Solve the equation. Show all steps of your work and justify each step with an algebraic property of equality.
4x-8/2=10

Write the phrase as an expression the quotient of 22 and a number [tex]a[/tex].The quotient of 22 and  [tex]a[/tex]  number = 22/[tex]a[/tex]

Given that

number = 22

quotient =   [tex]a[/tex]

To find

The mathematical equation or relation between quotient of 22 and a number [tex]a[/tex].

So according the question

We have

quotient = 22

divisor =   [tex]a[/tex]

For finding the relation between given quotient and divisor, let's firstly know about Dividend, Divisor, Quotient and Remainder,

In Mathematics, the dividend is the value that is divided by another value to get the result. The dividend is the base of any division method.

An integer that divides another integer to obtain a result is called a divisor. The result of this division, or quotient, is the dividend, which is the original number that was divided.

Quotient = Dividend ÷ Divisor

When we divide one number by another, the result is a quotient. As an illustration, when we divide 6 by 3, we obtain the answer 2, which is the quotient. A decimal or an integer can both be used as the quotient. When dividing exactly, as when 10 ÷5 = 2, the quotient is an integer, whereas when dividing roughly, as when 12÷ 5 = 2.4, the quotient is a decimal. Although a quotient can be greater than the divisor, it will never be greater than the dividend.

The value remaining after division is known as the Remainder. After division, we are left with a value if a number (dividend) cannot be divided entirely by another number (divisor). This value is called the remainder.

Now, from question  

We have a quotient of 22 that is [tex]a[/tex].

So, 22 fully divided by [tex]a[/tex].

In mathematical form,

                        = 22/[tex]a[/tex]

The quotient of 22 and [tex]a[/tex]  number = 22/[tex]a[/tex]

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The coordinates of the midpoint is M(x, y) = (17, 27) and its length is 6√34 units.

In this problem we have the coordinates of two endpoints of a line segment, of which we must find the location of its midpoint by using the midpoint formula, whose vector form shall be used. Later, we determine the length of the line segment by calculating the vector behind the line segment and its magnitude.

If we know that P(x, y) = (26, 12) and Q(x, y) = (8, 42), then the location of its midpoint and its length are, respectively:

Midpoint

M(x, y) = 0.5 · P(x, y) + 0.5 · Q(x, y)

M(x, y) = 0.5 · (26, 12) + 0.5 · (8, 42)

M(x, y) = (13, 6) + (4, 21)

M(x, y) = (17, 27)

Length

PQ = (8, 42) - (26, 12)

PQ = (- 18, 30)

PQ = √[(- 18)² + 30²]

PQ = 6√34

The coordinates of the midpoint is M(x, y) = (17, 27) and its length is 6√34 units.

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63,482.50-100,000=63,382.50                                                            

Answer:

Step-by-step explanation:

multiply the value in grains by the conversion factor '64.798'.

So, 50 grains = 50 × 64.798 = 3239.900 milligrams.

round 3240

Using the distance formula, the approximate distance between the points (1, -2) and (-9, 3) is: 11 units.

To find the distance of two points on a coordinate grid, the distance formula that is employed is: d = [tex]\sqrt{(x_2 - x_1)^2 + (y_2 - y_1)^2}[/tex].

Given the points are on a coordinate grid:

(1, -2) = (x1, y1)

(-9, 3) = (x2, y2)

Plug in the  values into the distance formula:

d = √[(−9−1)² + (3−(−2))²]

d = √[(−10)² + (5)²]

d = √(100 + 25)

d = √125

d = 11.18034

d ≈ 11 units.

Therefore, using the distance formula, the approximate distance between the points (1, -2) and (-9, 3) is: 11 units.

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The numbers that neither terminate nor repeat are called irrational numbers.

What are irrational numbers?

Any real number that is not rational is called an irrational number. These numbers can not be expressed in the form of p/q, where q is not equal to 0. Sometimes, irrational numbers are also called non-terminating and non-repeating numbers.

Filling the blank with an appropriate term

The decimal representation of ___Irrational__ number neither terminates nor repeats.

Hence, the answer is irrational.

