An equation was used to predict the number of possible enrollments in an afterschool program for the first 6 months of the year. The actual enrollments are also listed.


Actual enrollment 55 80 95 100 115 90
Predicted enrollment 75 80 85 90 95 100


The sum of the residuals is ______.

Answer:

Option C (28.0°)

Step-by-step explanation:

The questions which involve calculating the angles and the sides of a triangle either require the sine rule or the cosine rule. In this question, the three sides are given and one unknown angle has to be calculated. Therefore, cosine rule will be used. The cosine rule is:

a^2 = b^2 + c^2 - 2*b*c*cos(A°).

The question specifies that a=13, b=21, and c=27. Plugging in the values:

13^2 = 21^2 + 27^2 - 2(21)(27)*cos(A°).

Simplifying gives:

-1001 = -1134*cos(A°)

Isolating cos(A°) gives:

cos(A°) = 0.88271604938

Taking cosine inverse on the both sides gives:

A° = arccos(0.88271604938). Therefore, using a calculator, A° = 28.0 (correct to one decimal place).

This means that the Option C is the correct choice!!!

For this case we have that by definition, the cosine theorem states that:

[tex]a ^ 2 = b ^ 2 + c ^ 2-2bc * Cos (A)[/tex]

According to the data we have:

[tex]a = 13\\b = 21\\c = 27[/tex]

Substituting we have:

[tex]13 ^ 2 = 21 ^ 2 + 27 ^ 2-2 (21) (27) * Cos (A)\\169 = 441 + 729-1134 * Cos (A)\\169 = 1170-1134 * Cos (A)\\169-1170 = -1134 * Cos (A)\\-1001 = -1134 * Cos (A)\\Cos (A) = \frac {1001} {1134}\\Cos (A) = 0.8827\\A = arc cos (0.8827)\\A = 28.03[/tex]

Answer:

Option C

Answer:

[tex]\large\boxed{(f+g)(x)=4^x+17x-1}[/tex]

Step-by-step explanation:

[tex](f+g)(x)=f(x)+g(x)\\\\f(x)=4^x+12x,\ g(x)=5x-1\\\\(f+g)(x)=(4^x+12x)+(5x-1)=4^x+17x-1[/tex]

Answer:

c = 13.1

Step-by-step explanation:

* Lets explain how to solve the problem

- In Δ ABC

# ∠A is opposite to side a

# ∠B is opposite to side b

# ∠C is opposite to side c

- The sine rule is:

# [tex]\frac{sinA}{a}=\frac{sinB}{b}=\frac{sinC}{c}[/tex]

* Lets solve the problem

- In Δ ABC

∵ m∠A = 57°

∵ m∠B = 37°

∵ The sum of the measures of the interior angles of a triangle is 180°

∴ m∠A + m∠B + m∠C = 180°

∴ 57° + 37° + m∠C = 180°

∴ 94° + m∠C = 180° ⇒ subtract 94° from both sides

∴ m∠C = 86°

- Lets use the sine rule to find c

∵ a = 11 and m∠A = 57°

∵ m∠C = 86°

∵ [tex]\frac{sin(57)}{11}=\frac{sin(86)}{c}[/tex]

- By using cross multiplication

∴ c sin(57) = 11 sin(86) ⇒ divide both sides by sin(57)

∴ [tex]c=\frac{11(sin86)}{sin57}=13.1[/tex]

* c = 13.1

Answer:

55.5 feet

Step-by-step explanation:

the scenario is attached in the form of a picture

We have to find h.

We will use the trigonometric ratio of tan to find the height of the house.

[tex]tan\ 48 = \frac{h}{50}\\ 1.1106*50=h\\55.53=h[/tex]

Hence the height of the house is 55.53 feet

Rounding off to nearest 10th

height = 55.5 feet ..

The height of the house is approximately 55.5 feet.

To find the height of the house, let's use trigonometry based on the given information:

Given:

Distance from the point on the ground to the house (adjacent side of the triangle): ( AB = 50 ) feet

Angle of elevation from the ground to the top of the house [tex](\( \theta \))[/tex]: [tex]\( \theta[/tex] = [tex]48^\circ \)[/tex]

We need to find:

Height of the house (opposite side of the triangle): h

We use the tangent function because it relates the opposite side to the adjacent side in a right triangle:

[tex]\[ \tan(\theta) = \frac{\text{opposite}}{\text{adjacent}} \]Substituting the given values:\[ \tan(48^\circ) = \frac{h}{50} \]To find \( h \), multiply both sides by 50:\[ h = 50 \times \tan(48^\circ) \]Now, calculate \( \tan(48^\circ) \):\[ \tan(48^\circ) \approx 1.1106 \][/tex]

Therefore,

[tex]\[ h \approx 50 \times 1.1106 \]\[ h \approx 55.53 \]Rounding to the nearest tenth:\[ h \approx 55.5 \text{ feet} \][/tex]

So, the height of the house is approximately 55.5 feet.

