**, equations use the equal symbol (=).

Total Fees after x months

x = # of months y = total fees ($)

2 27

3 38 (11 x 3 + 5)

4 49 (11 x 4 + 5)

5 60

Let w = the monthly maintenance fee

Let z = the one-time opening fee

Equations:5w + z = 60 ... Equation 1

2w + z = 27 ... Equation 2

Subtract Equation 2 from Equation 1:

3w = 33

w = 11

b) The monthly maintenance fee is $11.00.

a) The initial (one-time) opening fee is $5.00.

z = 60 - 55

= 5

c) The total fees after x months is y = 11x + 5.

Thus, the one-time opening fee and the monthly maintenance fee can be computed using a **system of equations**.

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A school asks students what type of sports they play. Complete the two-way table for the survey data. Find the answer for the missing letters and show your work as to how you arrived at each answer.

**Answer: b: 58-22=36**

A=37 68-22-9

d=99 37+62

c=29 34-9

**Step-by-step explanation:**

Which expression is equivalent to 4^7/8

4^1/4?

the answer is option A

A student has 40 dimes and nickels. Their total value is $2.95. If

de number of dimes and n= number of nickels, this system of equations

represents the situation:

d+n=40

0.10d+0.05n 2.95

How many of each type of coin are there? Solve the system to answer the

question.

A. 10 dimes and 30 nickels

B. 21 dimes and 19 nickels

C. 19 dimes and 21 nickels

D. 20 dimes and 20 nickels

Answer: C. 19 Dimes and 21 Nickels

19 x .10 = 1.90$

21 x .05 = 1.05$

1.90 + 1.05= 2.95$

1 dime is .10 (10 cents)

1 nickel is .05 (5 cents)

19 x .10 = 1.90$

21 x .05 = 1.05$

1.90 + 1.05= 2.95$

1 dime is .10 (10 cents)

1 nickel is .05 (5 cents)

One shirt at H&M cost $7. what is the cost of 40 shirts

Answer:

$280

Step-by-step explanation:

7•40=$280

Which function has a horizontal asymptote at y = 3?

**Answer: A) **[tex]f(x)=\frac{6x^2-x+4}{2x^2-1}[/tex]

**Step-by-step explanation:**

Line [tex]y=L[/tex] is a horizontal asymptote of the function [tex]y=f(x)[/tex], if either [tex]\lim_{x \to \infty} f(x)=L[/tex] or [tex]\lim_{x \to \infty} f(x)=L[/tex], and [tex]L[/tex] is finite.

calculate the limits:

[tex]\lim_{x \to \infty} (\frac{6x^2-x+4}{2x^2-1})=3[/tex]

[tex]\lim_{x \to -\infty} (\frac{6x^2-x+4}{2x^2-1})=3[/tex]

Thus, the horizontal asymptote is [tex]y=3[/tex]

3. In a data set, the mode, median, and mean are all equal. Which data set below fits this description? A. 26, 39, 39, 39, 52 B. 26, 27, 28, 28, 39 C. 15.0, 15.5, 16.0, 16.0, 21.5 105, 110, 110, 116, 120

A. 39, In Order of Least to Greatest 39 is in Middle, Which is Median. Mean Equals to Add All Numbers and Then Divide By How Many are Left. Mode is the Most Frequent Number.

Can someone answer and provide an explanation for these problems?

The **equation **for **each circle** is given as follows:

**36) **(x - 2)² + (y - 15)² = 4.

**37)** (x + 8)² + (y + 18)² = 25.

**38)** (x - 11)² + (y + 9)² = 49.

**39)** (x - 13)² + (y + 8)² = 36.

The equation of a circle of **center **[tex](x_0, y_0)[/tex] and** radius r** is given by:

[tex](x - x_0)^2 + (y - y_0)^2 = r^2[/tex]

For **item 36**, the center is given as follows:

(-3, 11)

After the **translation**, the center will be given as follows:

(2, 15)

Hence the **equation **is given as follows:

(x - 2)² + (y - 15)² = 4.

For item 37, the **center **is given as follows:

(-3, -14)

After the **translation**, the center will be given as follows:

(-8, -18)

Hence the **equation **is given as follows:

(x + 8)² + (y + 18)² = 25.

For item 38, the **center **is given as follows:

(11, -9).