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The solution to the given  equation is 8±2√2 i

An algebraic expression in mathematics is an expression which is made up of variables and constants, along with algebraic operations

Given the equation below

(x - 8)^2 = -8

Take the square root of both sides to have:

√(x-8)^2 = √-8

x-8 = ±√-8

x-8=±2√2 i

x = 8±2√2 i

Hence the solution to the given  equation is 8±2√2 i

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Answer:12.3cm 4.5cm=

≈782.49

Step-by-step explanation:

V=πr2h=π·4.52·12.3≈782.49219

The coordinates of the midpoint of a segment with the given endpoints (-8.4, -5.6)

The endpoints are given as

J(-11.2,-3.4), K(-5.6,-7.8)

The coordinates of the midpoint is calculated as

Midpoint = 0.5(x1 + x2, y1 + y2)

So, we have

Midpoint = 0.5(-11.2 - 5.6, -3.4 - 7.8)

This gives

Midpoint = (-8.4, -5.6)

Hence, the coordinates of the midpoint of a segment with the given endpoints (-8.4, -5.6)

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Approximately 1 hour She plays soccer in a year.

Soccer on CBS Sports is various TV programs that have broadcasted soccer matches in the US on CBS, CBS Sports Organization, and Paramount+. These matches are from Global, European, and American contests. Affiliation football, all the more usually known as just football or soccer, is a group activity played between two groups of 11 players who essentially utilize their feet to impel the ball around a rectangular field called a pitch. Soccer, or football as it's known beyond North America, is the most famous game on the planet. Thus, how could it be played, who plays it, and a lot more inquiries are responded to here.

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Answer:

p = 12

Step-by-step explanation:

Angles in a straight line sum to 180 degrees. Given the two algebraic angles, this can be expressed as follows:

(6p + 3) + (9p - 3) = 180

Take out the brackets:

6p + 3 + 9p - 3 = 180

Combine the like terms:

15p = 180

Divide both sides by 15:

p = 180/15

Simplify:

p = 12

If you want to verify the answer is correct, substitute it back into the original equation:

(6(12) + 3) + (9(12) - 3) = 180

The smaller angle made by the hour hands of a clock at a given time is 137°30'. It is attained by using the concept of clocks on the problems.

What is a clock?

A clock is a device which is used for measuring and indicating the time. It has three hands, namely an hour hand, a minute hand and a second hand. A clock can be classified in two ways, one is a 12-hour clock and the other is a 24-hour clock.

Calculation of the smaller angle made by the hour hand  

For minute hand,

60 min makes an angle 360°

1 min = 6°

25 min = 6° × 25

= 150°

For hour hand,

12 hours makes an angle 360°

1 hour = 30°

1 min = 30° / 60

= 1/2°

25 min = 1/2° × 25

= 12°30'

The smaller angle made by hour hand is given by 150° - 12°30'

=137°30'

Hence, the smaller angle between the hour hands is 137°30'.

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Answer: 27

Step-by-step explanation:

The experimental probability that all three of the coins will be head is 1 / 10.

The theoretical probability that all three of the coins will be head is 1/8.

Probability determines the chances that an event would happen. The probability the event occurs is 1 and the probability that the event does not occur is 0.

The more likely the event is to happen, the closer the probability value would be to 1. The less likely it is for the event not to happen, the closer the probability value would be to zero.

Experimental probability is based on the result of an experiment that has been carried out multiples times.

Experimental probability = number of times all heads is gotten / total number of tosses

5/50 = 1/10

Theoretical probability = number of times all heads can be gotten / total number of possible outcomes

1/8

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The area of the rectangle is 576.

An area is the total amount of space enclosed by a shape or figures. In this case, the rectangle would be the shape or figure that is being defined and its area would be the total amount of space enclosed by it.

The length of the rectangle is 13 less than 2 and a half times its width means : L=2 [tex]\frac{1}{2}[/tex] w-13

Using the perimeter formula of the rectangle P= 2(L-W) we have

P=100

So

100=2(2( [tex]\frac{1}{2}[/tex])w-13+w)

Solve for W:

100= 2×[tex]\frac{5}{2}[/tex]w-26+2w

100=10/2w-26+2w

100=5w-26+2w

100=7w-26

100+26=7w

126=7w

126/7=w

W=18

We can find the length L=2 [tex]\frac{1}{2}[/tex]w-13 = [tex]\frac{5}{2}[/tex](18) -13

=45-13

L= 32

Area of the rectangle is A= L×W= 32×18=576

Hence, the area of rectangle is 576.

