When doing his homework, a student uses the addition property of equality to solve for c below. Which statement BEST applies to the sample? 6 + c = 10 6 + (–6) + c = 10 + (–6) c = 4 A. The student failed to keep both sides of the equation balanced. B. The student’s final answer does not have the variable c isolated. C. The use of the addition property of equality is sound, and the answer is correct. D. The student should have used the subtraction property of equality.

Answers

Answer 1

Answer:

The answer would be C


Related Questions

Pls help me I got it wrongg :((

Answers

Answer:

4 ounces

Step-by-step explanation:

I'm assuming when it says: [tex]33\frac{1}{3}%[/tex]% it means 33.3333333333 instead of 33/3.

Anyways under that assumption, we currently have 20 ounces in the grape juice, since 4 ounces is grape juice concentrate and 16 ounces is water. So currently let's just say that the total amount of grape juice concentrate is going to be: [tex](4+x)[/tex] where x is the amount of grape juice concentrate you need to add to make it 33.33%. The next thing to know is how to calculate how much percent a is of b. This can be calculated using the equation: [tex]\frac{a}{b}*100[/tex]. So in this case the a is going to be the grape juice concentrate, and the b is going to be the entire mixture (water and grape juice). Since the concentrate is having x added to it, that means the entire thing is also having x added to it. This means we have the equation: [tex]\frac{4+x}{20+x} * 100[/tex], since we already have 4 ounces of grape juice concentrate, and we already have 20 ounces in total (16 ounces of water + 4 ounces of grape juice). This is going to be equal to 33.33%, or in other words 33 1/3. So to make this a bit easier, I'm going to convert this mixed fraction into one fraction, this gives you the fraction: [tex]\frac{100}{3}[/tex]. So now that's all left to do is set these two expressions equal to each other and solve for x

Original equation

[tex]\frac{4+x}{20+x}*100=\frac{100}{3}[/tex]

Divide both sides by 100

[tex]\frac{4+x}{20+x}=\frac{100}{3}\div 100[/tex]

Keep fraction, change division to multiplication, flip 100

[tex]\frac{4+x}{20+x}=\frac{100}{3}* \frac{1}{100}[/tex]

The 100 in the numerator will cancel out the one in the denominator

[tex]\frac{4+x}{20+x}=\frac{1}{3}[/tex]

Multiply both sides by 20+x

[tex]4+x=\frac{20+x}{3}[/tex]

Multiply both sides by 3

[tex]3(4+x)=20+x[/tex]

Distribute the 3

[tex]12+3x=20+x[/tex]

Subtract x from both sides

[tex]12+2x=20[/tex]

Subtract 12 from both sides

[tex]2x=8[/tex]

Divide both sides by 2

[tex]x=4[/tex]

So Kahn needs to pour 4 more ounces of grape juice, to double check this, since the mixture already has 4 ounces of grape juice, this means the final mixture will have a total of 8 ounces of grape juice concentrate, and a total of 24 ounces, since it already had 16 ounces of water, and 4 ounces of grape juice and now there is 4 more ounces of grape juice being added, so a total of 24 ounces. this means that 8/24 will be grape juice concentrate or in other words: [tex]\frac{1}{3}[/tex] and when you multiply this by 100 (to convert to percent), you get 100/3 or 33 1/3%

You are on the right track but it’s G) 4

someone please help me with problem #7 !!!

Answers

Answer: b and d

Step-by-step explanation:

Since the roots are x=2 and x=6, we can write the equation as

[tex]f(x)=a(x-2)(x-6)[/tex]

Substituting in the coordinates of the vertex,

[tex]-4=a(4-2)(4-6)\\\\-4=-4a\\\\a=1[/tex]

So, the equation is [tex]f(x)=(x-2)(x-6)[/tex]

On expanding, we get [tex]f(x)=x^2 - 8x+12[/tex]

Area=
I need some help solving this question I'm stuck. Thanks

Answers

Answer:  36 square units

Work Shown:

area = base*height/2

area = 12*6/2

area = 72/2

area = 36

The base and height are always perpendicular to each other. The triangle formula above applies to obtuse triangles, as well as any other type of triangle. It might help to rotate the triangle so that side IJ is at the bottom rather than the top.

find the quotients in the exponential forms by using laws of indices.
8^{2} ÷2^{10}=?

