Mathematics College

## Answers

**Answer 1**

The** maximum value **of the **linear equation** is obtained as 52.

What is termed as the maximum value of function?The maximum value of such a function is the point on a graph where the **function **achieved its maximum point, or vertex.There are several ways to find the maximum value of the a quadratic equation.The first method is** **graphing**.** Visually, you can determine the highest value by graphing the equation and locating the maximum point of the graph. This is especially simple if you have a graphing calculator. There are three ways to calculate the maximum value of the a quadratic equation. Each of them can be employed to ascertain the maximum in their own specific context.

For the given question;

The** linear equation** is defined as;

C = x + 4y

The constraints are-

x ≥ 0

x≤ 12

y ≤ 10

2x + 3y ≥ 24

From the **constraints**, the maximum value for x and y are taken as;

x = 12 and y = 10.

Put the the equation, to find the maximum value.

C = x + 4y

C = 12 + 4×10

C = 52

Thus, the** maximum value **of the function is obtained as 52.

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## Related Questions

Choose the best estimate for the quotient.

27.2/178.6

A) 5

B) 6

C) 50

D) 60

### Answers

**Answer:**

B

**Step-by-step :**

The quotient is 6.5 so the estimate is closest to 6.

The answer is b that’s your answer 6

If Mary fails her classes then she cannot graduate

### Answers

True…I don’t know what the question is here???

What will be the length of the railing from point A to point B? Show or explain how you got your answer.

### Answers

To know the length of the railing from point A to point B you can use Pythagoras Theorem.

You draw a right triangle:

You use the given information to know the measure of the legs in the triangle:

You can see that the value of x is the height of 5 steps: 5(7.5 in).

Then:

[tex]x=5(7.5)=37.5in[/tex][tex]x=y=37.5in[/tex][tex]Z=2y=2(37.5in)=75in[/tex]

The B is equal to the lenght of 10 steps: 10(9.5in):

Then:

[tex]B=10(9.5in)=95in[/tex]

You have the next triangle:

You use the Pythagoras Theorem to find the h:

[tex]h=\sqrt[]{Z^2+B^2}[/tex][tex]h=\sqrt[]{75^2+95^2}[/tex][tex]h=\sqrt[]{14650}[/tex][tex]h=5\sqrt[]{586}\approx121.03in[/tex]The length of the railing from point A to point B is 121.03in

Use the limit definition of the derivative to find the instantaneous rate of change of

### Answers

SOLUTION:

Step 1:

In this question, we are given the following:

Use the limit definition of the derivative to find the instantaneous rate of change of

Step 2:

**The details of the solution are as follows:**

An alternative way to find the use the limit definition of the derivative to find the instantaneous rate of change of:

[tex]f(x)\text{ =}\sqrt[]{4x+8\text{ }}\text{ at x = 4}[/tex]

Let us take the derivative of the function and we have that:

[tex]\begin{gathered} f(x)\text{ = }\sqrt[]{4x+8}=(4x+8)^{\frac{1}{2}} \\ \end{gathered}[/tex][tex]\begin{gathered} f^I(x)\text{ = }\frac{1}{2}(4x+8)^{-\frac{1}{2}}(4) \\ f^I(x)=2(4x+8)^{-\frac{1}{2}},\text{ when x = 4, we have that:} \\ f^I(4)=2(4(4)+8)^{-\frac{1}{2}} \end{gathered}[/tex][tex]\begin{gathered} f^I(4)=2(16+8)^{-\frac{1}{2}} \\ f^I(4)\text{ = 2 x }\frac{1}{\sqrt[]{24}} \end{gathered}[/tex][tex]f^I(4)\text{ =}\frac{2}{\sqrt[]{24}}[/tex][tex]f^I(4)=\frac{2}{\sqrt[]{24}}=\frac{2}{\sqrt[]{4}X\sqrt[]{6}}=\frac{2}{2X\sqrt[]{6}}=\frac{1}{\sqrt[]{6}}[/tex][tex]f^I(4)\text{ =}\frac{1}{\sqrt[]{6}}[/tex]

!!!!!!!!!!!!!!!!!!!!!!!!!!!!helpppp!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!

