Find the equation of the line that contains The given point and is perpendicular to the given line. Write the equation in slope intercept form, if possible. (14,21); y = -7x + 4

Answer:

15 percent change

Step-by-step explanation:

1) 500 - 425 = 75

2) 75 / 500 = 0.15

3) 0.15 * 100= 15

Using the unit rate, the graphs that best represent the amount they earn for different amount of time is: C.

The slope of a graph can be interpreted as the unit rate of the scenario that is being represented by the graph. For example, money earned in dollars per hour worked is the unit rate or slope of the graph given in this scenario.

The larger the unit rate value, the steeper the slope of the line of the graph.

Let Lin's unit rate be represented as x, therefore,

Lin's unit rate = x

Diego's unit rate = 2x

Jada's unit rate = 2(2x) = 4x

This shows that unit rate of Jada is the highest, and therefore, the graph that would represent how much Jada earns would be the steepest, followed by Diego's, and the least is Lin's.

Therefore, the all the graphs would be: C.

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Answer:1.5 cars can be washed in 1 minute but realistically only 1 car can be washed

Step-by-step explanation: 24/16 =1.5 and that get you your answer of 1.5 but the correct answer is 1.5 or 1 depending on if they are asking you to round down or not.

The new conditional statement that follows from the pair of true statement is If 4x + 5 = 13; then -5x = -10

The law of Syllogism states that if the following two statements are true:

Statement 1: If x , then y

Statement 2: If y , then z

Then we can derive a third true statement:

Statement 3: If x , then z

From the given;

Statement 1: If x , then y

If 4x + 5 = 13; then x = 2

Statement 2: If y , then z

If x = 2; then -5x = -10

Statement 3: If x , then z

If 4x + 5 = 13; then -5x = -10

In conclusion, according to the law of Syllogism, the statement that follows from the pair of true statement is If 4x + 5 = 13; then -5x = -10

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Answer:

1

Step-by-step explanation:

the mean is calculated as

mean = [tex]\frac{sum}{count}[/tex]

let x be the fifth number , then

[tex]\frac{8+10+12+10+x}{5}[/tex] = 8.2 ( multiply both sides by 5 to clear the fraction )

40 + x = 41 ( subtract 40 from both sides )

x = 1

the fifth number is 1

Answer:

y = (3/2)x + 3

Step-by-step explanation:

Comment

The general equation is

y = mx + b

Finding m

The equation for the slope is

m = (y2 - y1)/(x2 - x1)

Givens

y2 = 3

y1 = 0

x2 = 0

x1 = - 2

m = (3 - 0)/(0 - -2)

m = 3 / 2

m = 3/2

Finding b

b is the y intercept which is (0,3)

x = 0

y = 3

3 = 0*3 + b

b = 3

So the equation is

y = (3/2) x + 3

Answer:

[tex]-2(x+5) = -2x -10[/tex]

Step-by-step explanation:

Hi there,

For us to answer the question we have to check if whether the end product on the both LHS and RHS are equal or not , so lets take each equation is whether both the sides are similar or not :

First eq :-

[tex]-2(x-5) = -2x + 5\\giving\\-2x+10\neq -2x+5[/tex]

Since it is not equal it is incorrect.

Second eq:-

[tex]-2(x+5) = -2x-5\\giving\\-2x-10\neq -2x-5[/tex]

Since it is not equal it is incorrect.

Third eq:-

[tex]-2(x+5) = -2x -10\\giving\\-2x-10=-2x-10\\[/tex]

Now we got the equation that equals both in LHS and RHS.

So our Answer is

[tex]-2(x+5) = -2x -10[/tex]

Hope this helped you out if so do mark me as the brainliest,

a fellow mate,

cheers!

Answer:

the vertical line is:

x = 5

The horizontal line is:

y = -9

Step-by-step explanation:

A vertical line has a fixed x-value, while a horizontal line has a fixed y-value.

Then we can write a vertical line as:

x = a

and a horizontal line as

y = b

Then, if we want a vertical line that passes through the point (5, -9), remember that the x-vale will be fixed, then we fix the x-value at the same x-value of the point, which we know that is 5, then the vertical line that passes through the point (5, -9) is:

x = 5

Step-by-step explanation:

Using an assumed value that the octagon must fit inside an 11 inch square space, tthe length of each side of the octagon would be 8.23 inches.

Since an assumed side of the square is 11 inches

Here, y is the two equal sides of the right-angle triangle

So y + x + y = 11

Using Pythagoras's theorem for the right angle triangle

y² + y² = x²

2y² = x²

y² = (x²)/2

y = x /√2

So substitute the value of y = x /√2 in the equation

x /√2 + x + x /√2 = 11

2x /√2 + x = 11

2x /√2 + x√2 /√2 = 11

x[2/√2 + √2 /√2] = 11

x[(2 + √2) /√2] = 11

x(2 + √2) = 11√2

x = 11√2/(2 + √2)

x = 15.5563/3.4142 = 12.1421

Round to the nearest hundredth of an inch

x = 12.1

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The given number 2/3 belongs to the subset of rational numbers.

