Mathematics College

## Answers

**Answer 1**

**Problem**

0.8 divided 40

**Solution**

We can do the following:

[tex]\frac{0.8}{40}=\frac{0.8\cdot10}{40\cdot10}=\frac{8}{400}[/tex]

and if we simplify we got:

[tex]\frac{8}{400}=\frac{4}{200}=\frac{2}{100}=\frac{1}{50}=0.02[/tex]

## Related Questions

Write the standard form of the equation of the circle described below￼. (6,-7) r=9

### Answers

**Solution**

**Step 1**

** **write out the expression for the equation of a circle

[tex](x-h)^2+(y-k)^2=r^2[/tex]

Where the centers are (h,k)

h = 6

k = -7

r = 9

**Step 2**

Write out the required equation of the circle using the parameters

[tex]\begin{gathered} \text{The required equation thus is} \\ (x-6)^2+(y-(-7))^2=9^2 \\ (x-6)^2+(y+7)^2=81_{} \end{gathered}[/tex]

A carnival ride is in the shape of a wheel with a radius of 25 feet. The wheel has 20 cars attached to the center of the wheel. Use 3.14 for pi and round answers to the nearest hundredth, if applicable.a.) What is the measure of each central angle between any two cars? (4 points)b.) What is the arc length of each sector between any two cars? (4 points)c.) What is the area of each sector between any two cars?

### Answers

The carnival ride is in shape of wheel with 25ft radius.

The wheel has 20 cars attached to the center of the wheel. Since the cars are evenly distributed, we can thus find the

the measure of the angle between each car by dividing 360 degrees by 20.

#A:

The measure of each central angle between any two cars is:

[tex]\frac{360}{20}=18^0[/tex]

#B:

Hence, we can find the length of the arch between any two cars is given by the length of arc formula given below:

[tex]\begin{gathered} \frac{\theta}{360}\times2\pi r \\ \text{where,} \\ r=\text{radius} \\ \theta=\text{measure of each central angle betw}een\text{ two cars} \end{gathered}[/tex]

Let us calculate this length below:

[tex]\begin{gathered} \theta=18^0 \\ \frac{18}{360}\times2\pi\times25 \\ =2.5\pi=7.85\text{ (to the nearest hundredth)} \end{gathered}[/tex]

#C:

We are asked to find the area of each sector between two cars.

The area of a sector of a circle is:

[tex]\frac{\theta}{360}\times\pi\times r^2[/tex]

Since we have all the parameters, let us calculate this area:

[tex]\begin{gathered} Area=\frac{18}{360}\times\pi\times25^2 \\ \\ Area=98.13\text{ (to nearest hundredth)} \end{gathered}[/tex]

**Therefore, the final answers are:**

**#A: angle = 18 degrees**

**#B length = 7.85 feet**

**#C Area = 98.13 squared feet**

1.) Your 3 year investment of $20,000 received 5.2% interested compounded semi annually. What is your total return? ASW

### Answers

Let's begin by listing out the information given to us:

Principal (p) = $20,000

Interest rate (r) = 5.2% = 0.052

Number of compounding (n) = 2 (semi annually)

Time (t) = 3 years

The total return is calculated as shown below:

A = p(1 + r/n)^nt

A = 20000(1 + 0.052/2)^2*3 = 20000(1 + 0.026)^6

A = 20000(1.1665) = 23,330

A = $23,330

Find the equation for a polynomial f(x) that satisfies the following:Degree 5- Root of multiplicity 1 at 2 = 1- Root of multiplicity 2 at x = 2- Root of multiplicity 2 at x = -2y-intercept of (0,–32)

### Answers

The equation for this polynomial is:

[tex]\begin{gathered} 2(x-1)(x-2)^2(x+2)^2 \\ 2x^5-2x^4-16x^3+16x^2+32x-32 \end{gathered}[/tex]

So that's the equation we're asking for.

Both could be the answers. However, this is the final one:

[tex]2x^5-2x^4-16x^3+16x^2+32x-32[/tex]

What is the slope of the points (3,64) and (9,79).

m=

m =

= 15

6

m =

Un Hồ

2-#1

m=2.5

6

15

### Answers

**Answer:**

[tex]\boxed{\bf Slope(m)=2.5}[/tex]

**Step-by-step explanation:**

We can use the slope formula to find the slope of a line given the coordinates of two points on the line:- (3,64) and (9,79).

