find the most general antiderivative of the function. (check your answer by differentiation. use c for the constant of the antiderivative.) f(x) = x2 − 5x 8

Answers

Answer 1

This is the same as the original function, so the antiderivative is correct.

The function is given as f(x) = x² - 5x + 8.

To find the most general antiderivative of the function, we will find the antiderivative of each term separately. Antiderivative of x² = (x³/3) Antiderivative of -5x = (-5x²/2) Antiderivative of 8 = (8x)

Therefore, the most general antiderivative of the function is:(x³/3) - (5x²/2) + 8x + c, where c is the constant of the antiderivative. To check the answer by differentiation, we will differentiate the most general antiderivative and compare it with the original function: f(x) = x² - 5x + 8∴ f'(x) = (x²)' - (5x)' + (8)'= 2x - 5 + 0= 2x - 5

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Related Questions

Someone help me pleaseee I’m so behind my work

Someone help me pleaseee Im so behind my work

Answers

simplify each expression.

1. 3 (x- 5) +8 x +1 =

13x−24

2.  5 (n+6) -21 =

5n+9

I could solve more but i need a bigger page I can't see half of the words.

Calculate the correlation coefficient of the following data:
X
1
4
8
6
2
y
9
16
22
24
12

Answers

Answer:

0.177

Step-by-step explanation:

A perfect correlation is 1. So .998 or even .863 is a good correlation.

since our decimal isn't close to that at all, we have a weak positive correlation.

Solve these problems.​

Solve these problems.

Answers

The area of the triangles in the picture are

1. 17.5 square units

2. 5 square units

3. 10 square units

How to find the area of the triangles

The formula for area of triangles is given by

= 1/2 * base * height

1.

base = 5

height = 7

= 1/2 * 5 * 7

= 17.5 square units

2.

base = 5

height = 2.1

= 1/2 * 5 * 2.1

= 5.25 square units

3.

base = 4

height = 4

= 1/2 * 4 * 5

= 10 square units

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A $99 skateboard is on sale for 10% off. How
much is it on sale for?

Answers

Answer:

89.10 trust me

Step-by-step explanation:

trust me bro

90% of $99 is $89.10

Which of the following is not included in the cost of merchandise inventory? O Purchase discounts. O Purchase returns and allowances. O Purchase price of the inventory. O Freight costs paid by the seller. O Freight costs paid by the buyer. 4 pts 0 Question 2 Sunshine Cleaning purchased $3,500 worth of merchandise. The seller offered a 2% cash discount. Transportation costs for the buyer were an additional $310. The company returned $240 worth of merchandise and then paid the invoice within the discount period. The total cost of this merchandise is: O $3.570.00. O $3,500.00 O $3,332.00 O $3,430.00. $3,504.80 Question 5 A company has not sales of $759.300 and cost of goods sold of $548.300. Its not income is $10.280. The company's gross margin and operating expenses, respectively, are: O $211.000 and $230,750 $739.550 and $191,720 O $529,020 and $230.750 O $211.000 and $191,720 $230,750 and $529,020 4 pts D D Question 5 A company has not sales of $750,300 and cost of goods sold of $548,300. Its not income is $10.280 The company's groas margin and operating expenses, respectively, arm O $211,000 and $230,750 O $739,550 and $191,720 $529,020 and $230,750 O $211.000 and $191,720 O $230.750 and $529,020 Question 6 Sales less sales discounts, less sales returns and allowances equals: Cost of Goods Sold Net Income O Net Sales O Gross Profit 4 pts 4 pts Goods in transit are included in a purchaser's inventory: O At any time during transit. O After the half-way point between the buyer and seller, When the supplier is responsible for freight charges. When the goods are shipped FOB shipping point. OIf the goods are shipped FOB destination. Question 11 The inventory costing method that smooths out erratic changes in costs is: O LCM. O FIFO. OLIFO. O Specific Identification. O Weighted average. 4 t ne 0 Question 12 Krusty Krab has the following products in its ending inventory Compute lower of cost or market for inventory. applied separately to each product Inventory by Product Product Quantity Cost per Unit 500 $ 500 $ 30 600 Scuba Masks Scuba Sults O $265,000 O $290,000. O $250,000 $268,000 O $275,000. Question 13 Market per Unit $ 550 $ 25 If equity is $368,000 and liabilities are $186,000, then assets equal: O $554,000. $922,000. $368,000. $186,000. O $182,000. 2 pts

Answers

Question 1: The item not included in the cost of merchandise inventory is "Purchase discounts."