Answers

Answer:

Step-by-step explanation:

[tex]\dfrac{8^2}{2^{10}}\\=\dfrac{(2^3)^2}{2^{10}}\quad (8=2^3)\\\\=\dfrac{2^6}{2^{10}}\\\\=\dfrac{1}{2^{4}}=\dfrac{1}{16} \\\\or \quad 2^{-4} .[/tex]

Solve the system of equations using substitution.
y = -2X +1
4x + 2y = -2

Answers

Answer:

Step-by-step explanation:

4x + 2(-2X +1) = -2

Order of operations -

4x + -4x +2 = -2

Combine terms

4x-4x=0x

2 = -2

Answer:

no solution

Step-by-step explanation:

y = - 2x + 1 → (1)

4x + 2y = - 2 → (2)

substitute y = - 2x + 1 into (2)

4x + 2(- 2x + 1) = - 2 ← distribute parenthesis and simplify left side

4x - 4x + 2 = - 2 ( subtract 2 from both sides )

0 = - 4 ← not possible

this indicates the system of equations has no solution

(Please help, quickly if possible.)

Which types of dilation are the given scale factors?



Select Expansion or Contraction to correctly describe the type of dilation for each given scale factor.

(See image attached for details.)

Answers

A scale factor is a contracting scale such that x < 1, where x is the scale factor.

For example, if the scale factor x is less than 1, then it must be decreasing in size, and thus be contracting in size.

But, if the scale factor is greater than 1, then it is expanding in size and increasing.

1) -5 is expanding. It is greater than one.

2) -1/4 is contracting. It is less than one.

3) 3.5 is expanding. It is greater than one.

4) 6/7 is contracting. It is less than one.

will give brainliest plus 10 points

Answers

Answer:

The distance is 7.3 units.

Step-by-step explanation:

Two given points: (-3, 1) and (4, -1)

[tex]\sf Distance \ between \ two \ points = \sqrt{(x_2 - x_1)^2 + (y_2 - y_1)^2}[/tex]

Here given:

x₂ = 4x₁ = -3y₂ = -1y₁ = 1

Applying the formula:

[tex]\sf d = \sqrt{(4 - (-3))^2 + (-1 - 1)^2}[/tex]

[tex]\sf d = \sqrt{(7)^2 + (-2)^2}[/tex]

[tex]\sf d = \sqrt{49 + 4}[/tex]

[tex]\sf d = \sqrt{53} \ \approx \ 7.28 \ \approx \ 7.3 \ (rounded)[/tex]

Answer:

7.3

Step-by-step explanation:

The distance of a line segment between two points (x1, y1) and (x2, y2) is given by the formula

[tex]d = \sqrt{(x2-x1)^2 + (y2-y1)^2}[/tex]

If we look at the graph,

the leftmost point of the line is at (-3, 1). Let's call this (x1, y1)

the rightmost point is at (4, -1). Let's call this (x2, y2)

Substituting these values into the distance formula gives us


[tex]d = \sqrt{(4-(-3)^2 + (1-(1)^2} \\ \\d = \sqrt{(7)^2 + (-2)^2} \\ \\d = \sqrt{49 + 4} \\\\d = \sqrt{(x2-x1)^2 + (y2-y1)^2}\\\\d = \sqrt{53} = 7.28[/tex]

Rounded to one decimal place, this is 7.3

which transformation below would map the polygon A to the polygon B?
a) Polygon A has been translated down then right
b) Polygon A has been translated to the right and reflected vertically
c) Polygon A has been reflected horizontally and reflected vertically
d) Polygon A has been rotated 180 degrees counterclockwise

Answers

Using translation concepts, the transformation is given as follows:

a) Polygon A has been translated down then right.

What is a translation?

A translation is represented by a change in the function graph, according to operations such as multiplication or sum/subtraction in it's definition.

In this problem, the orientation of the polygon is the same, hence there was no rotation nor reflection, which means that option A is correct.

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Consider the set of real numbers and the set of complex numbers. Is every real number also a complex number? Is every complex number also a real number? Explain.

Answers

You define complex numbers as the reals, i, as usually defined, and their linear combinations using real coefficients, then,

The reals are complex numbers, even if you haven’t fully defined their properties.

If you define complex numbers as the form (a,b) with and a, b are real numbers, then you can say that each real number a is isomorphic with that complex number,

if b=0 once you define their properties.

What is the complex number?

A complex number can be visually represented as a pair of numbers (a, b) forming a vector on a diagram called an Argand diagram, representing the complex plane.

Of course, (0,1) will be i. You’ll have to define the multiplication rule, etc.