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Bro each ticket is 4$. You just divide the money she earned with how much a ticket costs;

284/4 = 71 tickets

By unitary method we can say that it is better to buy the 4 inch radius pizza for $3.

According to the given question.

The price of 4 inch radius pizza = $3

And, the price of 8 inch radius pizza = $14

As we know that, the unitary method is a technique for solving a problem by first finding the value of a single unit, and then finding the necessary value by multiplying the single unit value.

Therefore, by unitary method.

Cost of 1inch radius pizza, when the price of 4 inch radius pizza is $3

= 3/4

= $0.75

And the cost of 1 inch radius pizza, when the price of 8 inch radius pizza is $ 14

= 14/8

= $ 1.75

Hence, by unitary method we can say that it is better to buy the 4 inch radius pizza for $3.

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Answer: 6

Step-by-step explanation:

A. The integer that represents the change of altitude to avoid the storm is 8,000

B. The integer representing the altitude after passing the storm is 30,000

A. We are given that the initial altitude of the plane was 30,000 ft. The plane flew at at altitude of 38,000 feet

Change of altitude = final altitude - initial altitude

Change of altitude = 38,000 - 30,000 = 8,000 ft

Therefore, the integer representing the change of altitude to avoid the storm is 8,000

B. After the storm:

We know that, after the storm, the plane returned to its initial altitude. Given that the initial altitude is 30,000 ft, this would mean that the integer representing the altitude after passing the storm is 30,000

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Answer:

10.375ft/s

Step-by-step explanation:

We need to read the number from the plot. The range from 10 to 11 is divided into 8 segments, so each segment is (11-10)/8=0.125

The answer is at 10 + 3 segments, so 10 + 3*0.125 = 10.375

The equation representing total cost of the shirt is c = 1.06p.

As per the question, we are representing the total cost of the shirt as c and price of the shirt as p.

Calculating sales tax on the shirt -

Sales tax = p × 6%

Converting percentage to fraction and hence decimal form

Sales tax = p× 6/100

Sales tax = 0.06p

Forming the equation now -

Total cost = price of the shirt + sales tax on the shirt

c = p + 0.06p

Performing addition on Right Hand Side of the equation to find the equation representing total cost

c = 1.06p

Therefore, the equation representing the total cost of the shirt is c = 1.06p.

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Answer:  correct

Step-by-step explanation:

The next five terms are ← ↑ → ↓ ← and the conjecture is each arrow is rotated 90 degrees clockwise to get the next

The first three terms are given as

↑ → ↓

From the above pattern, we have the following highlights:

Each arrow is rotated 90 degrees clockwise to get the next

Using the above as a guide, we have the next five terms to be:

← ↑ → ↓ ←

Also, we have the conjecture to be:

Each arrow is rotated 90 degrees clockwise to get the next

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To solve the equation, add 7 to both sides. The solution is a = 16.

A linear equation is an equation of which the highest degree of its variables is 1.

Steps to solve linear equations:

Recall that if  we subtract or add the same number to both sides of an equation, it does not change the equality.

The given problem:

Solve a-7=9

The variable is a. To isolate a, remove -7 by adding 7 to both sides:

a-7 +7 = 9 +7

a = 16 (solved)

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Answer:

the car would use 49 gallons because you get a decimal of 49.49 so you would put got decimal to the nearest 1's place and that would be 49

Answer:

yes.

Step-by-step explanation:

if the variable has a number in the problem, yes.

if the variable has no known value, you can't solve it, but you can solve everything else. so yes.

The unknown angles are as follows:

∠AIM is perpendicular to IR.

Therefore,

∠RIM = 90°

Line AM, ZG and RI intersect at point I.

Therefore,

3x - 56 = x + 2 (vertically opposite angles)

3x - x = 2 + 56

2x = 58

x = 58 / 2

x = 29

4z + 7 + x + 2 = 90

4z + 7 + 29 + 2 = 90

4z = 90 - 7 - 2 - 29

4z = 52

z = 52 / 4

z = 13

∠RIG = 4z + 7

∠RIG = 4(13) + 7

∠RIG = 52 + 7

∠RIG = 59°

∠ZIM = 4z + 7 + 90

∠ZIM = 4(13) + 7 + 90

∠ZIM = 52 + 7 + 90

∠ZIM =  59 + 90

∠ZIM = 149 degrees

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