### Answers

The answer is:

D. 4x + 3

**Answer:**

4x + 3

**Step-by-step explanation:**

Three more means you're adding three to the number. So, you have + 3 right now. Four times the number of shells Talia collects is 4x with x representing Talia's shells. We don't know how many she has so it's represented by x. Now, put everything we have together. 4x + 3.

Hope this helps! :)

Which of the following is a parent function?O A. f(x) = -3x° +1ОВ.B. f(x) = 2*O c.C. f(x)=23*O D. f(x)=3* - 5

### Answers

**ANSWER:**

**B.**

[tex]f(x)=2^x[/tex]

**STEP-BY-STEP EXPLANATION:**

A parent function is the simplest formula in which no transformations have been made. Therefore, the function that would be the parent one of the answer options is:

[tex]f(x)=2^x[/tex]

A total of 240 people drove to a meeting. Of those peoplewho attended the meeting, 80% drove there. How manypeople attended the meeting?

### Answers

The total number of people that drove to the meeting is 240

80% drove to the meeting

Let the total number of people who attended the meeting be x

Using the percentage and whole relationship

Part = percentage x whole

whole = x

part = 240

percentage = 80%

240 = 80/100 * x

240 = 0.8x

Divide both sides by 0.8

240/0.8 = 0.8x/0.8

x = 300

**The total number of people that attended the meeting is 300**

Can someone help me

Which graph represents the solution set of the system of inequalities?

{y<−3x−2y≤x−2

Responses

A system of 2 linear inequalities graphed on a coordinate plane. The horizontal x axis ranges from negative 5 to 5 in increments of 1. The vertical y axis ranges from negative 5 to 5 in increments of 1. A dashed line passes through begin ordered pair negative 1comma 1 end ordered pair and begin ordered pair 0 comma negative 2 end ordered pair. A solid line passing through begin ordered pair 2 comma 0 end ordered pair and begin ordered pair 0 comma negative 2 end ordered pair. The region below the dashed line and below the solid line is shaded.

Image with alt text: A system of 2 linear inequalities graphed on a coordinate plane. The horizontal x axis ranges from negative 5 to 5 in increments of 1. The vertical y axis ranges from negative 5 to 5 in increments of 1. A dashed line passes through begin ordered pair negative 1comma 1 end ordered pair and begin ordered pair 0 comma negative 2 end ordered pair. A solid line passing through begin ordered pair 2 comma 0 end ordered pair and begin ordered pair 0 comma negative 2 end ordered pair. The region below the dashed line and below the solid line is shaded.,

A system of 2 linear inequalities graphed on a coordinate plane. The horizontal x axis ranges from negative 5 to 5 in increments of 1. The vertical y axis ranges from negative 5 to 5 in increments of 1. A dashed line passes through begin ordered pair negative 2 comma 1 end ordered pair and begin ordered pair 0 comma negative 3 end ordered pair. A solid line passing through begin ordered pair 2 comma 0 end ordered pair and begin ordered pair 0 comma negative 2 end ordered pair. The region above the dashed line and above the solid line is shaded.

Image with alt text: A system of 2 linear inequalities graphed on a coordinate plane. The horizontal x axis ranges from negative 5 to 5 in increments of 1. The vertical y axis ranges from negative 5 to 5 in increments of 1. A dashed line passes through begin ordered pair negative 2 comma 1 end ordered pair and begin ordered pair 0 comma negative 3 end ordered pair. A solid line passing through begin ordered pair 2 comma 0 end ordered pair and begin ordered pair 0 comma negative 2 end ordered pair. The region above the dashed line and above the solid line is shaded.,

### Answers

The **graph** that represents the solution to the **system of inequalities** is given in the attachment below.

How to Determine the Graph to a System of Inequalities?

To find the correct **graph **that represents the solution to the **system of inequalities**, determine which **inequality** represents each of the line that is plotted on the **graph**.

The first **inequality**, y < -3x - 2, has a slope of -3, a y-intercept of -2, and an **inequality** sign "<" which means the shaded part will be below the a dotted or dashed boundary line.

The second **inequality**, y ≤ x − 2, has a slope of 1, a y-intercept of -2, and an **inequality** sign "≤" which means the shaded region is below a solid boundary line.

The **graph** that represents the above stated features is the **graph** of the **system of inequalities** shown below.