In actual usage, we gloss over the distinction, and real numbers are complex numbers with no imaginary part.

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need help with this question

Answers

(4,4) is the answer I think

Answer:

(4,6)

Step-by-step explanation:

To calculate the midpoint of two points, just calculate the arithmetic mean (average) of the x and y values of the two points given. For example, it is easy to see visually that the midpoint of (2, 0) and (4, 0) is (3, 0), since (3,0) falls right in the middle of the two points. However, the way to calculate this would be to take the average of 2 and 4 (3), along with the average of 0 and 0 (0). This process gives us our new point (3, 0). In case this doesn't make sense, here is the formula for the midpoint of two points - (x1,y1) and (x2,y2):

[tex]M=(\frac{x1+x2}{2},\frac{y1+y2}{2} )[/tex]

For this problem, E is (2,4) and F is (6,8). So, the midpoint would be:

[tex](\frac{2+6}{2},\frac{4+8}{2})=(\frac{8}{2},\frac{12}{2})=(4,6)[/tex]

Therefore, the midpoint is (4,6)

Math is literally so hard

Answers

Answer:

C

Step-by-step explanation:

negative exponent flips the fraction

4^2=16

x^2 becomes x^4

y becomes y^2

C

Sorry I didn’t know how to crop the photo

A Ski resort tracks the proportion of seasonal employees who are rehired each season. Rehiring a seasonal employee is beneficial in many ways, including lowering the costs incurred during the hiring process such as training costs. A random sample of 833 full-time and 386 part-time seasonal employees from 2009 showed that 434 full-time employees were rehired compared with 189 part-time employees (a) Is there a significant difference in the proportion of rehires between the full-time and part-time seasonal employees? (Use α = 0.10) (a-1) Choose the appropriate hypotheses. Assume TTF is the proportion of full-time employees and πrho is the proportion of part-time employees (a-2) Specify the decision rule. (A negative value should be indicated by a minus sign. Round your answers to 3 decimal places.)
(a-3) Find the test statistic Zcalc (Do not round the intermediate calculations. Round your answer to 3 decimal places.)

Answers

The test statistic z will be equal to -0.946 and it shows that there is no significant difference in the proportion of rehires between full time and part time.

Given sample sizes of 833 and 386 and result of samples 434 and 189.

[tex]n_{1} =833, n_{2}=386[/tex]

Proportion  of full time=434/833=0.52

Proportion of part time=189/386=0.49.

Difference in proportion =0.52-0.49

[tex]H_{0}:[/tex]TTF- i∈ rho=0

[tex]H_{1}:[/tex] TTF+i∈ rho≠0.

Mean of difference=0.03

Z=(X-μ)/σ

σ=[tex]\sqrt{0.4517/447}[/tex]

=0.0317

σ=0.0317

z=(0-0.03)/0.0317

=-0.03/0.0317

=-0.317

p value will be =0.1736.

Because p value is greater than 0.01 so we will accept the null hypothesis which shows that there is no significant difference in the proportions.

Hence there is no significant difference in the proportion of rehires between full time and part time.

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HURRY ANSWER NOW PLS
Which scenario is modeled by the equation (x) (0.6) = 86 dollars and 46 cents?
A. A picnic table is on sale for 60 percent off. The sale price of the picnic table is x, $144.10.
B. A picnic table is on sale for 40 percent off. The sale price of the picnic table is x, $144.10
C. A picnic table is on sale for 60 percent off. The original price of the picnic table is x, $144.10.
D. A picnic table is on sale for 40 percent off. The original price of the picnic table is x, $144.10

Answers

Using proportions, the scenario modeled by the equation 0.6x = 86.46 is:

D. A picnic table is on sale for 40 percent off. The original price of the picnic table is x, $144.10.

What is a proportion?

A proportion is a fraction of a total amount, and the measures are related using a rule of three.

When a product is 40% off, 100 - 40 = 60% of the original price x is paid, hence the expression for the price is:

0.6x.

In this problem, the expression is:

0.6x = 86.46

x = 86.46/0.6

x = 144.1.

Hence option D is correct.

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At a Phil's Cafe, a dinner meal is made up of an appetizer, a main course, a dessert and a drink. The choices for the appetizer are soup or salad; for the main course are chicken, fish, steak or lobster; for the dessert are ice cream, pie, sorbet, or a pastry; the drinks are coffee, tea or milk. How many different dinner meals are possible

Answers

The number of different meals possible is 96, computed using combinations.

