Which situation is best represented by the following equation?

40w + 12.50 = 492.50

A) Nicole paid $40 for self-defense classes. She paid a $12.50 registration fee and $492.50 for each week she was enrolled in the classes. What is w, the number of weeks Nicole was enrolled in self-defense classes?
B) Nicole paid $12.50 for self-defense classes. She paid a $492.50 registration fee and $40 for each week she was enrolled in the classes. What is w, the number of weeks Nicole was enrolled in self-defense classes?
C) Nicole paid $492.50 for self-defense classes. She paid a $40 registration fee and $12.50 for each week she was enrolled in the classes. What is w, the number of weeks Nicole was enrolled in self-defense classes?
D) Nicole paid $492.50 for self-defense classes. She paid a $12.50 registration fee and $40 for each week she was enrolled in the classes. What is w, the number of weeks Nicole was enrolled in self-defense classes?
Eliminate

Answer:

50% off would be $50

Step-by-step explanation:

20% + 30% = 50% original price was $100 but now with 50% off it is $50

Nike is having a sale $100 shoes is 30% off an additional discount 20% off. The amount to be paid for shoes now is $56.

Discount is the amount of off offered by the seller to the customer on a certain product. It is always offered as a percentage of the marked price of the product to lure the customer to buy the product.

Selling price is the price at which the product is finally sold. It is the marked price of the product minus the discount given.

Marked price = $100

initial discount = 30%

price of shoes becomes = $100 - 30% of $100 = [tex]100 - \frac{30}{100} *100 = 100- 30 = 70[/tex]

Additional discount offered =  20%

selling price of shoes = $70 - 20% of $70 = [tex]70 - \frac{20}{100} *70 = 56[/tex]

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Step-by-step explanation:

Given,

Kente invested part of money  for 2 yr in stock fund that earned the equivalent of 6.5 % simple interest.He put remaining money in a 18 month certificate of deposit that earn of 6.5%simple interest.

Let he invested in stock fund be$ x. Remaining money =$(8000-x)

∴He got interest from stock fund was = [tex]\frac{PRt}{100}[/tex]

                                                        =$[tex]\frac{x\times6.5\times2}{100}[/tex]   [here P =x , R = 6.5% and t = 2 yr]

                                                         =$  [tex]\frac{{13 x}}{{100} }[/tex]

Again he got interest from deposit was = [tex]\frac{PRt}{100}[/tex]

                                                               =$  [tex]\frac{(8000-x)\times 2.5\times\frac{18}{12} }{100}[/tex]     [here P = (8000-x), R=2.5% and t =[tex]\frac{18}{12} yr[/tex]]                              

                                                                =$ [tex]\frac{(8000-x) \times 7.5}{200}[/tex]

According to problem

[tex]\frac{{13 x}}{{100} }+\frac{(8000-x) \times 7.5}{200}= 855[/tex]

⇔[tex]\frac{26x + 60000 - 7.5}{200} =855[/tex]

⇔18.5 x =171000 - 60000

⇔x = [tex]\frac{11100}{18.5}[/tex]

⇔x = 6000

So he invested in stock fund was = $6000

and in certificate of deposit was =$(8000- 6000)= $ 2000

Answer:

1

Step-by-step explanation:

bc theyre even

Answer:

The First one To the right is The Correct Shape

Answer:

Option C. As x approaches positive infinity, f(x) approaches positive infinity, and g(x) approaches negative infinity.

Step-by-step explanation:

we know that

Observing the table

The function f(x) is a increasing function

As the value of x increases, the value of f(x) increases

so

As x approaches positive infinity, f(x) approach positive infinity

Find the slope of the linear equation g(x)

The formula to calculate the slope between two points is equal to

[tex]m=\frac{y2-y1}{x2-x1}[/tex]

we have the points (6, -2) and (3, 7)

substitute

[tex]m=\frac{7+2}{3-6}[/tex]

[tex]m=\frac{9}{-3}=-3[/tex]

The slope of the linear equation g(x) is negative

That means ----> Is a decreasing function

As the value of x increases, the value of g(x) decreases

so

As x approaches positive infinity, g(x) approach negative infinity

therefore

As x approaches positive infinity, f(x) approaches positive infinity, and g(x) approaches negative infinity.