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A person tosses a coin 14 times. In how many ways can he get 10 heads?

### Answers

1.4 because 14 divided by 10 is 1.4

HELP NEEDED ASAP PLS

### Answers

The** expression** in the **simplest form** is -9x/10 + (5).

What is termed as the simplification?

Simplify simply means making something easier to understand. Simply or simplification in mathematics refers to reducing an** expression** / fraction / problem to a simpler form. It simplifies the problem by calculating and solving it.

We can —

Simplify** fractions** by removing all common factors from the numerator and denominator as well as composing the fraction in its simplest form.By grouping as well as combining similar terms, you can simplify mathematical expressions. This makes this same expression simple to understand and solve.

For the given equation;

= (-3x/5 - 7) - (-12 + 3x/10)

open the parenthesis;

= -3x/5 - 7 + 12 - 3x/10

Bring the** variable part **together.

= -3x/5 - 3x/10 - 7 + 12

Add variables and constant separately.

= -9x/10 + 5

Thus, the** simplest form** of the given expression is found as -9x/10 + 5.

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in one year, a town recorded a total of 79 days it did not rain, how many days did it rain

### Answers

**Answer:**

286

**Step-by-step explanation:**

there are 365 in a year

365-79

286

A physician borrowed $100,000 from credit union for 9 months at annual interest rate of 4%. What is the simple interest due on the loan?

### Answers

**Givens.**

• The amount borrowed was $100,000.

,

• The time elapsed is 9 months.

,

• The annual interest rate of 4%.

The simple interest formula is

[tex]I=PRT[/tex]

Where P = 100,000, R = 0.04, and T = 9/12.

[tex]\begin{gathered} I=100,000\cdot0.04\cdot\frac{9}{12} \\ I=3,000 \end{gathered}[/tex]Therefore, the simple interest is $3,000.

the answer would be 3,000

hello thank you for viewing my question I seem to be stuck on this problem can you please help thank you

### Answers

We have 9 boy kittens and 6 girl kittens, a total of 15 kittens.

9 cats will be selected and we have to calculate the probability that 5 boy kitttens and 4 girl kittens are chosen.

We could have modeled as a binomial experiment, but the probability of choosing a boy kitten is not constant after each selection. Then, we have to select an alternative method.

We can think of it of a combinatorial problem.

In this case, it is a combination problem, as the order of selection does not matter and each kitten is equivalent within its category.

Repetition is not allowed: a kitten selected can not be selected again.

We can start finding all the possible combinations for 9 kittens out of the total 15 kittens:

[tex]C(15,9)=\frac{15!}{9!(15-9)!}=\frac{15!}{9!6!}=5005[/tex]

The probability of selecting 5 boys and 4 girls will be the relation between the outcomes where there are 5 boys and 4 girls and the total number of outcomes we have just calculated.

Then, we can now calculate how many combinations of 9 kittens have 5 boys and 4 girls as a product of two combinations: the combinations for the boys C(9;5) and the combinations for the girls C(6;4).

We can calculate this as:

[tex]\begin{gathered} C(9,5)=\frac{9!}{5!4!}=126 \\ C(6,4)=\frac{6!}{4!2!}=15 \\ =>C(9,5)*C(6,4)=126*15=1890 \end{gathered}[/tex]

We can now calculate the probability as the ratio of combinations 1890/5005:

[tex]p=\frac{1890}{5005}\approx0.378[/tex]

**Answer: the probability is 0.378.**

Im kinda lost on how to solve these could you help me and teach me!

### Answers

The **angles** **∠IDA, ∠YDA, and ∠RDI** measures **121°, 59°, and 29.5°**.

The angle ∠YDF is equal to 121°. The ∠IDA is **vertically opposite angle**. So, ∠ADI is equal to the ∠YDF. Hence, ∠IDA = 121°.

The angle ∠YDA and the angle ∠ADI form a **linear pair**. It means ∠YDA and ∠ADI are **complimentary angles**.

∠YDA + ∠ADI = 180°

∠YDA + 121° = 180°

∠YDA = 180° - 121°

∠YDA = 59°

The ∠FDI is vertically opposite angle to ∠YDA. So, ∠FDI is equal to the ∠YDA. Hence, ∠FDI = 59°. The ray DR bisects the ∠FDI. So, the **angle** ∠RDI is half of the angle ∠FDI.