All numbers on the number line, from negative to plus infinity, are considered to be real numbers. They are breaking up into the following groups:

1. We can count the components of a set using natural numbers.

2. Natural numbers and their opposites in the negative, such as zero, are known as integers.

3. Fractions can be used to express rational numbers.

4. Non-periodic infinite decimals are indicative of irrational quantities.

The answer to the given question is : It belongs to the rational numbers because it is a fraction.

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Based on the number of houses in the neighborhood and those that have a chain-link fence and a privacy fence, the number of houses with no fence in the backyard are 28 houses

First, find the number of houses in the neighborhood that have a chain-link fence:

= Number of houses x Proportion with a chain-link fence

= 80 x 1/4

= 20 houses

Then find the number of houses in the neighborhood that have a privacy fence:
= Number of houses x Proportion with a privacy fence

= 80 x 2/5

= 160 / 5

= 32 houses

The number of houses in the neighborhood that have no fence is:

= Total number of houses - Houses with a chain-link fence - Houses with a privacy fence

= 80 - 20 - 32

= 28 houses with no fence

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The equation would be y = 16/9x which represents the algebraic relationship between x and y which is the correct answer would be an option (A).

The equation is defined as mathematical statements that have a minimum of two terms containing variables or numbers that are equal.

Given that x and y vary directly and y = 32 when x = 18

Direct variation equation can be written as:

y = kx where "k" is a constant.

Substitute the values of y = 32 and x = 18 in the direct variation equation and solve for k:

⇒ 32 = k(18)

⇒ k = 32/18

⇒ k = 16/9

The direct variation equation :

⇒ y = 16/9x

Therefore, the equation would be y = 16/9x which represents the algebraic relationship between x and y.

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The expected area of a circular sampling region is 531.56 m²

Given,

The radius of the circular sampling region = 13m

f(r) = [tex]\left \{ {\frac{3}{4} } \atop {0}} \right.[/tex] [1 - (13 - r)²] 12 ≤ r ≤ 14

We have to find the area of the circular sampling region = E (π r²)

E (π r²) = π E (r²)

Lets find E (r²)

E (r²) =₁₂ [tex]\int\limits^[/tex]¹⁴ r² f(r) dr

= ₁₂∫¹⁴ (3r²/4) (1 - (13 -r)²) dr

=  3/4 ₁₂∫¹⁴ r² (1 - 169 - r² + 26r) dr

= 3/4 ₁₂∫¹⁴ r² (26r³ - r⁴ - 168r²) dr

= 3/4 [ 26r⁴/4 - r⁵/5 - 168r³/3]₁₂¹⁴

= 3/4 [ (26 × 14⁴)/4 - 14⁵/5 - (168 × 14³)/3] - [ (26 × 12⁴)/4 - 12⁵/5 (168 × 12³)/3]

= 3/4 [ (26 × 38416)/4 - 537824/5 - (168 × 2744)/3] - [ (26 × 20736)/4 - 248832/5 - (168 × 1728)/3]

= 3/4 [ 249704 - 107564.8 - 153664] - [ 134784 - 49766.4 - 96768]

= 3/4 [-11524.8] - [-11750.4]

= 3/4 [225.6]

= 169.2

∴ E(r²) = 169.2

Now lets find the expected area of the circular sampling region:

Area = E(π r²) =  π E (r²)

Here, E(r²) = 169.2

So, area = π × 169.2 = 531.56 m²

That is, the expected area of a circular sampling region is 531.56 m²

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Answer:

35+15 =50

50/2= 25 dollars

Answer:

[tex]a.[/tex] [tex]\frac{49}{50}[/tex]

[tex]b.[/tex] [tex]8[/tex]

Step-by-step explanation:

[tex]a.[/tex]  [tex]\frac{1}{2} +\frac{2}{5} +\frac{2}{25}[/tex]

To solve this, we must first find the LEAST COMMON MULTIPLE (LCM).

To find the LCM, we must list the multiples of the denominators, then find the smallest multiple that all three numbers have in common.

2: 2, 4, 6, 8, 10, 12, 14, 16, 18, 20, 22, 24, 26, 28, 30, 32, 34, 36, 38, 40, 42, 44, 46, 48, 50

5: 5, 10, 15, 20, 25, 30, 35, 40, 45, 50

25: 25, 50

The LCM is 50.

Now that we have found the LCM, we will change the fractions so that all three have a denominator of 50.

To do this, we multiply the numerator and the denominator by the same number.

[tex]\frac{1}{2} *\frac{25}{25} =\frac{25}{50}[/tex]

[tex]\frac{2}{5} *\frac{10}{10} =\frac{20}{50} \\[/tex]

[tex]\frac{2}{25} *\frac{2}{2} =\frac{4}{50}[/tex]

Now that all fractions have the same denominator, we can add them. Remember, when adding fractions, the denominators stay the same. Only add the numerators.