The coordinates of the first point represent x_1 and y_1. The coordinates of the second points are x_2, y_2.

[tex]\boxed{\bf \mathrm{Slope}=\cfrac{y_2-y_1}{x_2-x_1}}[/tex]

[tex]\sf \left(x_1,\:y_1\right)=\left(3,\:64\right)[/tex]

[tex]\sf \:\left(x_2,\:y_2\right)=\left(9,\:79\right)[/tex]

[tex]\sf m=\cfrac{79-64}{9-3}[/tex]

[tex]\sf m=\cfrac{5}{2}[/tex]

[tex]\sf m=2.5[/tex]

Therefore, the slope of (3,64) and (9,79) is **D) 2.5!!**

___________________

Hope this helps!

Have a great day!

**Answer:**

m = (y2 - y1)/(x2 - x1) m = 15/6 m = 2.5

**Step-by-step explanation:**

Formula we use,

→ m = (y2 - y1)/(x2 - x1)

Then the required slope is,

→ m = (y2 - y1)/(x2 - x1)

→ m = (79 - 64)/(9 - 3)

→ m = 15/6

→ [ m = 2.5 ]

Hence, the slope is 2.5.

Hey I need help on this math problem ignore the lines across the answer choices it’s a glitch I can’t change it and the lines don’t mean that the answer choice is wrong

### Answers

**Solution:**

**Given:**

Two box plots for city A and city B.

**A box plot with its representations is shown:**

From the box plot given:

**For City A :**

[tex]\begin{gathered} City\text{ A:} \\ Q_3=78 \\ Q_1=76 \\ Interquartile\text{ range \lparen IQR\rparen}=Q_3-Q_1 \\ IQR=78-76 \\ IQR=2 \end{gathered}[/tex]

**For City B :**

[tex]\begin{gathered} City\text{ B:} \\ Q_3=78 \\ Q_1=68 \\ Interquartile\text{ range \lparen IQR\rparen}=Q_3-Q_1 \\ IQR=78-68 \\ IQR=10 \end{gathered}[/tex]

From the IQR calculated, the correct answer is:

**The interquartile range for city B is greater.**

slove equations with variables on both sides-4k - 10 = -5k

### Answers

We will investigate how to solve an equation consisting of one variable

We have the following equation at hand:

[tex]-4k\text{ -10 = -5k}[/tex]

The basic rule applied in solving equation like above is mathematical operations. We apply basic operations like:

[tex]\text{adding, subtracting, multiplying, division}[/tex]

on both sides of the equation accompained by a variable or a number in an attempt to isolate the variable ( k ).

To isolate the variable ( k ) we need all the terms involving the variable ( k ) on one side of the equation.

We will add ( 4k ) on both sides of the equation as follows:

[tex]\begin{gathered} -4k\text{ -10 + 4k= -5k + 4k} \\ (\text{ 4k - 4k ) - 10 = -k} \\ -10\text{ = -k} \end{gathered}[/tex]

Now to remove the negative sign accompained by ( k ) on the right hand side of the equation. We wil multiply both sides with ( -1 ) as follows:

[tex]\begin{gathered} -1\cdot(-10)\text{ = -1}\cdot(-k) \\ 10\text{ = k} \end{gathered}[/tex]

Hence, the value of ( k ) is:

[tex]10[/tex]

IncorrectYour answer is incorrectA vehicle factory manufactures cars. The unit cost C (the cost in dollars to make each car) depends on the number of cars made. If x cars are made, then theunit cost is given by the function C()0.3x-66x + 13,267. What is the minimum unit cost?Do not round your answer.Unit cost: S1dxCheckSave For LaterSubmit AssignmentPrencyAceeshhy1125 PMWednesday1620212021 MMcGraw-H Education, All Riathts Resered.Torms of Use9Type here to search

### Answers

Please check that the expression for the cost you typed reflects what you read in the problem.

Isn't there a "square" in one of the "x" values of the cost equation?

Great. I see now the actual equation for cost to be:

Cost = 0.3 x^2 - 66 x + 13267.

The minimum unit cost will be given by the minimum of this quadratic function (a parabola) which has a minimum at the parabola's vertex. Notice this is a parabola with branches pointing UP because the coefficient of the term in x^2 is POSITIVE.