∠RDI = (1/2)∠FDI

∠RDI = (1/2)59

∠RDI = 29.5°

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RANGE AND DOMAIN. GRAPSWhat is the Range of this Relation:{(3,0), (-2,6), (-1,4), (-2,0), (1,5)}

### Answers

Given the relation:

[tex]\mleft\{\mleft(3,0\mright),(-2,6),(-1,4),(-2,0),(1,5)\mright\}[/tex]

The range of the relation can be thought of as the set of y-coordinates of a point (x, y). That is, as every second number of the ordered pairs. Additionally, the set should be ordered, and should not contain repeated values. This set is:

[tex]Range=\mleft\lbrace0,4,5,6\mright\rbrace[/tex]

What is the slope of y-9=3(x+12)

### Answers

**Answer:**

**Step-by-step explanation:**

When solving an equation for x if you get 4=10, that means what?

### Answers

Given: An equation where

[tex]4=10[/tex]

To Determine: the nature of the solution of the equation

Solution

Nature of solution: The example below relates to the nature of solution

[tex]\begin{gathered} Note:4=4(infinitely\text{ many solution\rparen} \\ a=4(one\text{ solution\rparen} \\ 4=10(no\text{ solution\rparen} \end{gathered}[/tex]

**Hence, the equation has no solution**

The graph of y=-2is is transformed to becomey=+5. Which of the folloA The graph is translated Sunits left and 2 units up.& The graph is translated 2 units left and Sunits ups.Oc.thegraph is mamiandumits left and sumits chosam.OD The graph is translated Sunits right and 2 units dow

### Answers

Given the following function:

[tex]y=\sqrt{x-2}[/tex]

notice that the transformation:

[tex]y=\sqrt{x}+5[/tex]

can be written like this:

[tex]y=\sqrt{(x+2)-2}+5[/tex]

first, the +2 means that the graph moves 2 units left, and the +5 makes the graph move 5 units up.

some one please help me! quick!

### Answers

m(4) = 110° due to the *Transitive Property*.

The Transitive Property states a that if a = b and b = c, then a = c.

m(3) + m(4) = 180 due to the definition of* Supplementary Angles.* All supplementary angles add up to 180°.

m(3) = 70° because 180 - 110 = 70.

Laying down my n buffer is concerned after receiving her weekly paycheck she believes that her deductions for social security,Medicare,and federal income ta withholding (fit) may be incorrect Larsen is paid a salary of 4330 she is married filling jointly and prior to this payroll check has total earnings of 140,460 what are the correct deductions for social security Medicare and fit assume a rate of 6.3% on 142,809 for social security and 1.45% for Medicare

### Answers

Correct **deduction** for social security **Medicare** and fit at 6.3% = 8,996.967

Correct deduction for **Medicare** at rate of 1.45% = 2,070.731

What is Medicare?

**Medicare** is defined as a type of health insurance that reduces the fees incurred by an individual following the reception of health services.

After **deductions** the total earning = 140,460

The correct deduction for social security, Medicare and fit at the rate of 6.3% of 142,809;

= 6.3/100 × 142,809

= 899696.7/100

= 8,996.967

The correct deduction for **Medicare** at the rate of 1.45%;

= 1.45/100 × 142,809

= 207,073.05/100

= 2,070.731.

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FIRST TO ANSWER ALL GETS BRAINEST

Question 1(Multiple Choice Worth 2 points)

(Interior and Exterior Angles MC)

In triangle DEF, m∠D = (3x + 27)°, m∠E = (4x + 22)°, and m∠F = 68°. Determine the degree measure of the exterior angle to ∠D.

54°

58°

122°

126°

Question 2(Multiple Choice Worth 2 points)

(Interior and Exterior Angles MC)

In ΔJKL, m∠J = 78° and m∠L = 90°. Determine the measure of the exterior angle to ∠K.