The combination is a method of choosing a number of articles from a larger set of articles in no particular order.

In the question, we are asked about the different dinner meals possible when a dinner meal is made up of an appetizer, a main course, a dessert, and a drink.

The choices for the appetizer are soup or salad, so the number of ways of choosing an appetizer = 2C1 = 2.

The choices for the main course are chicken, fish, steak, or lobster, so the number of ways of choosing a main course = 4C1 = 4.

The choices for the dessert are ice cream, pie, sorbet, or pastry, so the number of ways of choosing a dessert = 4C1 = 4.

The choices for the drink are coffee, tea, or milk, so the number of ways of choosing a drink = 3C1 = 3.

The total number of ways is the product of all of them.

Therefore, the total number of ways = 2*4*4*3 = 96.

The number of different meals possible is 96, computed using combinations.

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What is the central idea of this passage? human beings are creative when they get into trouble. because of one man’s actions, whales never eat human beings. whales always have a sore throat because of a grating. human beings should stay away from whales to avoid being swallowed.

Answers

Answer:

B) Because of one man’s actions, whales never eat human beings.

Step-by-step explanation:

I'm pretty sure :P

Answer:

Because of one man’s actions, whales never eat human beings.

Step-by-step explanation:

i really need help before tomorrow, but my question is,
what is x⋅(-1)⋅(-x)⋅(1) simplified?
thanks!!

Answers

Answer:

[tex] \tt \: x.( - 1).( - x).(1)[/tex]

[tex] \longrightarrow \tt ( - x). (- x)[/tex]

[tex] \longrightarrow \boxed{\tt{x}^{2} }[/tex]

Our final answer : x^2

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Rowena is proving that AD ≅ EB. Which statement does the ♣ represent in her proof?

Triangles A C D and E C B are shown. Point B of triangle E C B is on side A C of triangle A C D. Point D of triangle A C D is on side C E of triangle E C B. Angles C A D and B E C are congruent. The lengths of line segments A B and D E are congruent. The lengths of line segments B C and C D are congruent.
ΔACD ≅ ΔECB
ΔACD ≅ ΔEFD
ΔAFB ≅ ΔEFD
ΔAFB ≅ ΔECB

Answers

Using the ASA congruence theorem, the missing statement in her proof is: A. ΔACD ≅ ΔECB.

What is the ASA Congruence Theorem?

Two triangles are congruent by the ASA congruence theorem if they have two pairs of corresponding congruent angles and a pair of included congruent sides.

In the proof given in the diagram, using the ASA congruence theorem, Rowena has been able to prove that ΔACD and ΔECB have two pairs of corresponding congruent angles and a pair of included congruent sides.

Therefore, the missing statement in her proof is: A. ΔACD ≅ ΔECB.

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Answer:

A   see picture

Step-by-step explanation:

Use the graph of the piecewise function to answer the question.

Over which intervals is the function decreasing?

Select all that apply.

x > 6

x ≤ -6

1 < x ≤ 5

-5 < x ≤ 1

5 < x ≤ 6

-6 < x ≤ -5​

Answers

The decreasing interval of the function are x ≤ -6, 1 < x ≤ 5 and x > 6

How to determine the decreasing interval?

From the given graph, the function value decrease at the following x values

Negative infinity to x = -6x = 1 to x = 5x = 6 to x = infinity

This can be properly represented as:

x ≤ -6, 1 < x ≤ 5 and x > 6

Hence, the decreasing interval of the function are x ≤ -6, 1 < x ≤ 5 and x > 6

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What term best describes 3x + 5?

Answers

Answer: Algebraic expression

Step-by-step explanation:

A spinner is spun that has 15 equal-sized sections numbered 1 to 15. What is the probability the spinner lands on a multiple of five?

Answers

Answer:

1/5

Step-by-step explanation:

P(event) = # of favorable outcomes / # of total outcomes. Multiples of 5 are 5, 10, 15, 20, 25, 30, 35, 40 ... and there are 3 multiples of 5 within 1 to 15. So the # of favorable outcomes is 3. # of total outcomes is 15 because there are 15 equal-sized sections.

P = 3/15 = 1/5

MATH HELP!!! 100PTS!!!

Let p(x)=2x−4 and r(x)=6x−1/9x+1.
Solve p(x)=r(x) for x exactly. If there is more than one answer, enter your exact solution(s) in a comma separated list.

