|ax+b| = c
solve for a

The area of the circle, in terms of pi is calculated as: 72.25π in.²

The circumference/perimeter of a circle = 2πr

The area of a circle = πr², where the radius of the circle is represented as "r".

Given the following:

The circumference of the circle = 17π inches.

Therefore:

17π = 2πr [circumference formula]

Divide both sides by 2π to find r (radius of the circle)

17π/2π = 2πr/2π

17/2 = r

r = 17/2 or 8.5 inches

Area of the circle = πr² = π(17/2)²

Area of the circle = πr² = π(8.5)²

Area of the circle = πr² = 72.25π square inches.

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The vertex of the function is a = 1 , b = -8 and c = 15

The intercept of the function is 15

The equation is given as

                               g(t) = t² - 8t + 15

which gives us the parabolic graph and lets us keep the domain as

-6 ≤ t ≤ 6

The graph of this equation is attached.

The vertex of the function can be found by comparing it with the parabolic equation.

                      at² + bt + c = 0

                        t² -  8t + 15 = g(t)

Therefore, the vertex of the function is

           a = 1 , b = -8 and c = 15

The intercept can be found by taking t=0 , we get

   g(0) = 0² - 8(0) + 15

Therefore, the intercept of the function is 15

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Answer: q I made 2 quarts of lemonade using 1/4 quarts is x = 1/8 lemonade

q I made 8 quarts of lemonade using 1/4 quarts is x = 1/32 lemonade

q I made 12 quarts of lemonade using 1/4 quarts is x = 1/48 lemonade

q I made 18 quarts of lemonade using 1/4 quarts is x = 1/72 lemonade

Step-by-step explanation:

Given data,

If q I s the number of quarts of lemonade, then 1/4 quarts can be used the number of cups of lemonade mix.

we know that, first we can use 2 quarts,

Then,

q I made 2 quarts of lemonade using 1/4 quarts

so,

using proportion

Find out the amount of sugar needed to make 1 quart of lemonade

Let,

x ----> the amount of lemonade

[2/(1/4)]  lemonade/quarts of lemonade = (1/x)(quarts lemonade/quarts of lemonade)

                   [2/(1/4)] = 1/x

                    8/1 = 1/x

                    x = 1/8 lemonade

q I made 8 quarts of lemonade using 1/4 quarts

so, we can write,

                   [8/(1/4)] = 1/x

                   32/1 = 1/x

                   x = 1/32

q I made 12 quarts of lemonade using 1/4 quarts

so, we can write,

                   [12/(1/4)] = 1/x

                   48/1 = 1/x

                   x = 1/48

q I made 18 quarts of lemonade using 1/4 quarts

so, we can write,

                   [18/(1/4)] = 1/x

                  72 /1 = 1/x

                  x = 1/72

q I made 2 quarts of lemonade using 1/4 quarts is x = 1/8 lemonade

q I made 8 quarts of lemonade using 1/4 quarts is x = 1/32 lemonade

q I made 12 quarts of lemonade using 1/4 quarts is x = 1/48 lemonade

q I made 18 quarts of lemonade using 1/4 quarts is x = 1/72 lemonade

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Answer:

all of them are prime.

Step-by-step explanation:

Answer:

9. 4(x -4)

10, 6 (3k + 7)

11. Prime

12. 4(5m -2n)

Step-by-step explanation:

Answer:

  1

-------

  2

Step-by-step explanation:

    2                1

- ------- ×  - 1 -------

   5                 4

    2                5

- ------- ×  -   -------

   5                 4

   2(4)          5(5)

- ------- ×  -   -------

   5(4)          4(5)

   8               25

- ------- ×  -   -------

   20             20

--------------------------------------------------------------

(-8) × (-25) = 200

20 × 20 = 400

---------------------------------------------------------------

200 ÷ 200

-------

400 ÷ 200

  1

-------

  2

I hope this helps!

Answer:

C

Step-by-step explanation:

at starting time x = 0    the fish is at   -3 meters

 for each second the fish goes another -7 meters

The comparison statement which is true among the other given answer choices is; Choice A; -3/4<-2/3.