168°

102°

57°

12°

Question 3(Multiple Choice Worth 2 points)

(Interior and Exterior Angles MC)

Triangle UVW is shown with m∠WUV = 36°. The measure of ∠UVW is (5h − 66)°, and the measure of ∠AWB is (5h − 18)°.

triangle UVW with side VW extended through point A and side UW extended through point B, with angle U labeled as 36 degrees

Determine the value of h.

h = 22.8

h = 23

h = 25.4

h = 48

Question 4(Multiple Choice Worth 2 points)

(Interior and Exterior Angles LC)

One interior angle of a triangle is 95.5°, and the other two interior angles are congruent. What is the degree measure of one of the congruent angles?

42.25°

47.75°

84.5°

90°

Question 5(Multiple Choice Worth 2 points)

(Interior and Exterior Angles LC)

For ΔABC, m∠A = 28.7° and m∠B = 123.8°. Determine m∠C.

27.5°

62.5°

76.25°

152.5°

Question 6(Multiple Choice Worth 2 points)

(Interior and Exterior Angles MC)

For triangle XYZ, m∠X = 38°, m∠Y = (5x − 11)°, and m∠Z = (4x − 45)°. Find m∠Y.

m∠Y = 22°

m∠Y = 43°

m∠Y = 99°

m∠Y = 158°

Question 7(Multiple Choice Worth 2 points)

(Interior and Exterior Angles MC)

Triangle ABC is shown with exterior ∠z.

triangle ABC with angle A labeled 58 degrees, angle B labeled 44 degrees, and side AC extended with angle z labeled as exterior angle to angle C

Determine m∠z.

136°

102°

78°

58°

### Answers

The **sum **of all **interior** **angles **of a triangle is 180° thus the **measure **of the **exterior **angle to ∠D is 126° so option (D) is correct.

What is a triangle?

A triangle is a **3-sided shape** that is occasionally referred to as a **triangle**. There are 3 **sides **and three **angles** in every triangle, some of which may be the same.

It is known that the **sum** of all three angles **inside **a **triangle **will be 180°.

So, m∠D + m∠E + m∠F = 180°

(3x + 27) + (4x + 22) + 68 = 180

7x + 49 + 68 = 180

7x = 63

x = 9

So, m∠D = (3(9) + 27)° = 54°.

The **exterior **angle of D = 180- 54 = 126°.

Hence "The **sum** of all **interior** **angles **of a triangle is 180° thus the measure of the **exterior **angle to ∠D is 126°".

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I need help with a table to plot the points

### Answers

In order to plot a set of coordinates on a graph page, you would need to take account of every pair of x and y values provided. The line that goes horizontally is the x-axis (from left to right). All the negative values move from point zero (the origin).

The ordered pair, or the coordinates tells you where x and y intersect. For example, the first set of coordinates are (2, 9). That means, when x is 2, then y is 9.

Observe that x equals 2 on the right side of the horizontal axis. Next, you look for the spot where y equals 9.

Next step, you carefully trace the spot where x is 2, and trace it up a straight line and at the point where y equals 9 (at the upper part of the y axis), you put a tiny "X" to mark the spot where both values intersect.

Notice that while tracing from x, you move upwards, and while tracing from y, you move towards the right. That point defines the coordinates (2, 9) which is the first line on your table.

You follow a similar step for every one of the other coordinates, which are;

[tex]\begin{gathered} (2,9) \\ (4,3) \\ (6,-6) \\ (0,15) \\ (3,6) \\ (5,0) \\ (\frac{7}{3},8) \end{gathered}[/tex]

Please note that I've just attached the same graph, but this time I've labelled the points one by one.

This should help with reading the coordinates at every point.

Write the correct equation for the following statement.

You decide to rent a limo for prom. The rate is $250 plus $6 per mile

traveled. Write an equation to calculate your total cost (c) at the end of

the evening for a given number of miles (m).

250+6m

If you travel 45 miles what will be your total bill at the end

of the evening?

### Answers

**Answer:**

Easy;

Substitute m (miles) for 45.

250+6(45)

(6 dollars per mile, times 45 miles, plus the 250 flat rate)

250+270

520

So you would be charged 520 dollars total at the end of the evening.

Hope this helped!

Answer:

520

**Step-by-step explanation:**

so first you would multiply 6 by 45 which is 270 then add 250 which is 520

hope this helped, have a great day

determine which of the following relations is a function.Xyxy-1010-32-55-1100025-5110-104O3-8-2124y-4-22346XOx01225y24267

### Answers

The** relation between** the **function** is X cannot repeat itself.