Recall then the equation for the x position of the vertex of a pparabola with equation of the form:

y = a x^2 + b x + c

the x-position of the vertex is: x = - b / (2a)

which in our case gives:

x of the vertex = - (- 66) / (2 * 0.3) = 110

Then, since the x values represent the number of cars that are made , we now that that minimum occurs when the number of cars produced is 110.

We replace this value in the cost equation and get:

Cost = 0.3 (110)^2 - 66 (110) + 13267 = 9637

Then, the unit cost for making the 110 cars is **$9637**, which is in fact the minimum value we were looking for.

Find the simple interest on a $4,719 principal deposited for

six years at a rate of 6.11%.

### Answers

**Answer:**

The answer is 1,729.99

**Step-by-step explanation:**

The formula for calculating Simple interest is

Simple interest (A) = P×R×T

where,

P = Principal

R = Rate

T = Time

So after adding the values to the formula

we get

=4719×6.11×6/100

=1,72,998.54/100

=1,729.9854

So The simple interest is 1,729.99

For more Information search Simple Interest in Brainly.com

the graph of the functiony=f(x)+34can be obtained from the graph ofy=f(x)by which following action?shifting the graph f(x) to the left 34 unitsshifting the graph f(x) to the right 34 unitsshifting the graph f(x) downwards 34 units shifting the graph of f(x) upwards 34 units

### Answers

Given data:

The given expression is f(x)+34.

The given graph can be obtained by shifting f(x) in the positive direction of y by 34 units.

F(x)=f(x)+34

Thus, the last option is correct.

If you were to solve the following system by substitution, what would be the best variable to solve for and from what equation? 3x + 6v=9 2x – 10v=13

### Answers

**The best variable to solve is x=3-2v, after dividing the first equation by 3.**

**x=4, and v=-1/2**

**1**) Solving that system by Substitution

**2**) Making then

x=3-2v

2x-10v=13

**3**) Plugging into the 2nd equation

2(3-2v)-10v=13

6-4v -10v=13

6-14v=13

-14v=13-6

-14v=7

**v=-1/2**

Plugging into the first equation

x=3-2v

x=3-2(-1/2)

x=3+1

**x=4**

Find the area of each figure. 4. & 3 3 S 2 2 8 a square units

### Answers

area is

[tex]A=s^2=1^2=1[/tex]

and

[tex]\text{Atotal}=1\times11=11[/tex]

answer: 11 square units

34. A school admissions office accepts 2 out of every 7 applicants. Given that the school accepted 630 students, how many applicants were NOT accepted? F. 140 180 490 J. 1,260 K. 1,575

### Answers

We were told that the school admissions office accepts 2 out of every 7 applicants. Thus, the probability that the school accepts an applicant is 2/7

There are only two outcomes. It is either the school accepts an applicant or it doesn't. If the school accepts 630 students, It means that 2/7 of the total number of applicants were accepted

Assuming the totla number of applicants is x, it means that

2/7 * x = 630

2x = 630 * 7 = 4410

x = 4410/2

x = 2205

The total number of applicants is 2205

The number of applicants that were not accepted is

2205 - 630 = 1575

**1575 applicants were not accepted**

what are the first five terms of the recursive sequence aₙ = 3aₙ₋₁ + 3 where a₁ = 9

### Answers

The expression for the recursive sequence is :

[tex]a_n=3a_{n-1}+3[/tex]

where a1 = 9

**First term:**

Since first term is already given:

[tex]a_1=9[/tex]

**Second Term : **

Substitute n =2 in the recursive expression and simlify

[tex]\begin{gathered} a_n=3a_{n-1}+3 \\ a_2=3(a_{2-1})+3 \\ a_2=3(a_1)+3 \\ a_2=3(9)+3 \\ a_2=27+3 \\ a_2=30 \end{gathered}[/tex]

** ****Second Term : 30**

**Third Term:**

Substitute n = 3 in the given recursive expression:

[tex]\begin{gathered} a_n=3a_{n-1}+3 \\ a_3=3(a_{3-1})+3 \\ a_3=3(a_2)+3 \\ a_3=3(30)+3 \\ a_3=90+3 \\ a_3=93 \end{gathered}[/tex]

**Third Term = 93**

**Fourth Term:**

Substitute n = 4 in the given recursive expression:

[tex]\begin{gathered} a_n=3a_{n-1}+3 \\ a_2=3(a_{2-1})+3 \\ a_2=3(a_1)+3 \\ a_2=3(9)+3 \\ a_2=27+3 \\ a_2=30 \end{gathered}[/tex]

Linear function gis shown in the graph. Write the slope-Intercept form of the equation representing this function.