Answer:

The value of sum is 1323

Step-by-step explanation:

First of all we will find the value of n:

The value of n can be determined by the following formula:

an = a1 + (n - 1)d

where an= 113

a1= 13

d=5

Difference between the values = d=5

Now put the values n the formula:

113=13+(n-1)5

113=13+5n-5

Solve the like terms:

113=8+5n

Move constant to the L.H.S

113-8=5n

105=5n

Divide both sides by 5

21=n

Now put these values in the formula to find the sum:

Sn = n/2(a1 + an)

S21=21/2(13+113)

S21=21/2(126)

S21=21(63)

S21=1323

The value of sum is 1323....

Step-by-step explanation:

Considering Lisa's yard is allowing the dog to run around a circumscribed circle with a ray of 4 5/6 feet then the maximum of the area that he could cover is the area of that circle A= 3.14×(4 5/6)^2/2

Not being able to see the drawing, I assume that if the area of the yard has a value below the value described above then the dog would run around the yard untill the rope's fully swirled around the tree or untill Lisa comes home

Answer:

9÷2+4

Step-by-step explanation:

Answer:

[tex]h(x)=+-\sqrt{\frac{x+4}{9} }[/tex]

Step-by-step explanation:

Hello

I think  I can help you with this

Let

[tex]y = 9x^{2}-4\\h(x)=y^{-1}[/tex]

to find the inverse of y([tex]y^{-1}[/tex])

Step 1

switch x and y

[tex]y = 9x^{2}-4\\\\x= 9y^{2}-4[/tex]

Step 2

Now solve the equation for y (isolating y)

[tex]x= 9y^{2}-4\\Add\ 4\ to\ both\ sides\\x+4= 9y^{2}-4+4\\x+4=9y^{2}\\divide\ each\ side\ by\ 9\\\frac{x+4}{9} =\frac{9y^{2}}{9}\\\\x+4=y^{2} \\[/tex]

[tex]h(x)=+-\sqrt{\frac{x+4}{9} }[/tex]

Have a great day

115°

Got it right on the test.

Answer:

The experienced painter takes 3 hours to paint the room

The inexperienced painter takes 6 hours to paint the room

Step-by-step explanation:

* Lets explain how to solve the problem

- Two painters can paint a room in 2 hours if they work together

- Assume that the experienced painter can paint the room in a hours

∴ Its rate is 1/a

- Assume that the inexperienced painter can paint the room in b hours

∴ Its rate is 1/b

∵ When they working together they will finish it in two hours

∴ Their rate together is 1/2

- Equate the sum of the rate of each one and the their rate together

∴ [tex]\frac{1}{a}+\frac{1}{b}=1/2[/tex]

-To add two fraction with different denominators we multiply the 2

 denominators and multiply each numerator by the opposite

 denominator

∴ [tex]\frac{b+a}{ab}=\frac{1}{2}[/tex]

- By using the cross multiplication

∴ 2(b + a) = ab

∴ 2b + 2a = ab ⇒ (1)

- The inexperienced painter takes 3 hours more than the experienced

  painter to finish the job

∵ The experienced painter can finish the room in a hours

∵ The inexperienced painter can finish the room in b hours

∵ The inexperienced painter takes 3 hours more than the experienced

  painter to finish the job

∴ b = a + 3 ⇒ (2)

- Substitute equation (2) in equation (1)

∴ 2(a + 3) + 2a = a(a + 3)

∴ 2a + 6 + 2a = a² + 3a ⇒ add like terms

∴ 4a + 6 = a² + 3a ⇒ subtract 4a from both sides

∴ 6 = a² - a ⇒ subtract 6 from both sides

∴ a² - a - 6 = 0 ⇒ factorize it

∵ a² = (a)(a)

∵ -6 = -3 × 2

∵ -3(a) + 2(a) = -3a + 2a = -a ⇒ the middle term in the equation

∴ a² - a - 6 = (a - 3)(a + 2)

∵ a² - a - 6 = 0

∴ (a - 3)(a + 2) = 0

∴ a - 3 = 0 ⇒ add 3 to both sides

∴ a = 3

- OR

∴ a + 2 = 0 ⇒ subtract 2 from both sides

∴ a = -2 ⇒ rejected because there is no negative value for the time

- Substitute the value of a in equation (2) to find b

∵ b = 3 + 3 = 6

∴ The experienced painter takes 3 hours to paint the room

∴ The inexperienced painter takes 6 hours to paint the room

Experienced painter needs 3 hours to paint the room individually.