It follows from the task content that the comparison statement which is true among the answer choices given be determined.

On this note, one must recall that the arrangement of numbers on the number line is such that numbers are arranged in increasing order of value from left to right. For instance; -3 < -2 while; 2 < 3.

Hence, the answer choice which is correct is; Choice A; -3/4 < -2/3 as evident from the fact that; -0.75 < -0.667.

The concept above follows from the conversion of the numbers to decimals while using the number line arrangement of numbers.

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The value of the equation (6 x 10^-5)(7 x 10^11) in scientific notation is 4.2 x 10^7

The equation is given as

(6 x 10^-5)(7 x 10^11)

Rewrite properly as

(6 x 10^-5)(7 x 10^11) = (6 x 10^-5) x (7 x 10^11)

Remove the bracket

So, we have

(6 x 10^-5)(7 x 10^11) = 6 x 10^-5 x 7 x 10^11

Rewrite the product as

So, we have

(6 x 10^-5)(7 x 10^11) = 6  x 7 x 10^-5 x 10^11

Evaluate the product

So, we have

(6 x 10^-5)(7 x 10^11) = 42 x 10^6

Evaluate the product

So, we have

(6 x 10^-5)(7 x 10^11) = 4.2 x 10^7

Hence, the value of the the equation (6 x 10^-5)(7 x 10^11) in scientific notation is 4.2 x 10^7

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The expressions matched with their corresponding simplified expressions are

(5⁻⁹)⁴         →   1/5³⁶

5⁹/5⁴         →   5⁵

5⁴ × 5⁹      →   5¹³

(5⁴)⁹          →   5³⁶

5⁻⁹/5⁴       →   5⁻¹³

From the question, we are to match each of the given expressions on the left with the terms of the right

First, we will simplify each of the expressions

Multiplying the exponents

5⁻⁹ˣ⁴

= 5⁻³⁶

= 1/5³⁶

Applying the division law of indices

5⁹/5⁴ = 5⁹⁻⁴

= 5⁵

Applying the multiplication law of exponents

5⁴ × 5⁹ = 5⁴⁺⁹

= 5¹³

Multiplying the exponents

5⁴ˣ⁹

= 5³⁶

Applying the division law of indices,

5⁻⁹⁻⁴

= 5⁻¹³

Hence, the expressions matched with their corresponding simplified expressions is

(5⁻⁹)⁴         →   1/5³⁶

5⁹/5⁴         →   5⁵

5⁴ × 5⁹      →   5¹³

(5⁴)⁹          →   5³⁶

5⁻⁹/5⁴       →   5⁻¹³

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Answers:

The house's value decreased by   $31,760  

The current value is    $365,240  

===========================================================

Work Shown:

8% of 397,000 = 0.08*397000 = 31,760 is the amount of lost value in the home. In other words, the value has dropped by this much.

The current value is 397,000-31,760 = 365,240

---------------

If you didn't care about how much value was lost, and only cared about the current value, then you can take this slight shortcut

100% - 8% = 92%

92% of 397,000 = 0.92*397000 = 365,240

If the house lost 8% of its value, then it keeps the remaining 92% to be currently valued at $365,240

This shortcut is useful if you wanted to chain together many percentage increases or decreases together.

if 60 men do a piece of work in 27 days, then 18 men can do the same work in 90 days.

The unitary approach is a strategy for problem-solving that involves the first determining the value of a single unit, then multiplying that value to determine the required value.

Always write the items that need to be computed on the right side and the things that are known on the left side to simplify things. In the aforementioned issue, the number of apples is known, but it is unclear what they are worth. It should be highlighted that issues with this method are solved using the concepts of ratio and proportion.

From the unitary method:

Number of days required to complete a work by 60 men = 27 days

Number of days required to complete a work by 1 man =  27*60

Number of days required to complete a work by 18 men = [tex]\frac{27*60}{18}[/tex]= 90days

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Answer:

1/27

Step-by-step explanation:

pb.chips.juice

pb.chips.milk

pb.chips.water

pb.cookies.juice

pb.cookies.milk

pb.cookies.water

pb.fruit.juice.

pb.fruit.milk

pb.fruit.watet

time that by three (as every section has three )

or

1/3 of cheese

1/3 of cookies times 1/3 x 1/3 x 1/3 = 1/27

1/3 of water

Based on the calculations, the length of the arc of this circle is equal to: C. 61.3 ft.