Answers

Answer:

[tex]x =\dfrac{20 +\sqrt{454}}{18}, \quad \dfrac{20 -\sqrt{454}}{18}[/tex]

Step-by-step explanation:

Given functions:

  [tex]p(x)=2x-4[/tex]

  [tex]r(x)=\dfrac{6x-1}{9x+1}[/tex]

Solve for p(x) = r(x):

[tex]\begin{aligned}p(x) & = r(x)\\\implies 2x-4 & = \dfrac{6x-1}{9x+1}\\(2x-4)(9x+1)&=6x-1\\18x^2+2x-36x-4&=6x-1\\18x^2-40x-3&=0\end{aligned}[/tex]

As the found quadratic equation cannot be factored, use the Quadratic Formula to solve for x:

Quadratic Formula

[tex]x=\dfrac{-b \pm \sqrt{b^2-4ac} }{2a}\quad\textsf{when }\:ax^2+bx+c=0[/tex]

Therefore:

[tex]a=18, \quad b=-40, \quad c=-3[/tex]

Substitute the values of a, b and c into the quadratic formula and solve for x:

[tex]\begin{aligned}\implies x & =\dfrac{-(-40) \pm \sqrt{(-40)^2-4(18)(-3)} }{2(18)}\\\\& =\dfrac{40 \pm \sqrt{1816}}{36}\\\\& =\dfrac{40 \pm \sqrt{4 \cdot 454}}{36}\\\\& =\dfrac{40 \pm \sqrt{4}\sqrt{454}}{36}\\\\& =\dfrac{40 \pm2\sqrt{454}}{36}\\\\& =\dfrac{20 \pm\sqrt{454}}{18}\end{aligned}[/tex]

Therefore, the solutions are:

[tex]x =\dfrac{20 +\sqrt{454}}{18}, \quad \dfrac{20 -\sqrt{454}}{18}[/tex]

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13. A box contains about 250 marbles in 5 different colors. James selected a random sample of 30 marbles and counted 16 red, 5 blue, 5 green, 3 white, and 1 yellow.
Which statement is NOT a valid inference about all of the marbles in the box?

There is exactly 1 yellow marble in the box.

There are about 25 white marbles in the box.

There are about the same number of blue and green marbles.

There are more red marbles than any other color.

Answers

Answer:

Invalid statement: There is exactly 1 yellow marble in the box

Step-by-step explanation:

The probability of finding a yellow marble is Py = 1/30, according to the sample. Then, the number of yellow marbles expected to find in the box is:

N x Py > 1 ,

where N = 250 (number of marbles in the box).

Thus, we expect to find more than one yellow marble in the box and the Invalid statement is: "There is exactly 1 yellow marble in the box".

y≥-x+4 linear inequality graph

Answers

The slope m = -1 and the y-intercept = ( 0, 4 ).

The graph is a solid line, shaded area above the boundary line since y is greater than -x + 4.

What is the graph of the inequality?

Given that;

y ≥ -x + 4

First, we use the slope intercept form y = mx + b to determine the slope and y-intercept.

y ≥ -x + 4

y = mx + b

We can see that;

m = -1

b = 4

Hence, the slope m = -1 and the y-intercept = ( 0, 4 ).

The graph is a solid line, shaded area above the boundary line since y is greater than -x + 4.

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For two functions, a(x) and b(x), a statement is made that a(x) = b(x) at x = 2. What is definitely true about x = 2? (2 points) Group of answer choices Both a(x) and b(x) have a maximum or minimum value at x = 2. Both a(x) and b(x) have the same output value at x = 2. Both a(x) and b(x) cross the x-axis at 2. Both a(x) and b(x) cross the y-axis at 2.

Answers

The statement that is definitely true about x = 2 is Both a(x) and b(x) have the same output value at x = 2.

How to find the statement that is true about the functions a(x) = b(x) at x = 2?

If we have two functions a(x) and b(x), a statement is made that a(x) = b(x) at x = a, this implies that the values of the functions a(x) and b(x) are equal at x = a.

Given that the two functions a(x) and b(x), a statement is made that a(x) = b(x) at x = 2.

Then the statement that is definitely true about x = 2 is Both a(x) and b(x) have the same output value at x = 2.

So, the statement that is definitely true about x = 2 is Both a(x) and b(x) have the same output value at x = 2.

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Solve x ^ 2 + 13x + 22 = 0using the quadratic formula.