### Answers

To find the equation of the line in slope intercept form the first step is to find the slope of the given line:

[tex]m=\frac{y2-y1}{x2-x1}[/tex]

In this formula, m is the slope of the function, y2 and y1 are the y coordinates of 2 points on the line, and x2 and x1 are the x coordinates of the same 2 points, for example, they can be (-1,3) and (0,1):

[tex]m=\frac{1-3}{0-(-1)}=-\frac{2}{1}=-2[/tex]

The slope of the line is -2.

Now, we can use the y intercept of the graph of g, which is 1.

The slope intercept form of the equation follows the following general structure:

[tex]y=mx+b[/tex]

Where m is the slope of the line and b is the y intercept. Use the known values to replace them on the equation. The intercept form of the equation is:

[tex]y=-2x+1[/tex]

Find the area of this irregular shape.

[Round off to the nearest whole number.]

sq. units

### Answers

**Answer:**

**Step-by-step explanation:**

number of complete squares=14

number of half or more than half squares=4

whole squares=4/2=2

area≈14+2=16 sq. units

Evaluate: 4+8/2 x (6 - 3)163325

### Answers

We have to evaluate the expression:

[tex]\begin{gathered} 4+\frac{8\cdot(6-3)}{2}_{} \\ 4+\frac{8\cdot3}{2} \\ 4+\frac{24}{2} \\ 4+12 \\ 16 \end{gathered}[/tex]

To solve this, we have to solve the operations in this order:

- First, the operations within the parenthesis.

- Second, the multiplications and quotients.

- Lastly, the additions and substractions.

**Answer: 16**

1) Compare the following numbers. Choose the correct inequality symbol 10 pointsto go in the circle. *Remember the inequality symbol “eats” the biggernumber!√8 + 3 ? 8 + √3

### Answers

√8 + 3 ? 8 + √3

√8 is between √4 (= 2) and √9 (= 3), then

√8 + 3 < 3 + 3 = 6

Therefore,

√8 + 3 **<** 8 + √3

b -6(46 - 2) = 150A) 4-6 B) -5C) 9 D) (3)

### Answers

To solve this equation, we need to follow the next steps:

1. Apply the distributive property:

[tex]b-6\cdot4b+6\cdot2=150\Rightarrow b-24b+12=150[/tex]

2. Add the like terms, and subtract 12 to both sides of the equation:

[tex]-23b+12=150\Rightarrow-23b=150-12[/tex]

3. Divide both sides of the equation by -23 (to isolate b):

[tex]\frac{-23}{-23}b=\frac{150-12}{-23}\Rightarrow b=\frac{138}{-23}\Rightarrow b=-6[/tex]

**Then, the answer to this equation is {-6} (option A).**

consider parallelogram JKLM below.use the information given in the figure to find m

### Answers

Here, we have a parallelogram JKLM.

Given:

JK = 3x

LM = 3

m∠J = 106°

m∠KMJ = 34°

A parallelogram is a quadilateral that has equal opposite angles and the opposite sides are also equal.

Thus, we have:

• m∠L = m∠J = 106°

**m∠L = 106°**

• x:

Here, JK is opposite side LM. SInce they are opposite sides, they have equal length.

Thus, we have:

JK = LM

3x = 3

Divide both sides by 3:

[tex]\begin{gathered} \frac{3x}{3}=\frac{3}{3} \\ \\ x=1 \end{gathered}[/tex]

**x = 1**

• m∠LKM:

Apply the alternate interior angles theorem. Alternate interior angles are congruent.

∠LKM and ∠KMJ are alternate interior angles. This means they are congruent.

Thus, we have:

m∠LKM = m∠KMJ = 34**°**

**m∠LKM = 34°**

**ANSWER:**

• m∠L = 106°

• x = 1

• m∠LKM = 34°

A card is drawn from a well-shuffled deck of 52 cards. What is the probability of drawing an ace or a spade?A. 4/13B. 16C. 1/4D. 17

### Answers

The number of ace in a deck of 52 cards is =4

The number of spade in a deck of 52 cards is = 13.