2: The total cost of the merchandise is $3,332.00.

5: The company's gross margin and operating expenses, are $211,000 and $191,720.

What is the cost of merchandise inventory?

Merchandise inventory expenses normally consist of the price paid for the inventory, deductions from the purchase price resulting from purchase returns and allowances, and freight expenses paid by the purchaser.

Although purchase discounts reduce the cost of merchandise inventory, they are not considered part of it. Instead, they are treated as a distinct discount in the accounting records.

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1 point) find a basis of the subspace of r3 r3 defined by the equation −3x1−3x2−8x3=0−3x1−3x2−8x3=0. basis: {{ ⎡⎣⎢⎢⎢⎢⎢⎢[ ⎤⎦⎥⎥⎥⎥⎥⎥], ⎡⎣⎢⎢⎢⎢⎢⎢[ ⎤⎦⎥⎥⎥⎥⎥⎥] }.

Answers

A basis for the subspace is {{1,0,-3/8}, {0,1,-3/8}}. This can be answered by the concept from Sets.

To find a basis of the subspace of R3 defined by the equation −3x1−3x2−8x3=0, we can first rearrange the equation as x3 = (-3/8)x1 - (3/8)x2.

Then we can rewrite the subspace as Span{{1,0,-3/8}, {0,1,-3/8}} since these two vectors span the subspace of solutions to the equation.

Therefore, a basis for the subspace is {{1,0,-3/8}, {0,1,-3/8}}.

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What is the answer?
A?
B?
C?
D?

What is the answer? A?B?C?D?

Answers

Answer:B or C

Step-by-step explanation:

Answer:

c

Step-by-step explanation:

Find the slope of the line represented by the data below x| 0 2 4 6 8
y|15 9 3 -3 -9
Slope=[?]

Find the slope of the line represented by the data below x| 0 2 4 6 8 y|15 9 3 -3 -9Slope=[?]

Answers

Answer:

it's answer is 10/-15.........

Twenty-Five Decreased By One Fifth Of A Number Is Eighteen. Find The Number.

Answers

25 decreased by 1/5 of a number=18, it would be 1/5 of 115

The equation of the given condition is written as 25 - (1/5)x = 18. And the solution of the equation will be 35.

What is the solution to the equation?

The allocation of weights to the important variables that produce the calculation's optimum is referred to as a direct consequence.

The act of converting a specified statement into an expression or equation is known as a sentence-to-equation transformation.

Twenty-Five Decreased By One-Fifth Of A Number Is Eighteen.

Let the number be 'x'. Then the equation is given as,

25 - (1/5)x = 18

Simplify the equation, then the value of the variable 'x' is calculated as,

25 - (1/5)x = 18

(1/5)x = 25 - 18

(1/5)x = 7

x = 7 (5)

x = 35

The equation of the given condition is written as 25 - (1/5)x = 18. And the solution of the equation will be 35.

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the common factor of 6x 66xy​

Answers

Answer:

6x and 1x or x

Step-by-step explanation:

the highest common factor of 6x and 66xy in 6x

6x ÷ 6x = 1

66xy ÷ 6x = 11y

the lowest common factor of 6x and 66xy is 1x or x

6x÷ 1x =6

66xy÷ 1x = 66y

6x÷ x = 6

66xy ÷ x = 66y

NOTE

1x and x is the same

Which system of equations is equivalent to this system? 5x+10=3(x+y) x+7=3x+7

Answers

Answer:

In equation form the answer is x=0y=10/3 but in point form the answer is (0,10/3)

Step-by-step explanation:

A quadratic equation can be written in vertex form or standard form. Sometimes one form is more beneficial than the other. Identify which form would be more helpful if you needed to do each task listed below and EXPLAIN why.
a. factor the equation
b. graph the parabola
c. identify the vertex, minimum, or maximum of the parabola
d. solve the equation using the quadratic formula

Answers

Answer: Any really

Step-by-step explanation:

a) Factor:

.. (x -h +√(-k/a)) * (x -h -√(-k/a))

b) Graph:

.. It is a graph of y=x^2 with the vertex translated to (h, k) and vertically stretched by a factor of "a".

c) Vertex and Extreme:

.. The vertex is (h, k). It is a maximum if "a" is negative; a minimum otherwise.

d) Solutions:

.. The quadratic formula is based on the notion of completing the square. In vertex form, the square is already completed, so the roots are

.. x = h ± √(-k/a)

Use the equation below to find y, if m= 10, x= 3, and b = 8.
y=mx+b

Answers

Answer:

y = 38

Step-by-step explanation:

y=mx+b

y = 10 x 3 + 8

y = 30 + 8

y = 38

Can you help me plz!
I hope you can see it

Can you help me plz!I hope you can see it

Answers

Step-by-step explanation:

a. 102

b. 78

c. 102

d. 102

e. 102

f. 78

in infant's Tylenol, 5 ml contains 160 mg of Acetaminophen. If you child's pediatrician says that your child can take 48 mg of Acetaminophen, how many milliliters (ml) should you give the child?​

Answers

The amount of milliliters (ml) you should give the child is 1.5 ml

How to determine how many milliliters (ml) you should give the child?​

The given parameters are:

infant's Tylenol, 5 ml = 160 mg

This can be represented as

5 ml = 160 mg

Let the number of ml to give a child that requires 48 mg be x

So, we have:

5 ml = 160 mg

x = 48 mg

Cross multiply

x * 160 = 48 * 5 ml

Divide both sides by 160

x = 1.5 ml

Hence, the amount of milliliters (ml) you should give the child is 1.5 ml

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find the indicated maximum or minimum value of f subject to the given constraint.maximum: f(x,y,z)=x^2y^2z^2; x^2 y^2 z^2=6

Answers

For the function f(x, y, z) = x^2y^2z^2, subject to the constraint x^2y^2z^2 = 6, there is no maximum value. The function f(x, y, z) does not have a maximum value since the constraint equation x^2y^2z^2 = 6 does not impose any upper limit on the variables x, y, and z.

To find the maximum or minimum value of the function f(x, y, z) = x^2y^2z^2 subject to the constraint x^2y^2z^2 = 6, we can use the method of Lagrange multipliers. However, in this case, the constraint equation x^2y^2z^2 = 6 does not impose any upper limit on the variables x, y, and z. This means that the function f(x, y, z) does not have a maximum value within the given constraint.

The constraint equation only restricts the values of x, y, and z to satisfy x^2y^2z^2 = 6, but it does not bound them from above. As a result, the function f(x, y, z) can increase indefinitely as x, y, and z approach infinity, and therefore, there is no maximum value.

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PLEASE HELP ME ASAP URGENTLY

PLEASE HELP ME ASAP URGENTLY

Answers

Hello!

it's the Thalès theorem

CB'/CB = CA'/CA = B'A'/BA

7/CB = 6/(6+3) = 5/BA

7/CB = 6/9 = 5/BA

CB = 7 x 9 ÷ 6 = 10.5

BA = 5 x 9 ÷ 6 = 7.5

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

Find f(7)

Answers

Answer:

7−x2−3x

Step-by-step explanation:

sorry if it's not right

5y - 4x = -7
2y + 4z = 14
Solve for x and y

Answers

Answer:

et's solve for x.

5y−4x=−72y+4z

Step 1: Add -5y to both sides.

−4x+5y+−5y=−72y+4z+−5y

−4x=−77y+4z

Step 2: Divide both sides by -4.

−4x

−4

=

−77y+4z

−4

x=

77

4

y−z

Answer:

x=

77

4

y−z

Let's solve for y.

5y−4x=−72y+4z

Step 1: Add 72y to both sides.

−4x+5y+72y=−72y+4z+72y

−4x+77y=4z

Step 2: Add 4x to both sides.

−4x+77y+4x=4z+4x

77y=4x+4z

Step 3: Divide both sides by 77.

