Solve the following equation below. Show each step and check your work.
72y - 126 = 522 + 144

Answer:

Step-by-step explanation:

Adding 5 m to the width of a rectangle makes it a square with area 144 m². You want the length and width of the original rectangle.

The formula for the area of a square is ...

  A = s²

The side length of the square formed from the rectangle is ...

  144 = s²

  √144 = s = 12 . . . . . meters

The length of the rectangle is unchanged when it is made into the square, so the length is 12 m.

The width of the rectangle had 5 m added to make it 12 m, so the width of the rectangle is 7 m.

__

Additional comment

The given relation between length and width is given as L = 2W -2. It is true that 12 = 2(7) -2, but that is not needed in order to solve this problem. It does serve as a check on our answer.

Answer:

10 minutes.

Step-by-step explanation:

8 houses are done in 4 minutes

The ratio is 2:1

20 houses are done in 10 minutes
20:10 = 2:1

Answer:

It would take Angelo 10 minutes to construct 20 playing card houses.

first way to solve it (recommended):

Step one: See how much it takes to build one house

4 / 8 = 0.5

0.5 minutes to build one house

Step two: multiply by amount of houses (20)

0.5 x 20

Step three: get your answer!

It would take Angelo 10 minutes to make 20 houses.

second way to solve it (ratios):

Step one: see the ratio of minutes to houses

minutes : houses

          4 : 8

Step two: simplify the ratio

4 : 8

1 : 2 (divide both sides by four)

Step three: multiply

x minutes : 20 houses

1 minutes : 2 houses

multiply both sides by 10

10 minutes : 20 houses

Step four: get your answer!

It would take Angelo 10 minutes to make 20 houses.

I hope my answer helped you!

Monthly payment would be $956.24
Loan APR is 4.892%

The profit function for the revenue R(x) = 12x and the cost, C(x) = x + 264 is  11x-264 and units must be produced for the business to break even is 24 units.

Profit refers to net income after deducting expenses from earnings, whereas revenue refers to income generated through business operations. Sales, fee-based income, and property-based income are just a few of the different ways that money can come in.

Here,

R(x)=12x

C(x)=x+264

It represents the difference between total revenues and total outlays.

Revenue minus costs equals profit.

Profit = Revenue - Cost

P(x)=R(x)-C(x)

P(x)=12x-x-264

P(x)=11x-264

For  the company to break even,

R(x) = C(x)

12x=x+264

11x=264

x=24

The break-even point for the business is 24 units, and the profit function for the revenue R(x) = 12x and the cost C(x) = x + 264 is 11x-264.

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Answer:

Coordinates of A are (-2.5, -1.5)

Coordinates of B are (4.5, -3.5)

The simplified form of the expression  √10•√8 is 4√5.

Expression:

Expression refers the mathematical statements that have two terms at least that contain variables, numbers, or both.

Given,

Here we have the expression √10•√8.

Now we have to find the simplified form of these expression.

Now, we have to multiply the values inside the square root then we get,

=> √10 x √8 = √(10  x 8)

After the multiplication we can get,

=> √80

Now, we have to expand this as the following,

=> √16 x 5

We know that √16 is equivalent for 4²,

So, it can be written as,

=> √4² x 5

Now, we have to simplify this as,

=> 4√5

Therefore, the simplified expression is 4√5

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The set of side lengths that would not create a triangle is; 10, 20, 30.

It follows from the task content that the set of side lengths which will not create a triangle are to be determined from the given task content.

Since the triangle inequality theorem states that; the sum of two side lengths of a triangle is always greater than the third side length and also, the difference of two side lengths of a triangle is less than the third side length.

On this note, for a triangle with side-lengths a, b and c; the inequalities which hold are;

a + b > c and a - b < c.

Therefore, the set of side-lengths which will not create a triangle is; 10, 20, 30.

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According to the imaginary number, the real solution between 30 and 80 is 60

Imaginary number

An imaginary number refers a real number multiplied by the imaginary unit i, which is defined by its property i² = −1.

Given,

Here we have to use the digits -9 to 9 (each only once) to create a real solution between 30 and 80 (a+bi)(c+di).

We know that the digits from -9 to 9 are listed as follows:

(-9,-8,-7,-6,-5,-4,-3,-2,-1,0,1,2,3,4,5,6,7,8,9)

Now, we have to choose the digits -9 to 9, as the value of a, b, c and d,

For that we have to choose the value of a = 3, b = -9, c = 2 and d = 6,

Now, we have to apply these value on the given imaginary equation, then we get,

(a + bi) (c + di) = (3 + -9i) (2 + 6i)

When we simplify this one then we get,

=> 6 + 18i + (-18i) – 54i²

We know that value of i² =  -1, then the equation is written as,

=> 6 - 54(-1)

=> 6 + 54

=> 60

Therefore, 60 is a real solution between 30 and 80.