Inexperienced painter needs 6 hours to paint the room individually.

This problem is related to the speed of completing the work.

To solve this problem, we must state the formula for the speed.

[tex]\large {\boxed {v = \frac{x}{t}} }[/tex]

where:

v = speed of completing the work( m³ / s )

x = work ( m³ )

t = time taken ( s )

Let's tackle the problem!

Painter A can complete work by herself in t_a hours.

[tex]\text{Painter A's Speed} = v_a = x \div t_a[/tex]

[tex]v_a = x \div t_a[/tex]

Painter B can complete work by herself in t_b hours.

[tex]\text{Painter B's Speed} = v_b = x \div t_b[/tex]

[tex]v_b = x \div t_b[/tex]

The inexperienced painter takes 3 hours more than the experienced painter to finish the job

[tex]\text{Painter B's Time} = 3 + \text{Painter A's Time}[/tex]

[tex]t_b = 3 + t_a[/tex]

Two painters can paint a room in 2 hours if they work together

[tex]\text{Total Speed} = v = v_a + v_b[/tex]

[tex]\frac{x}{t} = \frac{x}{t_a} + \frac{x}{t_b}[/tex]

[tex]\frac{1}{t} = \frac{1}{t_a} + \frac{1}{t_b}[/tex]

[tex]\frac{1}{2} = \frac{1}{t_a} + \frac{1}{3 + t_a}[/tex]

[tex]\frac{1}{2} = \frac{3 + t_a + t_a}{t_a(3 + t_a)}[/tex]

[tex]\frac{1}{2} = \frac{3 + 2t_a}{t_a(3 + t_a)}[/tex]

[tex]t_a(3 + t_a) = 2(3 + 2t_a)[/tex]

[tex]t_a^2 + 3t_a = 6 + 4t_a[/tex]

[tex]t_a^2 + 3t_a - 4t_a - 6 = 0[/tex]

[tex]t_a^2 - t_a - 6 = 0[/tex]

[tex](t_a -3)(t_a + 2) = 0[/tex]

[tex](t_a -3) = 0[/tex]

[tex]t_a = \boxed{3 ~ hours}[/tex]

[tex]t_b = 3 + t_a[/tex]

[tex]t_b = 3 + 3[/tex]

[tex]t_b = \boxed {6 ~ hours}[/tex]

Grade: High School

Subject: Mathematics

Chapter: Linear Equations

Keywords: Linear , Equations , 1 , Variable , Line , Gradient , Point

Answer:

a=192

b=96

c=64

d=48

Step-by-step explanation:

So we have [tex]a+b+c+d=400[/tex] where [tex]a,b,c,[/tex] and [tex]d[/tex] are integers.

We also have [tex]a=2b[/tex]and [tex]a=3c[/tex]and [tex]a=4d.[/tex]

[tex]a=2b[/tex] means [tex]a/2=b[/tex]

[tex]a=3c[/tex] means [tex]a/3=c[/tex]

[tex]a=4d[/tex] means [tex]a/4=d[/tex]

Let's plug those in:

[tex]a+b+c+d=400[/tex]

[tex]a+\frac{a}{2}+\frac{a}{3}+\frac{a}{4}=400[/tex]

Multiply both sides by 4(3)=12 to clear the fractions:

[tex]12a+6a+4a+3a=4800[/tex]

Combine like terms:

[tex]25a=4800[/tex]

Divide both sides by 25:

[tex]a=\frac{4800}{25}[/tex]

Simplify:

[tex]a=192[/tex].