77y

77

=

4x+4z

77

y=

4

77

x+

4

77

z

Answer:

y=

4

77

x+

4

77

z

Step-by-step explanation:

I think that can help :) wanna chat add me as  friend

Answer:

1.)x=5/4y+7/4

2.) y=−2z+7

Step-by-step explanation:

Find the percent of each number
350% of 96

Answers

Answer:

336

Step-by-step explanation:

\( \frac{350}{100} \times 96 = 336\)

convert 350% in to 3.5 and the multiple 3.5 x 96 = 336 and you get your answer

the price of a gallon of regular gasoline at 75 gas stations acoss the state is normally distrubuted wuith a mean of $2.05 and a standard deviavtion of 4
a) What percent of gas stations sell a gation of regular gas for less than $1.973
b) What percent of gas stations sell a gallon of regular gas for at least $2.17?
c) What is the probability that a gas station sells gallon of regular gas for less than $1.97 or greater than $2.05?
d) About how many stations sell a gallon of regular gas for no more than $2.013

Answers

The estimated number of stations selling gas for no more than $2.013 is approximately 0.1772 times 75, which is about 13.29, rounded to the nearest whole number, or 13.

To find the percentage of gas stations that sell a gallon of regular gas for less than $1.973, we need to standardize this value using the formula z = (x - mu) / sigma, where x is the value of interest, mu is the mean, and sigma is the standard deviation.

Thus, z = (1.973 - 2.05) / 0.04 = -1.925. Using a standard normal distribution table or calculator, we find that the percentage of gas stations selling gas for less than $1.973 is about 2.28%.

To find the percentage of gas stations selling gas for at least $2.17, we again standardize the value using z = (x - mu) / sigma. Thus, z = (2.17 - 2.05) / 0.04 = 3.00.

Using a standard normal distribution table or calculator, we find that the percentage of gas stations selling gas for at least $2.17 is about 0.14%.

To find the probability that a gas station sells gas for less than $1.97 or greater than $2.05, we need to calculate the z-scores for both values and use the standard normal distribution table or calculator to find the probabilities. Thus, z1 = (1.97 - 2.05) / 0.04 = -2.00 and z2 = (2.05 - 2.05) / 0.04 = 0.00.

The probability of a gas station selling gas for less than $1.97 is about 0.0228, and the probability of selling gas for greater than $2.05 is about 0.5. Therefore, the probability of selling gas for less than $1.97 or greater than $2.05 is approximately 0.0228 + 0.5 = 0.5228.

To estimate the number of stations selling gas for no more than $2.013, we need to standardize this value using the z-score formula and then use the standard normal distribution table or calculator to find the probability.

Thus, z = (2.013 - 2.05) / 0.04 = -0.925. Using a standard normal distribution table or calculator, we find that the probability of selling gas for no more than $2.013 is about 0.1772. Therefore, the estimated number of stations selling gas for no more than $2.013 is approximately 0.1772 times 75, which is about 13.29, rounded to the nearest whole number, or 13.

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About 2.74% of gas stations sell a gallon of regular gas for less than $1.973.

About 0.13% of gas stations sell a gallon of regular gas for at least $2.17.

The probability that a gas station sells a gallon of regular gas for less than $1.97 or greater than $2.05 is 2.28% + 50% = 52.28%.

About 17.88% of gas stations sell a gallon of regular gas for no more than $2.013, which is approximately 0.1788 x 75 = 13.41 or about 13 stations.

a) We need to find the area to the left of $1.973. z-score for $1.973 is given by:

z = (x - μ) / σ = (1.973 - 2.05) / 0.04 = -1.925

Using a standard normal table or calculator, we can find that the area to the left of z = -1.925 is 0.0274 or 2.74%.

b) We need to find the area to the right of $2.17. z-score for $2.17 is given by:

z = (x - μ) / σ = (2.17 - 2.05) / 0.04 = 3

Using a standard normal table or calculator, we can find that the area to the right of z = 3 is 0.0013 or 0.13%.

c) We need to find the area to the left of $1.97 and the area to the right of $2.05, and add them up. z-scores for $1.97 and $2.05 are given by:

z1 = (x1 - μ) / σ = (1.97 - 2.05) / 0.04 = -2

z2 = (x2 - μ) / σ = (2.05 - 2.05) / 0.04 = 0

Using a standard normal table or calculator, we can find that the area to the left of z = -2 is 0.0228 or 2.28%, and the area to the right of z = 0 is 0.5 or 50%.

d) z-score for $2.013 is given by:

z = (x - μ) / σ = (2.013 - 2.05) / 0.04 = -0.925

Using a standard normal table or calculator, we can find that the area to the left of z = -0.925 is 0.1788 or 17.88%.