[tex]\frac{25}{50} +\frac{20}{50} +\frac{4}{50} \\\\=\frac{49}{50}[/tex]

_______________________________________________________

[tex]b.[/tex]  [tex]\frac{2}{3} *\frac{30}{7} *\frac{14}{5}[/tex]

To multiply fractions, multiply the numerators, then the denominators. Lastly, simplify the product.

[tex]2*30*14=840\\3*7*5=105[/tex]

[tex]\frac{840}{105} =\frac{8}{1}[/tex]

Answer:

-4 11/15

Step-by-step explanation:

The values of x when f(x) = 0 are 2 and 8

Graphs are used mostly to show the relationship between two variables (usually x and y).

The graph of y = f(x) is attached

To get the values of x when f(x) = 0 , we  consider where the line of the graph crosses the x-axis.

The graph crosses the x-axis at:

x = 2

x = 8

This means that the values of x when f(x) = 0 are 2 and 8

Therefore, in the graph of y = f(x), the values of x where f(x) = 0 are 2 and 8

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Disclaimer : The question mentined is not provided with a graph, the above solution is done as per the graph attached.

By using the basics of the number system the calculated number from the given statement is 10.

What is number system?

In mathematics, the number system can be used to express the numbers in a way of writing to make the mathematical expression. Basically, it provide the unique representation of the number with the help of the algebraic structures and operations.

According to the question, the expression can be formed by the given statement is as follows:

Let us assume the number be 'a'

Using basics of the number system for the formation of an expression:

Therefore,

(2/5)a - 3 = 1

⇒ (2/5)a = 4

⇒ a = 10

Hence, by using the basics of the number system the calculated number from the given statement is 10.

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Answer:

32.64

Step-by-step explanation:

Lisa spent 90% of the total money on the fruits.

In mathematics, a percentage is a number or ratio expressed as a fraction of 100.

Given is Lisa spent $27 on fruits at the grocery store. She spent a total of $30 at the same store.

Money spent by Lisa on fruits = $27

Total money spent by Lisa = $30

Therefore, percentage of the total money she spend on fruits will be -

(27/30) x 100 = 90%

Hence, Lisa spent 90% of the total money on the fruits.

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Answer:

1. P

2. U

3. K

4. A

5. M

6. C

7. E

8. J

9. L

10. I

Answer:

18. m<EBC = 43°, m<CBD = 47°

19. m<EBC = 50°, m<ABC = 130°

Step-by-step explanation:

18. Find m<EBC and m<CBD

m<EBC = (5x + 8) and m<CBD = (6x + 5)

these two angles add up to a right angle, therefore their sum is 90°

5x + 8 + 6x + 5 = 90

11x + 13 = 90 , 11x = 77 , x = 7

m<EBC: 5(7) + 8 = 43

m<CBD: 6(7) + 5 = 47

19. Find m<EBC and m<ABC

m<EBC = (3x + 20) and m<ABC = (17x - 40)

these two angles are supplementary, meaning that they add up to 180°

3x + 20 + 17x - 40 = 180

20x - 20 = 180, 20x = 200, x = 10

m<EBC: 3(10) + 20 = 50

m<ABC: 17(10) - 40 = 130

Answer:

7. 45

8. 19

9. 15

10. 24

11. 23

12. 6

13. 8

14. 15

15. 12

16. 3

17. 26

18. 12

19. 21

20. 34

21. 2

hope this helps!:)

Mr mole descend at the rate of 2.3 meters per minutes.

A rate in mathematics is the comparison of two related values expressed in dissimilar units.

The given equation to represent the position of Mr. Mole is

A = -2.3 t - 7

where A denotes the depth and t is the time.

Now the rate can be found out by dividing the change in depth by the change in time.

Differentiating we get

ΔA = -2.3 Δt

or, ΔA / Δt = -2.3

hence the rate of the mole is 2.3 meters per minutes.

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Answer:

Formula for gradient is given as (y2-y1)÷(x2-x1) or (y1-y2)÷(x1-x2), where x and y are the coordinates of the points.

(k-4)÷(0-1) = 9

k-4 = 9(0-1)

k-4 = -9

k = -5

The machine will use 90 gallons of water to wash 24.5 pounds of laundry.

                     y ∝ x

Consequently, y = kx, where k is the proportionality constant.

Given:

The amount of water used by a washing machine varies directly with the weight of the load being washed.

Let's assume,

The amount of water used by a washing machine is y.

The weight of the load being washed is x.

According to the question,

y = 28 gallons

x = 7 pounds

Putting the values we get,

y = kx

28 = k × 7

k = 4

Now, we have to find y when x = 24.5

y = 4 × 24.5 = 98

Hence the machine will use 90 gallons of water to wash 24.5 pounds of laundry.

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Answer:

$8.50 ? let me know if im wrong

Step-by-step explanation:

Answer: 31, 34, 17

Step-by-step explanation:

From the question;

we are to calculate average rate of change of distance with respect to time

The average rate of change is given as

From the question we are given the table below

a. we are to find the average rate of change of the distance driven from 0 secons to 3 seconds

From the information

we have