Hence:

(x - 11)² + (y + 9)² = r².

Point (18, -9) is on the circle, hence the **radius **squared is obtained as follows:

r² = (18 - 11)² + (-9 + 9)²

r² = 49.

Hence the **equation **is:

(x - 11)² + (y + 9)² = 49.

For item 39, the **center **is given as follows:

(13, -8).

Hence the **equation **is:

(x - 13)² + (y + 8)² = r².

Point (7, -8) is on the circumference of the circle, hence the **radius **squared is obtained as follows:

r² = (7 - 13)² + (-8 + 8)²

r² = 36.

Hence the **equation **is given as follows:

(x - 13)² + (y + 8)² = 36.

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can someone please help me on this algebra 13 homework! PLS QUICK!

The **function** y=x+3 has the greatest **y intercept.**

The slope intercept form of a line is y=mx+b, where m is slope and b is the **y intercept.**

The given function is y=x, it has y intercept which is zero

The given function is y=-x, it has y intercept which is zero

**Function** is y=x+3, it has y intercept which is three

Function is y=2x, it has y intercept which is zero

Hence, the **function** y=x+3 has the greatest y intercept.

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what is the vertical distance betweenj (2, 11/3) and (2, -4/3)

The vertical **distance** between the two **points** given are (2, 11/3) and (2, -4/3) is 5 units.

The two points given are (2, 11/3) and (2, -4/3). These points have the same **x-coordinate** of 2, which means they lie on a vertical line. The vertical distance between the two points is simply the difference between their y-coordinates.

So, the **vertical** distance between the two points is:

11/3 - (-4/3) = 15/3 = 5

This means that if we were to draw a **line** **segment** connecting the two points, the length of the segment would be 5 units, and the segment would be parallel to the y-axis.

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PLEASE HELP ASAP!!!!!!

Answer:

A. Using the commutative property

Step-by-step explanation:

Because there is no use of commutative property in the solution process.

**Answer:**

A) Using Commutative property

**Step-by-step explanation:**

In step 1, it used distributive property when the number 5 is distributed inside of the equation in the parenthesis.

In Step 4, dividing both sides by 10 to further simplify the equation

In step 2, you combined like terms and it results to the equation in step 3

What is the length of side CB to one decimal place?

B

A

10

53°

C

▸

The length of side CB to one **decimal **place is 89.3.

To find the length of side CB in the given **triangle**, we can use the sine rule. The sine rule states that in a triangle, the ratio of the length of a side to the sine of its opposite **angle **is constant.

In this case, we have the angle C as 53° and the side opposite to it, side CB, as the unknown. Let's denote the length of side CB as x.

According to the sine rule:

sin(C) / x = sin(A) / AB

We know that angle A is 37° and AB is 120 units. Plugging in the values:

sin(53°) / x = sin(37°) / 120

To find x, we can rearrange the equation:

x = (120 * sin(53°)) / sin(37°)

Calculating this expression gives us:

x ≈ 89.32

Rounding this value to one decimal place, the **length **of side CB is approximately 89.3.

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x=1

x=3

z=x-25y

print(z)

The **output** of the program for the **variable **z is -22 or it returns an **error **if z = x - 25y

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

x = 1

x = 3

z = x - 25y

print(z)

The value of the variable y is not given

So, the program would **return **an **error**

However, if the complete **program** is as follows (removing the **variable** y)

x = 1

x = 3

z = x - 25

print(z)

Using the above as a guide, we have the following:

The **final value **of x is 3

So, we have

z = 3 - 25

Evaluate

z = -22

This means that the **output** of the **program** for z is -22

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What’s the value of x?

**Answer:**

The answer is 8

**Step-by-step explanation:**

/x/ // /8/

x=8

determine what type of model bets fits the given situation: A $500 raise in salary each year

Answer:A linear modelExplanation:

The type of model that best fits the situation of a $500 raise in salary each year is a linear model.

In a linear model, the dependent variable changes a constant amount for constant increments of the independent variable.

In the given case, the dependent variable is the salary and the independent variable is the year.

You may build a table to show that for increments of 1 year the increments of the salary is $500:

Year Salary Change in year Change in salary

2010 A - -

2011 A + 500 2011 - 2010 = 1 A + 500 - 500 = 500

2012 A + 1,000 2012 - 2011 = 1 A + 1,000 - (A + 500) = 500

So, you can see that every year the salary increases the same amount ($500).