In Geometry, an arc can be defined as a trajectory that is generally formed when the distance from a given point has a fixed numerical value.

In Mathematics, if you want to calculate the length of an arc formed by a circle, you will divide the central angle that is subtended by the arc by 360 degrees and then multiply this fraction by the circumference of the circle.

Mathematically, the length of an arc formed by a circle is given by:

Arc length = 2πr × θ/360

Substituting the given parameters into the formula, we have;

Arc length = 2 × 3.142 × 13 × 270/360

Arc length = 61.269 ≈ 61.3 feet.

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After modelling the mathematical statement and solving its equivalent mathematical relation, we get x = -36.

Equation modelling is the process of writing a given mathematical statement in the form of a numeric mathematical expression taking into considerations the operations, constants and other variables.

Given in the question is a number such that twice the difference of a number and 9 is equal to three times the sum of the number and 6.

Assume that the number is x. Now, we will model the equation and solve for x. According to the question, the following mathematical relation represents the statement-

2(x - 9) = 3(x + 6)

2x - 18 = 3x + 18

x = - 36

Therefore, the number is -36.

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Answer:

[tex]\frac{5}{4}[/tex]

Step-by-step explanation:

To find the slope on a graph, the easiest way is to use the "rise-over-run method."

First, from the leftmost point, count how many points it takes to get to the same y-coordinate as the point.(only count UP and DOWN. If you have to go up to reach the point, the numerator is positive. Otherwise it is negative) Next, figure out how many points it takes to get to the same x-coordinate starting from where you counted up from, therefore landing on the rightmost point. (only count LEFT and RIGHT. If you have to go right to reach the point, the denominator is positive. Otherwise it is negative)

In this graph, we go up 5 and right 4. Therefore the answer is [tex]\frac{5}{4}[/tex].

(I like starting on the leftmost point first and then doing rise-over-run. You don't necessarily have to but remember, if both the numerator and denominator are negative, then the fraction is positive)

Answer:

slope: [tex]\frac{5}{4}[/tex]

Step-by-step explanation:

Slope Formula:  [tex]\frac{rise}{run}[/tex]

tip:

EASIER WAY to find the slope: From the bottom dot (-1,-1) count up until you reach the line where the other dot (3,4) so this would be 5 (the RISE)

then count ACROSS (run) it until you reach the dot. This would be 4.

Answer: 5/4 is the slope of the line.

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The answer is C.....................

[tex] \large \bf \implies \: \boxed{ \tt{y = {4x}^{2} + 24x + 38}}[/tex]

[tex] \bf \longrightarrow \: x = - \frac{24}{2 \times 4} = - 3 \\ \\ \bf \longrightarrow \: y = \frac{4 \times 4 \times 38 - {24}^{2} }{4 \times 4} = 2 \\ \\ \\ \bf \longrightarrow \: y = {4x}^{2} + 24x + 38[/tex]

-3/8 - 7/12 =

First we need to get the denominators same.

(-3 x 3/8 x3) - (7 x 2/12 x 2) =

-9/24 - 14/24 =

-9 - 14/24 =

-23/24

Answer = -23/24

Answer:

5/24

Step-by-step explanation:

y-x y is 7/12 so its positive x is -3/8 so its negative the answer is 5/24

The value of Log0.5 16 is -4.

Let log0.5 16 = x ⇒ 0.5x = 16 ⇒ ( 5 10 ) x = 2 × 2 × 2 × 2. ⇒ ( 1 2 ) x = 2 4. ⇒ 1 2 x = 2 4. ⇒ 2- x = 24 ⇒ - x = 4 ⇒ x = - 4.

Thus, log0.516 = - 4.

Examples of this include sound (measured in decibels), earthquakes (measured on the Richter scale), starlight brightness, and chemistry (pH balance, a measure of acidity and alkalinity). Let's examine the Richter scale, which uses a logarithmic function to determine the size of earthquakes.