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Answer:

The Answer is C.

Step-by-step explanation:

It's important to know how the standard form of an equation works.

Remember that y = mx + b, where y is the output value, m is the slope of the equation, and b is the y-intercept (the initial value) of the equation. We know that the pool starts with 25 inches of water in it, so the initial value, or y-intercept is 25, because the pool starts with 25 inches of water after 0 hours. We know that the pool fills up 4 inches per hour, meaning as each hour progresses, the equation will increase by 4. This is the slope. y has been replaced with h in this equation. So, your answer would be h = 4t + 25.

If she did some research and learned that the exchange rate is 6 Tala for $2. The number of tala she get if she exchanged $6 is 18 tala.

Given data:

Exchange rate = 6 Tala for $2

Let x represent the tala Ming will get if she exchange $6

$2/6 = $6/X

Cross multiply

2x = 6× $6

2x = 36

Divide both side by 2x

x = 36/2

x = 18 tala

Therefore she would get 18 tala.

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The information about the Falcon fly is represented below

Part A: 800 000 = 4r

part B: 200 000 meters per hour

Part C: 200 kilometer per hour

Part D: Kilometers makes more sense because it makes the number easier to write and remember

The rate as used refers to speed which is distance / time

using the representation 800 000 = 4r

rate, r = 800 000 / 4

r = 200 000 meters per hour

converting meter to kilometer is achieved by dividing by 1000

r = 200 000 meters per hour / 1000

r = 200 kilometers per hour

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The question that can be represented by the equation ? × 1/8 = 3 is C. how many 1/8s are in 3?

An equation is the statement that illustrates that the variables given. In this case, two or more components are taken into consideration to describe the scenario.

In this case, the question is how many 1/8s are in 3. This will be:

= 3 ÷ 1/8

= 3 × 8

= 24

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The value of the first term in the sequence is 21.

Let the second term teen be x.

Since the term to term rule is subtract 2 and then multiply by 3. This will be:

(x - 2) × 3 = 165

3(x - 2) = 165

3x - 6 = 165

Collect like terms

3x = 165 + 6

3x = 171

Divide

x = 171 / 3.

x = 57

Second term = 57

We will do same thing again to get first term. Let first term be a.

(a - 2) × 3 = 57

3a - 6 = 57

Collect like terms

3a = 57 + 6

3a = 63

Divide

a = 63/3

a = 21

The first term is 21.

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The value of the coin after five years is 535 when the value increases with the function f(x) = 100(1.07)x

The value of a rare coin rises in accordance with the function f(x)

f(x) = 100(1.07)x

where x represents the number of years that the coin is owned and value is measured in US dollars

Now, Simplifying the given function, we have :

f(x) = 100(1.07)x

f(x) = 107x

Now, we need to find the value of the coin after five years, then

Putting x = 5 in the function,

f(x) = 107 * 5 = 535

Hence, the value of the coin after five years is 535 when the value increases with the function f(x) = 100(1.07)x

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Answer:

x=3

Step-by-step explanation:

any horizontal line is equal to x

the y is equal to 0

a horizontal line is undefined

Answer: -15 degrees

Step-by-step explanation:

Answer:

The degree of the polynomial is 4.  That is the highest exponent.

Step-by-step explanation:

Answer:

4

Step-by-step explanation:

to find degree you look at what the highest exponent when simplified is and that is your answer and inThis case it’s 4

Hopes this helps please mark brainliest

Answer: 3/1

Step-by-step explanation:3   ÷  1   =1÷3 =3

5       5   = 5÷5=1

therefore, 3 by five divided by 1 by five is equal to 3 by 1 ,

The numbers of ladies and gentlemen in the club are 2 and 18 respectively.

The percentage is a ratio that can be expressed as a fraction of 100

Given that, there are 90% of ladies in the club, and the number of ladies is 12 more than 3 times the number of gentlemen.

Let the number of gentlemen is x and the number of ladies be y.

Since the number of ladies is 12 more than 3 times the number of gentlemen, it follows:

y  = 12 + 3x     (1)

Now, the total number of members in the club is:

x + y

Since there are 90% ladies in the club, it follows:

90%(x + y) = y

90(x + y)/100 = y

90x + 90y = 100y

90x = 100y - 90y

90x = 10y

9x = y             (2)

Now, substitute y = 9x into equation (1):

9x = 12 + 3x

9x -3x = 12

6x = 12

x = 2

Substitute x = 2 into equation (2):

9(2) = y

18 = y

Hence, the numbers of ladies and gentlemen in the club are 2 and 18 respectively.