The number of ace of spade in a deck of 52 cards is =1

The event is non-exclusive hence the probablity can be determined as,

[tex]\begin{gathered} P(A\cup S)=P(A)+P(S)-P(A\cap S) \\ =\frac{4}{52}+\frac{13}{52}-\frac{1}{52} \\ =\frac{16}{52} \\ =\frac{4}{13} \end{gathered}[/tex]

**Thus, option (A) is correct.**

J(7, -2), K(-4, 9), L(-3,-1)

### Answers

what are we trying to find?

A new model of shirt at the clothing store comes in 4 colors: black, white, red, and blue

### Answers

The data provided of the 16 sold shirts can be used to count the frequency of each color.

The results are shown below:

White = 5

Black = 2

Blue = 4

Red = 5

We can check the total is 5 + 2 + 4 + 5 = 16

Now we are ready to draw the bar graph, where each color must have a height that equals its frequency.

Which of the following numbers is irrational? (A)-1.325 (B)√8 (C)2 (D)4

### Answers

**Answer:**

(B)√8

**Explanation:**

Irrational numbers are numbers which when converted to decimal can be written indefinitely without repeating.

Irrational Numbers are numbers that cannot be written as a terminating or repeating decimal.

Examples of Irrational Numbers are:

[tex]\sqrt{2},\text{ }\pi,\text{ }\frac{22}{7},\text{ }\sqrt{5}\text{, etc.}[/tex]

**From the given options, the number which is irrational is √8.**

At the grocery store, halibut costs $20 per pound and salmon costs $17 per pound. Which of the following situations can be modeled by the equation below? 20(x-5) = 17xA) The cost of x pounds of salmon is $5 less than the cost of x pounds of halibutt B) The cost of x pounds of halibut is $5 less than the cost of x pounds of salmon C) The cost of pounds of salmon is the same as the cost of x-5 pounds of halibutD) The cost of x pounds of halibut is the same as the cost of x-5 pounds of salmon.

### Answers

**Answer: C.**

**The cost of x pounds of salmon is the same as the cost of x-5 pounds of halibut**

[tex]\begin{gathered} \text{halibut }\rightarrow\text{ \$20 and (x-5) pounds} \\ \text{salmon }\rightarrow\text{ \$17 and x pounds} \end{gathered}[/tex]

**Explanation:**

Given the model;

[tex]20(x-5)=17x[/tex]

where x is the number of pounds.

The cost per pound of Halibut is;

[tex]\text{ \$20}[/tex]

So, the corresponding number of pounds of Halibut on the model is;

[tex]x-5[/tex]

Also, the cost per pound of Salman is;

[tex]\text{ \$17}[/tex]

the corresponding number of pounds of Salmon on the model is;

[tex]x[/tex]

Since they are equal to each other, then **the cost of x pounds of salmon is the same as the cost of x-5 pounds of halibut**

[tex]\begin{gathered} \text{hailbut }\rightarrow\text{ \$20 and (x-5) pounds} \\ \text{salmon }\rightarrow\text{ \$17 and x pounds} \end{gathered}[/tex]

What is the first step to solving the following equation?5x – 11 = 42

### Answers

**Answer:**

add 11 on both sides

**Step-by-step explanation:**

to solve this, you want x alone on one side. To achieve this, you first add 11 on both sides, so you only have the 5x alone.

Second step then is something to get only one x on the left side ;-)

(divide both sides by 5)

**Answer:**

the first step is to get the x term by itself on one side

For the data shown, answer the questions. Round to 2 decimal places. 5.2 18.8 5.7 5 14.9 4.4 Find the mean : Find the median : Find the standard deviation :

### Answers

Median:

1. Order the data from less to greater:

4.4

5

5.2

5.7

14.9

18.8

2. As it is a even number of data you take the average of the two data in the middle to find the median:

[tex]\frac{5.2+5.7}{2}=5.45[/tex]The median is 5.45

Standard deviation formula (for a sample):

[tex]s=\sqrt{\frac{\Sigma(x_i-\bar{x})\placeholder{⬚}^2}{n-1}}[/tex]

To find the standard deviation of the given data:

1. Find the difference between each data and the mean:

[tex]\begin{gathered} (x_i-\bar{x}) \\ \\ 5.2-9=-3.8 \\ 18.8-9=9.8 \\ 5.7-9=-3.3 \\ 5-9=-4 \\ 14.9-9=5.9 \\ 4.4-9=-4.6 \end{gathered}[/tex]