Answers

Answer:

x= -2, -11

Step-by-step explanation:

A company has two large computers. The slower computer can send all the company's email in minutes. The faster computer can complete the same job in minutes. If both computers are working together, how long will it take them to do the job

Answers

Both the computers will take 18 minutes to do the job together.

The slower computer sends all the company's email in 45 minutes.

The faster computer completes the same job in 30 minutes.

Let's take minutes t  to complete the task together.

As they complete one job, we get the following equation:

[tex]\frac{t}{45}[/tex]+[tex]\frac{t}{30}[/tex]=1

LCM of 45 and 30 is:

45 = 3 x 3 x 5

30 = 2 x 3 x 5

LCM = 2 x 3 x 3 x 5 = 90

Now, solving for t;

⇒[tex]\frac{2t+3t}{90} = 1\\\frac{5t}{90} =1\\5t=90\\[/tex]

Dividing both sides by 5;

[tex]\frac{5t}{5}=\frac{90}{5}[/tex]

We get t = 18

Hence, it will take both the computers 18 minutes to do the job together.

A company has two large computers. The slower computer can send all the company's emails in 45 minutes. The faster computer can complete the same job in 30 minutes. If both computers are working together, how long will it take them to do the job?

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The amount of soda in a half-liter bottle follows a normal distribution. Assume μ = 500 ml and σ = 10 ml. A government auditor will fine the company if a random sample of 5 bottles has a sample mean under 490 ml. Find the probability the company will be fined.

Answers

The probability that the company will be fined is 0.1587.

How to illustrate the probability?

From the information given, it was assumed that μ = 500 ml and σ = 10 ml.

Also, the random sample of 5 bottles has a sample mean under 490 ml.

Here, the probability will be:

= P(x < 490)

= P[(z < (490 - 500)/10]

= P (z < -10/10)

= P(z < -1)

Looking at this under the z table, the probability will be 0.1587

The probability is 0.1587.

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A scuba diver is 30 ft below sea level. Which of the following best describes this situation?
1. |30|
2. |-30|
3. -30
4. ±30

Answers

Answer is #3. -30
Reason
1 and 2 are absolute values so they are 30, the 4th answer is plus or minus, the question says “below sea level” which is a negative number so it is -30.

Which triangle is a 30°-60°-90° triangle?

Answers

Answer:

Option A

Step-by-step explanation:

30° - 60° - 90° triangle:

       The ratio of the side of 30-60-90 triangle is x : x√3 : 2x

 The angle opposite to 90° = 2x

            2x = 10

              x = 10÷2

               x = 5

The side opposite to 30° is x which is 5.

The side opposite to  60° is x√3 = 5√3

The ratio of sides of 30-60-90 triangle:

        5 : 5√3 : 10

Answer:

The first one is correct

Step-by-step explanation:

I got a 100 on the test, hope this helps

Determine the vertex of the quadratic relation y=2(x+2)(x-6)

Answers

Answer:

(2, -32)

Step-by-step explanation:

1) Expand them.

y = 2(x² - 6x + 2x - 12)

y = 2(x² - 4x - 12)

y = 2x² - 8x - 24.

2) Complete the square to find the vertex.

y = 2([x² - 4x)] - 24

y = 2[(x - 2)² - 4] - 24

y = 2(x - 2)² - 8 - 24

y = 2(x - 2)² - 32

The vertex: (2, -32)

or you can use this: x = -b/2a

x = -(-8)/2(2)

x = 8/4

x = 2

Substitute the value into the original equation for y.

y = 2(2)² - 8(2) - 24

y = 2(4) - 16 - 24

y = 8 - 16 - 24

y = -32

Vertex: (2, -32)

Answer:

  (2, -32)

Step-by-step explanation:

The vertex of the graph of a quadratic equation is on the line of symmetry, halfway between the x-intercepts. It can be found by evaluating the equation at that point.

Line of symmetry

The given function is written in factored form, so the x-intercepts are easy to find. They are the values of x that make the factors zero:

  (x +2) = 0   ⇒   x = -2

  (x -6) = 0   ⇒   x = 6

The midpoint between these values of x is their average:

  x = (-2 +6)/2 = 4/2

Then the x-coordinate of the vertex, and the equation of the line of symmetry is ...

  x = 2

Vertex

Using this value of x in the quadratic relation, we find the y-value at the vertex to be ...

  y = 2(2 +2)(2 -6) = 2(4)(-4)

  y = -32

The coordinates of the vertex are (x, y) = (2, -32).

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