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Answer: The two lines intersect at (-4,3)

Step-by-step explanation:

So our first step would be to turn both of these into standard slope-intercept form.

1.)

4y + 3x = 0

4y = -3x

y = -3/4x

2.)

4y - x = 16

4y = x + 16

y = 1/4x + 4

Now that we have our 2 equations, y = -3/4x and y = 1/4x + 4 we can graph them to get an intersection at (-4,3)

The probability of being dealt an ace=4/52

The probability of being dealt another ace = 3/51

What is probability?

Simply put, probability measures how probable something is to occur. We can discuss the probabilities of various outcomes, or how likely they are, whenever we are unsure of how an event will turn out. Statistics is the study of events subject to probability.

The likelihood that a population parameter will be less than a given value when the null hypothesis is true is expressed as the p-value, also known as a probability value or a measure of significance, for a particular statistical model.

The probability of drawing one of the four aces from a typical 52-card deck is 4/52; but, the probability of drawing a second ace is merely 3/51 since, after the first ace was drawn, there were only three more aces remaining in the remaining 51 cards.

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For a year, 1750 students were able to donate to the school.

A % in mathematics is a quantity or ratio that is stated as a fraction of 100 (from the Latin per centum, "by a hundred"). Although the abbreviations "pct.", "pct.", and occasionally "pc" are also used, the percent sign, "%," is frequently used to indicate it  by % lacks dimensions and has no associated unit of measurement.

The Latin word per centum, which means "hundred" or "by the hundred," is where the word "percent" originates. The % calculator computes a variety of percentage-based numbers, such as the percentage difference between two provided values.

Given,

The annual salary of a football player is 210000

1 student ----------$120

x  ------------$210000$

x=(210000/120)

x=1750 students

1750 students could send their donation to the school for 1 year.

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The relation y = x² represents y as a function of x because every x-value returns a unique y-value.

Using the definition of a function, y=x² is a function because you will only get one unique y-value for each x-value in your domain.

The vertical line test is a quick check you can perform. The function y=x² is a parabola, and if you draw vertical lines anywhere on it, they will only cross the parabola once.

As a result, it is a function. A circle is not an example of a function because a vertical line drawn on a circle crosses at two different points.

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Work Shown:

x = monthly budget

45.50% of x = 0.4550x = 4500

0.4550x = 4500

x = 4500/0.4550

x = 9,890.1098901099 approximately

x = 9,890.11

Answer: y=3x

Step-by-step explanation:

The equation can be found by finding the slope of the given line. Visually, this can be found by counting the distance between two points. From (1,3) and (2,6), the line "rises" 3 units and "runs" 1 unit to the right. Since slope is calculated as rise over run, this gives us 3/1, or just 3 for slope. In slope-intercept form, this becomes y=3x.

Just to note, we know it is not negative because of the direction of the slope. Visually, if the slope "moves" in the direction of upwards and to the left, it will be positive. This can be calculated more accurately using the slope formula (y2-y1/x2-x1)

The correct expression will be;

⇒ 3n - 15 - n = 101

What is an expression?

Mathematical expression is defined as the collection of the numbers variables and functions by using operations like addition, subtraction, multiplication, and division.

Given that;

The algebraic expression is;

''A number, n, is added to 15 less than 3 times itself. The result is 101.''

Now,

Since, The algebraic expression is;

''A number, n, is added to 15 less than 3 times itself. The result is 101.''

So, We can formulate;

⇒ 3n - (15 + n) = 101

⇒ 3n - 15 - n = 101

Thus, The correct expression will be;

⇒ 3n - 15 - n = 101

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Answer:

She distributed incorrectly.

Step-by-step explanation:

In the first step, [tex]3(x-3)=3x-9[/tex], not [tex]3x-3[/tex].

The number of days it would take to collect 2600 cans is; 11 days

We are given the equation that represents the number of cans that Nicholas collected as; y = 235x + 15

where;

x represents the number of days.

y represents the number of cans collected.

Now, we want to make x the subject of the formula;

y = 235x + 15

Subtract 15 from both sides to get;

y - 15 = 235x

divide through by 235 to get;

(y - 15)/235 = x

When y = 2600;

x = (2600 - 15)/235

x = 11 days

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Answer:

117

Step-by-step explanation:

20% = 1/5

585 x 1/5 = 117!