Scottish mathematician John Napier (1550–1617) created logarithms in the 17th century as a tool for computation. He derived the term from the Greek words for ratio (logos) and number (arithmos).

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The correct statement for y = x - 13 is C. It is the graph of y = x translated 13 units to the right to the parent function y = x.

A function can be thought of as output for the given or specified set of inputs.

Given a parent function y = x and it is a linear function and also reflexive.

The function y = x - 13 implies

x - 13 = 0 or x = 13.

∴ The graph of the function y = x - 13 will shift to the right along the x-axis by 13 units to the right. This is also known as translation.

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Answer:The correct statement for y = x - 13 is C. It is the graph of y = x translated 13 units to the right to the parent function y = x.

Step-by-step explanation:

What is a function?

A function can be thought of as output for the given or specified set of inputs.

Given a parent function y = x and it is a linear function and also reflexive.

The function y = x - 13 implies

x - 13 = 0 or x = 13.

∴ The graph of the function y = x - 13 will shift to the right along the x-axis by 13 units to the right. This is also known as translation.

8.75

-1 2/3 × (-5 1/4)

=35/4

= 8 3/4

= 8.75

There are 5/9 groups in 1

6 divided by 9/5 is 3 1/3.

An improper fraction is a non integer where the numerator is greater than the denominator. An example is 9/5.

In order to determine the the number of groups of 9/5 that are in 1, divide 1 by 9/5

1 ÷ 9/5

1 × 5/9

9/9 × 5/9 = 5/9

6 ÷ 9/5

6 × 5/9 = 10 / 3 = 3 1/3

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Answer:

I think (2x−3)(3x+5)

The proposed skyscraper is 172.8 m tall

From the question, we are to determine the how tall the proposed skyscraper is in meters

From the given information,

The scale of the model is

1 in : 7.2 m

and

The model is 2 ft tall

First, convert 2 ft to inches

NOTE: 1 foot = 12 inches

∴ 2 feet = 2 × 12 inches

= 24 inches

Now,

If 1 inch represents 7.2 m

Then,

24 inches will represent 24 × 7.2 m

24 × 7.2 m = 172.8 m

Hence, the proposed skyscraper is 172.8 m tall

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Answer:

[tex]7x + 6[/tex]

Step-by-step explanation:

We can combine all terms that share the same variable.

For example, we can combine [tex]3x + 5x[/tex], which is 8x, however, we cannot combine [tex]3x + 4t[/tex], as 3x and 4t are terms with different variables. The latter applies to combining terms that include variables and terms that do not - You cannot combine them.

The trick to combining terms with common variables is to combine them like you'd combine any pair of regular numbers.

Just like [tex]6 + 3 = 9[/tex], then [tex]6x + 3x = 9x[/tex].

Just like [tex]6 - 3 = 3[/tex], then [tex]6x - 3x = 3x[/tex].

This is done through a process known as factorizing, however, I believe you will learn this later if you are just now studying combining terms with variables.

Onto your question, we can combine 10x and -3x together, however, we cannot combine either of those terms with 6.

[tex]10x - 3x + 6 \to 7x + 6[/tex]

Answer:

6

Step-by-step explanation:

5+3−2

=8−2

=6

---------

Answer:

0.1764    

0.2025  

Step-by-step explanation:

Let x be a perfect square such that √x lies between 0.4 and 0.5

Then y = √x

Then we have the inequality
0.4 < √x < 0.5

==> 0.4 < y < 0.5

So the number x must lie between 0.4² = 0.16 and 0.5² = 0.25

So the square of any number between 0.4 an 0.5 will be a perfect square fitting the requirement

Let's take y = 0.42. Then y² = 0.42² = 0.1764

y = 0.45 gives y² = 0.2025

So two perfect squares whose square root values lie between 0.4 and 0.5 are 0.1764 and 0.2025

In fact squaring any value between 0.4 and 0.5 will provide such a number

Answer:

The answer is 5x+17

Answer:

X = 7

Step-by-step explanation:

2(x+7) +3(x+7)

2x + 14 + 3x + 21

2x +3x +14 +21

5x ÷5 + 35 ÷5

x. = 7