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which statement about equations and expressions is true? an example of an equation is because it shows that two expressions are equal. an example of an expression is because it shows that two equations are equal. an example of an equation is because it is a mathematical phrase represented by numbers, a variable, and an operation. an example of an expression is because it is a mathematical phrase represented by numbers, a variable, and an operation.

Answers

The statement that is true about equations and expressions is that an example of an equation is because it shows that two expressions are equal.

While an example of an expression is because it is a mathematical phrase represented by numbers, a variable, and an operation.

An equation is a mathematical statement where two expressions are equal. It's important to note that an equation has an equals sign, so the left side of the equation is equal to the right side of the equation.

Expressions are combinations of numbers, symbols, and operators that represent a value. A symbol or letter that represents a value is a variable. It's important to note that an expression does not have an equals sign, so the value of the expression is not defined.Why is an example of an equation true?An equation can be written in the form x = y. The equals sign indicates that x and y are equal. This means that two expressions, x and y, are equal. Therefore, an equation shows that two expressions are equal.

An example of an equation is 3x + 4 = 10. This equation is an example of an equation because it shows that two expressions, 3x + 4 and 10, are equal. The left side of the equation (3x + 4) equals the right side of the equation (10). Therefore, this statement is true: "An example of an equation is because it shows that two expressions are equal."

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two dice are rolled in a random experiment. (a) what is the probability that at most one is a six? (1 point) (b) if the two faces are different, what is the probability that at most one is a six?

Answers

a) The probability that at most one is a six is 5/6.

b) The probability that at most one is a six is 2/3.

In the question two dice are rolled in a random experiment and we have to find what is the probability that at most one is a six and if the two faces are different, what is the probability that at most one is a six.

a) The probability that at most one is a six is 5/6. There are only 6 possible outcomes when rolling two dice, and 5 of those outcomes involve at most one six: (1,2), (1,3), (1,4), (1,5), (2,5).

b) The probability that at most one is a six is 2/3. If the two faces are different, there are only 3 possible outcomes: (1,2), (2,3), (3,4). 2 of those outcomes involve at most one six: (1,2), (2,3). Thus, the probability is 2/3.

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3. Which three lengths could be the lengths of the sides of a triangle?

A.) 10 cm, 14 cm, 23 cm
B.) 9 cm, 22 cm, 11 cm
C.) 7 cm, 25 cm, 11 cm
D.) 6 cm, 22 cm, 10 cm

Answers

Answer:

  A.) 10 cm, 14 cm, 23 cm

Step-by-step explanation:

The sum of the two shortest lengths must exceed the longest length for the lengths to be able to form a triangle. This is only the case for ...

  A.) 10 cm, 14 cm, 23 cm . . . . . 10+14=24>23

__

The other choices don't make it:

  B.) 9+11=20<22

  C.) 7+11=18<25

  D.)6+10=16<22

A researcher is investigating the effect of sleep deprivation on learning. She recruits 30 participants and randomly assigns half to a "no sleep" group and half to a "regular sleep" group. The "no sleep" group are required to stay up all night and report to a testing room at 2PM the following day. The "regular sleep" group are instructed to have a normal night's sleep and report to the testing room at 9AM the following day. Unfortunately, a water pipe broke outside the testing room window and there was noisy construction crew working the whole day of testing. Which of the following statements is true?
a. The study may be affected by a situational variable.
b. The construction noise may contribute to variability in test scores.
C. The study has a confounding variable. The groups differ in the time they are to report to the testing room.
d. All of these are true.

Answers

The study has a confounding variable since the two groups differ in the time they were supposed to report to the testing room. Since the groups differed in terms of sleep deprivation and the time they were supposed to report to the testing room, the effect of sleep deprivation on learning could not be isolated.