In general, a linear model is represented by the general equation y = mx + b, where x is the change of y per unit change of x, and b is the initial value (y-intercept).

In this case, m = $500 and b is the starting salary: y = 500x + b.

A square has an area of 56 units, find the length of the side in simplest form. Has to be an Improper fraction.

The** length** of the side of the square in simplest form is 2sqrt(14).

The** area** of a square is given by the formula [tex]A = s^2[/tex], where A is the area and s is the length of a side.

We are given that the area of the square is 56 units, so we can set up the equation:

[tex]56 = s^2[/tex]

To solve for s, we can take the square root of both sides of the equation:

sqrt(56) = [tex]sqrt(s^2)[/tex]

We can simplify the square root of 56 by factoring it:

sqrt(56) = sqrt(222*7) = 2sqrt(14)

So, we have:

2sqrt(14) = s

This is an improper** fraction** because the numerator is larger than the denominator. Therefore, the length of the **side of the square** in simplest form is 2sqrt(14).

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100 Points! Algebra question. Photo attached. Sketch the angle. Then find its reference angle. Show your calculations. Thank you!

The required **reference angle **of 13π/8 is 3π/8.

The reference angle of an angle in standard position is the positive acute angle formed between the **terminal** **side **of the angle and the x-axis.

Given an angle of 13π/8, we can determine its reference angle as follows:

Angle: 13π/8

Since the angle is in the **fourth quadrant**, we subtract it from 2π (one full revolution) to find the reference angle:

Reference angle: 2π - 13π/8 = 3π/8

Therefore, the reference angle of 13π/8 is 3π/8.

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Divide the sum 200 and 300 by the difference 80and 30.

**Answer:**

10

**Step-by-step explanation:**

300 plus 200 is 500

80 minus 30 is 50

500 divided by 50 is 10

What is the end behavior of:

(2x ^ 2 - 5) / (x ^ 2 - 1)

A) x -> ∞ : f(x) -> 0

B) x -> ∞ : f(x) -> 2

C) f(x) -> - ∞ : x -> ∞

D) x -> ∞ : f(x) -> ∞

The given function does not have an **end behavior** because it is not a **polynomial function**.

The **end behavior** of a function refers to how the function behaves or approaches as the input values (x-values) of the function become extremely large (approaching positive infinity) or extremely small (approaching negative infinity).The long term behavior of the function when x moves towards the ends of the coordinate plane can be predicted.

In a **polynomial function**, the leading coefficient and degree of the function often determine the polynomial function.

The given function is;

f(x) = 2x² - 5 / x² - 1

The** end behavior** of this function does not exist because this is not a polynomial.

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A family drove 592 miles during their trip this summer. In the winter they drove 376 miles during their trip . How many more miles did the family drive over the summer than over the winter . Explain !

**Answer: 216**

**Step-by-step explanation:**

**592-376**

**592-300= 292**

**292-70= 222**

**222-6= 216**

Select the correct answer.

Which coefficient matrix represents a system of linear equations that has a unique solution?

The **coefficient **matrix A represents a system of **linear **equations that has a **unique **solution.

In a system of linear equations, the **unique solution **exists when the **coefficient **matrix has **full rank **and the determinant of the matrix is non-zero.

The other **coefficient matrices **listed do not have these properties.

1. [[6, 0, - 2]

- 2, 0, 6

1, - 2, 0]

has a **determinant **of **zero**, indicating that the system of equations is dependent and does **not **have a **unique **solution.

Similarly, the matrices

[5, 10, 5

4, 1, 4

- 1, - 2, - 1]

and, [2, 0, - 2

- 7, 1, 5

4, - 2, 0]

also do **not satisfy **the conditions for a unique solution.

Therefore, the **coefficient **matrix A represents a system of **linear **equations that has a **unique **solution.

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A researcher wishes to conduct a study of the color preferences of new car buyers. Suppose that 30% 30 % of this population prefers the color green. If 20 20 buyers are randomly selected, what is the probability that exactly 1 1 buyer would prefer green? Round your answer to four decimal places.