2. Find the square of each difference:

[tex]\begin{gathered} (x_i-\bar{x})\placeholder{⬚}^2 \\ \\ (-3.8)\placeholder{⬚}^2=14.44 \\ (9.8)\placeholder{⬚}^2=96.04 \\ (-3.3)\placeholder{⬚}^2=10.89 \\ (-4)\placeholder{⬚}^2=16 \\ (5.9)\placeholder{⬚}^2=34.81 \\ (-4.6)\placeholder{⬚}^2=21.16 \end{gathered}[/tex]

3. Find the sum of the squares:

[tex]\begin{gathered} \Sigma(x_i-\bar{x})\placeholder{⬚}^2 \\ \\ 14.44+96.04+10.89+16+34.81+21.16=193.34 \end{gathered}[/tex]

4. Use the formula of the standard deviation for n=6:

[tex]s=\sqrt{\frac{193.34}{6-1}}=\sqrt{\frac{193.34}{5}}=\sqrt{38.668}\approx6.22[/tex]Then, the standard deviation is 6.22

Given the surface area of a sphere is 324ππ sq km, what is the radius of the sphere?

### Answers

The surface area S of sphere is given by

[tex]S=4\pi r^2[/tex]

In our case

[tex]S=324\pi[/tex]

Then, we have

[tex]324\pi=4\pi r^2[/tex]

By moving 4Pi to the left hand side, we have

[tex]\frac{324\pi}{4\pi}=r^2[/tex]

We can cancel Pi out in numerator and denominator, then ,we get

[tex]\begin{gathered} \frac{324}{4}=r^2 \\ 81=r^2 \\ \text{therefore} \\ r=\sqrt[]{81} \end{gathered}[/tex]

**and the answer is r= 9 kilometers, that is, the radius is 9 km**

Find the equation of the line through (2,-4) and parallel to the line 5x-2y-4=0. Write your answer in general form.

### Answers

We can find the equation of a line given one point and its slope.

Remember that two parallel lines have the same slope; therefore, the slope of 5x-2y-4=0 is equal to the slope of the line we are trying to find.

[tex]\begin{gathered} 5x-2y-4=0 \\ \Rightarrow2y=5x-4 \\ \Rightarrow y=\frac{5x}{2}-\frac{4}{2}=\frac{5x}{2}-2 \\ \Rightarrow y=\frac{5x}{2}-2 \\ \Rightarrow m=\frac{5}{2} \end{gathered}[/tex]

Then, we have got everything we need, the slope is equal to 5/2 and a point in the line is (2,-4)

The equation is:

[tex]\begin{gathered} y-(-4)=\frac{5}{2}(x-2) \\ \Rightarrow y+4=\frac{5}{2}(x-2) \\ \Rightarrow y+4=\frac{5x}{2}-5 \\ \Rightarrow y=\frac{5x}{2}-9 \\ \Rightarrow y+9=\frac{5}{2}x \\ \Rightarrow2y+18=5x \\ \Rightarrow5x-2y-18=0 \end{gathered}[/tex]

**The answer is 5x-2y-18=0**

PLS HELP 99 POINTS! GEOMETRY & ALGEBRA QUESTION

find m

a-52

b-142

c-24

d-50

e-64

### Answers

hey!! So let’s start off by knowing that we have to sue the exterior angel theorem- which states that the two remote angles of a triangle (the ones that are NOT next to the exterior angle) will add up to equal the exterior angles measure.

Since we know that a right angle (Q) is 90 degrees we can use it to add to (x+2) to get the exterior angles measure.

So our equation would be X+2+90= 3x-8

Then : X+92=3x-8

X+100 =3x

100= 2x

50 = x

BUT THATS NOT OUR ANSWER!

Now we must substitute X into the exterior angles equation!

So: 3(50) -8

150-8

142

So your exterior angle (PRS) would be B.) 142 degrees

**Answer:**

b

**Step-by-step explanation:**

∠ QRP and ∠ PRS are a linear pair and sum to 180° , that is

∠ QRP + 3x - 8 = 180 ( subtract 3x - 8 from both sides )

∠ QRP = 180 - (3x - 8) = 180 - 3x + 8 = 188 - 3x

the sum of the 3 angles in Δ PQR = 180° , that is

188 - 3x + x + 2 + 90 = 180

- 2x + 280 = 180 ( subtract 280 from both sides )

- 2x = - 100 ( divide both sides by - 2 )

x = 50

Then

∠ PRS = 3x - 8 = 3(50) - 8 = 150 - 8 = 142°