The statement that is true is: d. All of these are true.Explanation:A study may have various sources of variability, including participant selection, the setting in which the study is conducted, and the measure used. The following options are as follows:a. The study may be affected by a situational variable.b. The construction noise may contribute to variability in test scores.c. The study has a confounding variable. The groups differ in the time they are to report to the testing room.d. All of these are true.Therefore, all of these options are true. For example, the study may be affected by a situational variable if a natural disaster or other unforeseen event happens that causes the study to be disrupted. In this case, the study was disrupted by a noisy construction crew, which may have contributed to variability in test scores. The study has a confounding variable since the two groups differ in the time they were supposed to report to the testing room. Since the groups differed in terms of sleep deprivation and the time they were supposed to report to the testing room, the effect of sleep deprivation on learning could not be isolated.

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If she has enough or not

If she has enough or not

Answers

Answer:

enough is the correct worf

(2.9x10^3)-(6.4x10^-1)

Answers

Not sure if this is correct but I got 2899.36
Hope this helps!

a scatterplot shows: a. the average value of groups of data. b. scores on one variable plotted against scores on a second variable. c. the frequency with which values appear in the data d. the proportion of data falling into different categories.

Answers

Scores on one variable plotted against scores on a second variable.

The correct answer is (b)

Now, According to the question:

Let's know:

A scatterplot shows:

A scatterplot shows the relationship between two quantitative variables measured for the same individuals. The values of one variable appear on the horizontal axis, and the values of the other variable appear on the vertical axis. Each individual in the data appears as a point on the graph.

Hence, The correct answer is (b) i.e.,

Scores on one variable plotted against scores on a second variable.

Given,

In the question:

A scatterplot shows:

a. the average value of groups of data.

b. scores on one variable plotted against scores on a second variable.

c. the frequency with which values appear in the data

d. the proportion of data falling into different categories.

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Data was collected on​ h, the number of hot dogs​ sold, and​ p, the number of people attending a fair over a two week period. The least squares regression line has equation 0. 6p10. 0. The residual for the day when 520 people attended was 35. How many hot dogs were sold that​ day?.

Answers

There were 357 dogs that were sold that day.

What is least squares regression line?

The line that best matches a linear connection between two variables in data is called a least-squares regression line because it minimizes the vertical distance between the data points and the regression line.

The given equation is,

y = 0.6p + 10.0

The residual for the day when 520 people attended was 35.

So, p = 520.

Plug 520 in the above equation, we get

y = 0.6(520) + 10.0

y = 312 + 10

y = 322

As, people attended was 35

So,

y = 322 + 35

y = 357

Hence, there are 357 dogs are sold that day.

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Solvethefollowing:a) 7 − 4 + 12 = 2 + 8b) 14 + 15 − 9 + 1 = −7 + 1 − 9c) 4 − 10 = 8( + 2)

Answers

(a)\(7x-4x+12=2x+8\)

First, we subtract 2x on each side.

\(\begin{gathered} 7x-4x-2x+12=2x-2x+8 \\ x+12=8 \end{gathered}\)

Then, we subtract 12 on each side.

\(\begin{gathered} x+12-12=8-12 \\ x=-4 \end{gathered}\)The solution is -4.

(b)\(14x+15x-9+1=-7x+1-9\)

We sum 7x on each side.

\(\begin{gathered} 14x+15x+7x-9+1=-7x+7x+1-9 \\ 36x-8=-8 \end{gathered}\)

Then, we add 8 on each side.

\(\begin{gathered} 36x-8+8=-8+8 \\ 36x=0 \end{gathered}\)

At last, we divide the equation by 36.

\(\begin{gathered} \frac{36x}{36}=\frac{0}{36} \\ x=0 \end{gathered}\)The solution is 0.

(c)\(4x-10=8(x+2)\)

First, we use the distributive property.

\(4x-10=8x+16\)

Then, we subtract 8x on each side.

\(\begin{gathered} 4x-8x-10=8x-8x+16 \\ -4x-10=16 \end{gathered}\)

Now, we add 10 on each side.

\(\begin{gathered} -4x-10+10=16+10 \\ -4x=26 \end{gathered}\)

At last, we divide the equation by -4.

\(\begin{gathered} \frac{-4x}{-4}=\frac{26}{-4} \\ x=-6.5 \end{gathered}\)The solution is -6.5.
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