The **probability **that exactly 1 buyer would prefer **green **P ( A ) = 0.1854

Given data ,

A researcher wishes to conduct a study of the color preferences of new car buyers

And , 30 % of this population prefers the color **green**

where 20 buyers are randomly selected

Now , **binomial distribution **problem with n = 20, p = 0.30 and we want to find the probability of exactly 1 buyer preferring green.

The formula for the **probability **mass function of a **binomial distribution **is:

P(X = k) = (n choose k) * p^k * (1-p)^(n-k)

where (n choose k) = n! / (k! * (n-k)!)

Plugging in the values, we get:

P(X = 1) = (20 choose 1) * 0.30¹ * 0.70¹⁹

= 20 * 0.30 * 0.70¹⁹

= 0.1854 (rounded to four decimal places)

Hence , the **probability **that exactly 1 buyer would prefer **green **is 0.1854

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Suppose that 15% of all American use CNN as their primary source of news. A random sample of 200 Americans is selected. What is the probability that is your sample of 200 Americans that proportion that us CNN as their primary news source is at least 0.21?

The **probability** that in a sample of 200 Americans, the proportion that uses CNN as their primary news source is at least 0.21 is 49.6%.

The **probability** is determined using the normal approximation to the **binomial distribution.**

Given that the sample size is large (n = 200) and the probability of success (p = 0.15) is not too close to 0 or 1, the mean (μ) and standard deviation (σ) of the binomial distribution, will be:

μ = n * p

μ = 200 * 0.15

μ = 30

σ = √(n * p * (1 - p))

σ = √(200 * 0.15 * (1 - 0.15))

σ ≈ 4.29

Then, the z-score corresponding to the proportion of 0.21 is:

z = (x - μ) / σ

z = (0.21 - 0.15) / 4.29

z ≈ 0.014

Using a calculator, the probability of a** z-score** of 0.014 is approximately 0.504.

Hence, the probability of obtaining a proportion at least 0.21, is:

Probability = 1 - 0.504

Probability ≈ 0.496

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Erik has been collecting comic books for the past few years. The number of total comic books in his collection each year is as follows. • 30 comic books the first year • 60 comic books the second year • 90 comic books the third year • 120 comic books the fourth year Write a function that represents the number of comic book as a function of the number of years, t.

The **function** that represents the number of comic book as a **function **of the number of years, t is expressed as y = 30x or f(t) = 30t.

We can use the given data to create a **linear equation **of the form y = mx + b, where y represents the number of comic books and x represents the number of years.

To find the **equation**, we can use any two pairs of (x, y) values. Let's use the first and fourth years:

First year: (1, 30)

Fourth year: (4, 120)

The **slope**, m, of the line can be calculated using the formula:

m = change in y / change in x = (120 - 30) / (4 - 1)

m = 90 / 3

m = 30

The **y-intercept**, b, can be found by substituting one of the (x, y) values and the **slope **into the **linear equation, **y = mx + b:

30 = 30(1) + b

b = 0

Therefore, the **equation **that represents the number of comic books, y, as a **function **of the number of years, x, is:

y = 30x

or

f(t) = 30t [where t represents the number of years.]

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which point lies in the solution set?

A. (4, –0.5)

B. (3, –2.5)

C. (–2.5, 4)

D. (–4.5, –3)

The **point **that lies in the **solution set **of (x - 2)²/25 + (y + 3)²/4 < 1 is B. (3, –2.5)

From the question, we have the following **inequality expression **that can be used in our computation:

(x - 2)²/25 + (y + 3)²/4 < 1

Also, we have

A. (4, –0.5)

B. (3, –2.5)

C. (–2.5, 4)

D. (–4.5, –3)

Next, we test the options as follows

A. (4, –0.5)

(4 - 2)²/25 + (-0.5 + 3)²/4 < 1

1.7225 < 1 -- **false**

B. (3, –2.5)

(3 - 2)²/25 + (-2.5 + 3)²/4 < 1

0.1025 < 1 -- **true**

Hence, the **point **that lies in the **solution set **is B. (3, –2.5)

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We are using the formula I=PRT (Interest=Principal x Rate x Time) or P=%W (Part=Percent x Whole)Sonya purchases the electronics on a payment plan for 30 months with a 9.75% annual interest rate.
HELP I NEED HELP ASAP
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