The equation of line parallel to given line is: [tex]y = \frac{2}{3}x-\frac{5}{3}[/tex]

Step-by-step explanation:

Given equation of line is:

[tex]y = \frac{2}{3}x+2[/tex]

As the line is in slope-intercept form, the co-efficient of x is the slope of the line

So,

[tex]m_1 =\frac{2}{3}[/tex]

Let m2 be the slope of required line

As both the lines are parallel,

[tex]m_1 = m_2[/tex]

So,

[tex]m_2 = \frac{2}{3}[/tex]

The slope intercept form of line is:

[tex]y = mx+b[/tex]

Putting the value of the slope

[tex]y = \frac{2}{3}x+b[/tex]

To find the value of b, putting (1,-1) in the equation

[tex]-1 = \frac{2}{3}(1) +b\\-1 = \frac{2}{3} +b\\b = -1-\frac{2}{3}\\b = \frac{-3-2}{3}\\b = \frac{-5}{3}[/tex]

Putting b=-5/3 in the equation

[tex]y = \frac{2}{3}x-\frac{5}{3}[/tex]

Hence,

The equation of line parallel to given line is: [tex]y = \frac{2}{3}x-\frac{5}{3}[/tex]

Keywords: Equation of line, slope

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Person A takes 2.3 days to paint the house working alone

Person B takes 13.8 days to paint the house working alone

Solution:

Let "x" be the number of days it takes person A  to paint the house

Person A can paint the neighbor's house 6 times as fast as Person B

Therefore.

Number of days it takes person B to paint the house = 6x

Their rates of painting are added to get  the rate working together

[tex]\frac{\text{1 house}}{\text{x days}} + \frac{\text{1 house}}{\text{6x days}} = \frac{\text{1 house}}{\text{2 days}}[/tex]

[tex]\frac{1}{x} + \frac{1}{6x} = \frac{1}{2}\\\\\frac{1 \times 6}{6x} + \frac{1}{6x} = \frac{1}{2}\\\\\frac{7}{6x} = \frac{1}{2}\\\\\ x = \frac{7}{3}= 2.3[/tex]

Thus person A takes 2.3 days to paint the house working alone

Person B = 2x = 6(2.3) = 13.8

Thus person B takes 13.8 days to paint the house working alone

Answer:

Step-by-step explanation:

From the graph given,

In order to find the equation, we need to consider the points where the curve cuts x- axis

From the graph, we have

[tex]x=-4, x= -3 \, and \, x= -1[/tex]

In factor form

[tex]x+4=0, \, x+3=0, \, and \, x+1=0[/tex]

Now, combine the factors above by multiplying together to form the equation, we have

[tex]f(x)=(x+1)(x+3)(x+4)[/tex]

Therefore, the equation of the graph in factored form is [tex]f(x)=(x+1)(x+3)(x+4)[/tex]

The question requires the equation of a graph in factored form, with the graph cutting the x-axis at -4, -3 and -1. These roots correspond to the factored form of the equation as f(x) = (x + 4)(x + 3)(x + 1). However, this equation is not listed among the choices provided. The correct option is C.

The question is asking for the equation of a graph in factored form. The graph cuts the x-axis at -4, -3, and -1.

This implies these are the roots of the equation. When a graph crosses the x-axis at a particular point, it implies the x-value of that point is a root (or zero) of the polynomial.

Therefore, the roots of the function are -4, -3, and -1. We can then convert these roots into factors by changing their signs and setting them as (x - root).

Therefore, the factored form of the equation would then be: f(x) = (x + 4)(x + 3)(x + 1). However, this equation is not listed among the choices. There might be a mistake the options provided.

It's always vital to carefully check the roots and ensure they correspond to the x values where the graph intersects the x-axis.

Therefor the correct option is C.

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Answer:

45

Step-by-step explanation:

12/15=4/5

4/5=36/x

cross product

5*36=4*x

180=4x

x=180/4

x=45

Answer:

3^4 and 9^2

Step-by-step explanation:

Answer:

X=2

Step-by-step explanation:

FIRST YOU SUBTRACT 3 FROM BOTH SIDES:

4=1/2X+3

-3         -3

1=1/2X

THEN U DIVIDE BOTH SIDES BY 1/2:

1=1/2X

1/1/2=X

1*2/1=X

2=X

Answer: B and d has a dark blue section that is 1/3 x 2/5 of a square

Step-by-step explanation:

Answer:

sorry was there suppost to be a picture with this? which dark blue square? or do we draw it ourselves?

Step-by-step explanation:

sorry i wish i could help :(

Final answer:

To solve the problem, two equations were set up and solved for the number of adult tickets (A). The equations A + S = 631 and S = A - 69 led to finding that 350 adult tickets were sold for the school play.

Explanation:

The school play ticket problem is a basic algebraic question involving setting up and solving equations. We need to determine the number of adult tickets and student tickets sold, given the total tickets and the difference between them.