Let's go back and find [tex]b,c,d[/tex] now.

b is half of a so half of 192 is 96 which means b=96

c is a third of a so a third of 192 is 64 which means c=64

d is a fourth of a so a fourth of 192 is 48 which means d=48

So

a=192

b=96

c=64

d=48

Answer:

a=192

b=96

c=64

d=48

Step-by-step explanation:

hope this helps

a) (2a - b)² = (4a² - 4ab + b²)

b) (10m - n²)² = (100m² - 20mn² + n⁴)

c) (4x - 4²) = (16x² - 8x + 4⁴)

d)[tex] {( \frac{1}{3} x - y) }^{2} = ({ \frac{1}{9}x }^{2} - \frac{2}{3} xy + {y}^{2} )[/tex]

e)

[tex](0.25 - a) ^{2} = (0.25^{2} - (2)(0.25)a + {a}^{2} ) \\ \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: = ( \frac{1}{16} - \frac{1}{2} a + {a}^{2} )[/tex]

f)

[tex] {( \frac{2x}{3} - \frac{1}{2} )}^{2} = ( \frac{4 {x}^{2} }{9} - \frac{2x}{3} + \frac{1}{4} )[/tex]

Answer:

Fig A

Step-by-step explanation:

in fig A, we can see that the subset that represents "trees", lies inside the subset that "has leaves". Hence in figure A, we can say that "All trees have leaves" or "if it is a tree, it has leaves"

in fig B however, we see that "has leaves" is inside of "trees", this means that the area in-between  "has leaves" and "tree" represents the subset that there are trees without leaves. This is in contradiction to the statement "if it is a tree, it has leaves", hence this is not the answer.

Answer

A

Step-by-step explanation:

hope this helps :)

[tex]\huge{\boxed{(x-2, y+4)}}[/tex]

[tex]x_1 \bf{-2} =x_2[/tex]

[tex]y_1 \bf{+4} =y_2[/tex]

This means that the answer is the subtract [tex]2[/tex] from the [tex]x[/tex] and add [tex]4[/tex] to the [tex]y[/tex], which is represented as [tex]\boxed{(x-2, y+4)}[/tex]

Also, thank you for posting your first question, and welcome to the community! If you have any questions, don’t hesitate to reach out to me!

The translation that maps (3,-4) to its image (1,0) is given by:

(x, y) ⇒ (x - 2, y + 4)

Transformation is the movement of a point from its initial location to a new location. Types of transformation are translation, rotation, reflection and dilation.

Translation is the movement of a point either up, down, left or right.

If a point A(x, y) is moved a units left and b units up, the new point is at A'(x - a, y + b).

The translation that maps (3,-4) to its image (1,0) is given by:

(x, y) ⇒ (x - 2, y + 4)

Find out more at: https://brainly.com/question/18303818

Answer:

B.  3 and 4

Step-by-step explanation:

In order to find the numbers between which √11 lies, let us first guess the nearest perfect squares to √11. These are 9 and 16. Where 9 comes just before 11 and 16 comes just after 11. Now we have to write all three of them in ascending order.

√9 , √11  ,  √16

also

√9= 3 and √16 = 4

and

√9 < √11 < √16

3 < √11 < 4

hence we can see that √11 must lies between 3 and 4  

Answer:

B.3 and 4

Step-by-step explanation:

3x3=9

4x4=16

so, 11 goes between 3 and 4

I just gave myself a bad rating because I did not want you guys to get the answer wrong because I posted an answer that was wrong and forgot that I could edit so now that I fixed it is a safe answer

Answer:

Assuming you have [tex]f(n)=0.4f(n-1)+12[/tex] with [tex]f(1)=4[/tex], the answer is f(2)=13.6.

Step-by-step explanation:

I think that says [tex]f(n)=0.4f(n-1)+12[/tex] with [tex]f(1)=4[/tex].

Now we want to find [tex]f(2)[/tex] so replace n with 2:

This gives you:

[tex]f(2)=0.4f(2-1)+12[/tex]

[tex]f(2)=0.4f(1)+12[/tex]

[tex]f(2)=0.4(4)+12[/tex]

[tex]f(2)=1.6+12[/tex]

[tex]f(2)=13.6[/tex]

Answer:

13.6 (Answer C)

Step-by-step explanation:

I think you meant  f(n) = 0.4 * f(n-1) + 12, where * represents multiplication.

Then f(2) = 0.4 * (4) + 12, or 1.6 + 12, or 13.6.

Answer: 40% or 2/5

Step-by-step explanation:

10 total marbles

6 yellow

4 red

Probability of blindly picking a red marble is 4/10 or 2/5 which can be written as 40%

The probability of picking a red marble from a bag containing 10 marbles, where 4 are red, is 4 out of 10 or 0.4.

The question asks about the probability of picking a red marble from a bag containing 6 yellow marbles and 4 red marbles, totaling 10 marbles. To calculate the probability, you divide the number of favorable outcomes (picking a red marble) by the number of possible outcomes (total marbles). In this case, the probability of picking a red marble is 4 out of 10, which can be simplified to 2 out of 5 or 0.4.