We have given that,

functions table

We have to **determine** which relation is a **function.**

What is the function?

A **function** from a set X to a set Y assigns to each element of X exactly one element of Y. The set X is called the domain of the function and the set Y is called the **codomain** of the function. Functions were originally the idealization of how a varying quantity depends on another quantity.

The relation between the** function** is

X cannot repeat itself

Therefore option C is correct.

Complete question: Determine which of the following relations is a function [see in attachment]

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1 yard =3 feet1 meter= 100 cmNicholas walked 20 yards to get his mail. About how many meters did he walk?

### Answers

Given:

1 yard = 3 feet

1 meter = 100 cm

Nicholas walked 20 yards to get his mail.

Here, we are required to convert 20 yards to meters.

Where,

1 yard = 0.9144 meter

20 yards = x meters

thus, we have:

[tex]20\text{ }\times0.9144\text{ = 18.29 meters}[/tex]

Therefore, Nicholas walked 18.29 meters to get to his mail.

**ANSWER:**

**18.29 meters**

Which of the following could be the end behavior of f(x) = -x2 – 4?

### Answers

**Answer:**

**f(x) = -∞ as x → ±∞**

**Explanation:**

The given function is

f(x) = -x² - 4

To know the end behavior, let's replace x by a greater number and by a smaller number, so

If x = 100

f(x) = -100² - 4

f(x) = -10000 - 4

f(x) = -10004

If x = -100

f(x) = -(-100)² - 4

f(x) = -10000 - 4

f(x) = -10004

So, we can see that no matter if x is negative or positive, the value of f(x) will be positive. Then, we can say that the end behavior is

f(x) = -∞ as x → ±∞

For each function graphed below, state whether it is one to one !!

### Answers

[tex]\begin{gathered} G1\Rightarrow Yes \\ G2\Rightarrow No \\ G_3\Rightarrow Yes \\ G4\Rightarrow No \\ G5\Rightarrow No \\ G6\Rightarrow Yes \end{gathered}[/tex]

2. Refer to the figure shown.a. What is JK?b. What is KM?

### Answers

Point J is located at 5

Point K is located at 12

Point M is located at 27

**a. **The length of the segment JK is: 12 - 5 = **7**

**b. **The length of the segment KM is: 27 - 12 = **15**

help meeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeee

### Answers

**Answer:**

C(x) = 75x + 1908

**Step-by-step explanation:**

C(x) is the cost function.

The cost of making x bicycles is the sum of the fixed costs and the cost per bicycle.

The fixed cost is $1908.

The cost per bicycle is $75, so the per bicycle cost for x bicycles is 75x.

Add the two costs, and you get:

C(x) = 75x + 1908

Which equation is perpendicularl to 2x+3y=12A y=2/3X+5B y=-2/3X+5C y=3/2X+5D y= -3/2X+5

### Answers

**The equation of the line perpendicular to the given equation is;**

[tex]y\text{ = }\frac{3}{2}x\text{ + 5}[/tex]

**Option C is the correct answer**

Here, we want to select which of the equations in the option is perpendicular to the given equation

Firstly, we need to understand that for two equations to be perpendicular, then the product of their slopes must be equal to -1

Before we proceed to compare, we need to write the equation in the general form

The equation of the line written in the general form will be;

[tex]y\text{ = mx + b}[/tex]

where m represents the slope and the term b represents the y-intercept

Now, let us proceed to write the equation in the standard form;

We have this as;

[tex]\begin{gathered} 3y\text{ = -2x + 12} \\ \\ y\text{ = -}\frac{2}{3}x\text{ + 4} \end{gathered}[/tex]

Compared with the general form, we can see that the slope of this line is -2/3

Now let us get the slope of the line that would be perpendicular to it;

[tex]\begin{gathered} \frac{-2}{3}\times\text{ m = -1} \\ \\ m\text{ = }\frac{3}{2} \end{gathered}[/tex]

Now, the equation perpendicular to what was given will have a slope of 3/2

Fortunately, all the options in the question have been written in the general form

The one with a slope of 3/2 is option C

[tex]y\text{ = }\frac{3}{2}x\text{ + 5}[/tex]