Answer:

false

Step-by-step explanation:

if you do 4/4 it is 1 which is odd

Answer:

No, the result is not always even.

Step-by-step explanation:

No, this is not necessary.

There is no general rule that states that an even number divided by another even number will always be an even number.

Few example are:

[tex]\frac{6}{2}=3[/tex]

[tex]\frac{10}{2}=5[/tex]

[tex]\frac{60}{4}=15[/tex]

Answer:

B and C

Step-by-step explanation:

- The answer in the attached file

The correct rule that describes the composition of transformations mapping AABC to AA"B"C" is:

- Ro. 900 ◦ T-6, -2(x, y)

Here's a step-by-step explanation:

1. "Ro. 900" stands for a 900 degrees counterclockwise rotation.

2. "T-6, -2" represents a translation of 6 units to the left and 2 units down.

3. When these transformations are applied in sequence to the original figure AABC, you first rotate it 900 degrees counterclockwise and then translate it 6 units to the left and 2 units down, resulting in the figure AA"B"C".

This rule combines rotation and translation to map AABC to AA"B"C". This composition of transformations is what leads to the desired outcome.

The complete question is : Which rule describes composition of transformations that maps ABC to A"B"C"?

Answer:

D. 88 degrees

Answer:

D. 88 degrees

Step-by-step explanation:

it is an inscribed angle

Answer:

Quotient: x^4+7x^3-2x^2-9x-3

Remainder: -10

Step-by-step explanation:

x5 + 15x+ + 54x3 – 25x2– 75x – 34 by x + 8.

Since the exponents are arranged in descending order so, 15x^4

x^5 + 15x^4+ + 54x^3 – 25x^2– 75x – 34 by x + 8

The division is shown in figure attached.

Quotient: x^4+7x^3-2x^2-9x-3

Remainder: -10

Answer:

Explanation:

Angles may be named by three letters, each represented a point on each of the angle's ray or by the vertex.

The angle EAD is the angle A (the letter of the center is the vertex).

In this case it is indicated the measure of the angle on the diagram using a small square.

The small square is a conventional symbol to indicate that the angle is 90°, which is named right angle. That determines that the rays, segments or lines meet perpendicularly.

That is one fourth (1/4) of the complete circle (1/4 × 360° = 90°).

By using the dagram, the measure of the given angle include the following:

m∠EAD = 90°

In Mathematics and Euclidean Geometry, a right angle is a type of angle that is formed in a triangle by the intersection of two (2) straight lines at 90 degrees.

Generally speaking, a perpendicular bisector can be used to bisect or divide a line segment exactly into two (2) equal halves, in order to form a right angle that has a magnitude of 90 degrees at the point of intersection;

In this context, we can logically deduce that segment AE is the perpendicular bisector of diameter ED in circle A. Therefore, the measure of angle EAD must be 90 degrees;

m∠EAD = 90°

[tex]-2(k+3) < -2k - 7\\-2k-6<-2k-7\\-6<-7\\k\in\emptyset[/tex]

Answer:

No solutions

Step-by-step explanation:

-2(k+3) < -2k - 7

Distribute the -2

-2k-6 < -2k - 7

Add 2k to each side

-2k+2k-6 < -2k+2k - 7

-6 < -7

This is always false, so the inequality is never true

There are no solutions

Answer:

Step-by-step explanation:

[tex]\left\{\begin{array}{ccc}x-3y=6&\text{multiply both sides by (-2)}\\2x+2y=4\end{array}\right\\\\\underline{+\left\{\begin{array}{ccc}-2x+6y=-12\\2x+2y=4\end{array}\right}\qquad\text{add both sides of the equations}\\.\qquad\qquad8y=-8\qquad\text{divide both sides by 8}\\.\qquad\qquad y=-1\\\\\text{Put the value of y to the first equation:}\\\\x-3(-1)=6\\x+3=6\qquad\text{subtract 3 from both sides}\\x=3[/tex]

Answer: y = -1 and x = 3

Step-by-step explanation:

x - 3y = 6 --------(1)

2x + 2y = 4 -------(2)

we multiply (1) by 2

2x - 6y = 12 --------(3)

(3) - (1)

-8y = 8

y = -1

Putting y = -1 into equation (1)

x - 3 (-1) = 6

x + 3 =6

collect the like term

x = 6 - 3

x = 3

Therefore x= 3 and y = -1

Answer:

True

Step-by-step explanation:

It would be true.

"Two arcs of a circle are congruent if and only if their associated chords are congruent." is False statement.

If it is possible to superimpose one geometric figure on the other so that their entire surface coincides, that geometric figure is said to be congruent, or to be in the relation of congruence. When two sides and their included angle in one triangle are equal to two sides and their included angle in another, two triangles are said to be congruent.

If and only if the related chords of two arcs are congruent, they are said to be congruent.

The radii of the circles that the arcs are in are the related radii of the arcs. Yet, it is possible to have two arcs that are incongruent in a single circle.

The arcs wouldn't necessarily be congruent, but the circle wouldn't have two distinct radii either.

Thus, the given statement is False.

Learn more about Congruency here:

https://brainly.com/question/10677854

#SPJ7

Answer:

Option A

Step-by-step explanation:

The domain must be

[a,∞)

That means that x must have as an argument a square root, because, it cannot take negative arguments for real numbers (a>0)

√(x-a)

x-a≥0

x ≥ a

The only possible option is

Option A.

Please take a look at the attached graph

Answer:

A) (x-3) is not a factor of x^3+4x^2+2

Step-by-step explanation:

(x-3) is a factor of f(x)=x^3+4x^2+2 if f(3)=0. This is by factor theorem.

So let's check it.

f(x)=x^3+4x^2+2

f(3)=3^3+4(3)^2+2

f(3)=27+4(9)+2

f(3)=27+36+2

f(3)=63+2

f(3)=65

Since f(3) doesn't equal 0, then x-3 is not a factor.

Answer:

A. (x-3) is not a factor

Step-by-step explanation:

You can find if (x-3) is a factor of the polynomial by dividing the polynomial by (x-3) by using long division or synthetic division.

Long division:                          

          x^2+x+3

(x-3)/x^3+4x^2+0x+2

      -(x^3-3x^2)

                 x^2+0x

                -(x^2-3x)

                         3x+2

                        -(3x-9)

                               -7  

Here you can see that (x-3) is not a factor of the polynomial because when you divide x^3 + 4x^2 + 2 by (x-3), there is a remainder of -7

Synthetic Division (A shortcut version of long division just to see if there is a remainder and if the supposed factor is really a factor) :

3          1            4           0           2    

           -           3           21          63

           1            7           21          65

As seen before (x-3) is not a factor of the polynomial because there is a remainder.  If 65 were 0, the (x-3) would be a factor of the polynomial.

Answer:

B

Step-by-step explanation:

The average rate of change of f(x) in the closed interval [ a, b ] is

[tex]\frac{f(b)-f(a)}{b-a}[/tex]

Here [ a, b ] = [ 3, 5 ]

From the table of values

f(b) = f(5) = 32

f(a) = f(3) = 8

Hence

average rate of change = [tex]\frac{32-8}{5-3}[/tex] = [tex]\frac{24}{2}[/tex] = 12

Answer:

The average rate of change is [tex]12[/tex]

Step-by-step explanation:

Given:

Interval; x = 3 to x = 5

We'll represent these by

x1 = 3

x2 = 5

The corresponding y values are:

When x = 3, y = 8

When x = 5, y = 32

This will also be represented

y1 = 8

y2 = 32

Average rate of change is then calculated as follows

[tex]m = \frac{y_{2} - y_{1}}{x_{2} - x_{1}}[/tex]

Where m represent average rate of change

By Substitution, we have

[tex]m = \frac{32 - 8}{5 - 3}[/tex]

[tex]m = \frac{24}{2}[/tex]

[tex]m = 12[/tex]

Hence, the average rate of change is [tex]12[/tex]

[tex]\bf (\stackrel{x_1}{-3}~,~\stackrel{y_1}{5})\qquad (\stackrel{x_2}{4}~,~\stackrel{y_2}{-2}) \\\\\\ slope = m\implies \cfrac{\stackrel{rise}{ y_2- y_1}}{\stackrel{run}{ x_2- x_1}}\implies \cfrac{-2-5}{4-(-3)}\implies \cfrac{-7}{4+3}\implies \cfrac{-7}{7}\implies -1 \\\\\\ \begin{array}{|c|ll} \cline{1-1} \textit{point-slope form}\\ \cline{1-1} \\ y-y_1=m(x-x_1) \\\\ \cline{1-1} \end{array}\implies y-5=1[x-(-3)]\implies y-5=1(x+3) \\\\\\ y-5=x + 3\implies y=x+8[/tex]