Let's denote the number of adult tickets as A and the number of student tickets as S. According to the information provided:

A + S = 631 (The total number of tickets sold)

S = A - 69 (There were 69 fewer student tickets sold than adult tickets)

By substituting the second equation into the first, we get:

A + (A - 69) = 631

2A - 69 = 631

2A = 631 + 69

2A = 700

A = 350

So, 350 adult tickets were sold.

The weight in 1980 is [tex]\frac{4k}{5}[/tex] kilograms

Solution:

From 1980 to 1990, Lior’s weight increased by 25%

His weight is "k" kilograms in 1990

To find: weight in 1980

This is a percentage increase problem

Let "x" be the weight in kilograms in 1980

The percentage increase is given by formula:

[tex]\text{Percentage increase } = \frac{\text{Final value - initial value}}{\text{initial value}} \times 100[/tex]

Here,

Initial value in 1980 = x

Final value in 1990 = k

Percentage increase = 25 %

Substituting the values in formula,

[tex]25 = \frac{k-x}{x} \times 100\\\\25x = 100(k-x)\\\\x = 4(k-x)\\\\x = 4k - 4x\\\\5x = 4k\\\\x = \frac{4k}{5}[/tex]

Thus the weight in kilograms in 1980 is [tex]\frac{4k}{5}[/tex]

The football thrown by Steve has a speed of 20 meters per second, as it covers a distance of 60 meters in 3 seconds.

To calculate the speed of the football that Steve throws, we can use the basic physics concept of speed which is the distance traveled divided by the time taken. Since Steve throws the football a distance of 60 meters in 3 seconds, the calculation for the speed v is:

v = distance / time = 60 meters / 3 seconds = 20 meters per second.

Therefore, the football is traveling at a speed of 20 meters per second.

Final answer:

The speed of the football thrown by Steve is 20 meters per second, calculated by dividing the distance thrown, 60 meters, by the time taken, 3 seconds.

Explanation:

If Steve throws a football 60 meters in 3 seconds, we can calculate the speed of the football by using the formula for speed: speed = distance/time. To find the speed of the football, we simply divide the distance Steve's throw covered by the time it took for the football to cover that distance.

The calculation is as follows:

Speed = Distance / Time
Speed = 60 meters / 3 seconds
Speed = 20 meters/second

Therefore, the speed of the football is 20 meters/second

Answer:

430 billion (430,000,000,000) is 4.3 x 10^11 in scientific notation

To convert 430 billion into scientific notation, express it as 4.3 multiplied by 100 billion. In scientific notation, 100 billion becomes 10^11. Therefore, the scientific notation of 430 billion is 4.3 x 10^11.

The process of writing large numbers or small numbers in scientific notation involves expressing the number as a product of a number between 1 and 10 (inclusive) and a power of 10. To write 430 billion dollars in scientific notation, firstly express it as 4.3 multiplied by 100 billion. In scientific notation, 100 billion is 10^11. So, Amazon's worth in scientific notation is 4.3 x 10^11.

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The sprinkler covers an area that is shaped like a circle, with its range as the radius. Using the formula for the area of a circle, πr², and substituting 7 feet for the radius, we find that the sprinkler covers approximately 154 square feet.

The total area that the sprinkler covers can be found by considering the sprinkler's range as the radius of a circle. The formula to find the area of a circle is πr² where π (Pi) is a constant approximately equal to 3.14, and r is the radius of the circle. In this case, the radius of the area the sprinkler covers is 7 feet. So, we plug this value into the formula:

Area = π(7ft)²

Thus, the total area the sprinkler covers is approximately 154 square feet.

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Answer:

I believe it is the fourth graph

Step-by-step explanation:

The only graph that correctly represents the exponential function f(x) = 2ˣ  is the fourth graph

The exponential function is given as:

f(x) = 2ˣ

Thus:

When x = -2, we have:

f(-2) = 2⁻²

f(-2) = 1/2² = 1/4

When x = -1, we have:

f(-1) = 2⁻¹

f(-1) = 1/2¹ = 1/2

When x = 0, we have:

f(0) = 2⁰

f(0) = 1

When x = 1, we have:

f(1) = 2¹

f(1) = 2

When x = 2, we have:

f(1) = 2²

f(1) = 4

Thus, the only graph that correctly represents these values is the fourth graph

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Answer:

it would take 3881040 minutes to complete the entire mural

Answer:

least is 51%

Step-by-step explanation:

so 51%, .57,6/10 and .61

Answer:

Step-by-step explanation:

d=-1-4=-5

[tex]t_{60}=4+(60-1)(-5)=4-295=-291[/tex]

Answer:720

Step-by-step explanation: think about it, 6 packages, 10 per box hold 12 crayons, 10•12=120. 120•6 boxes equals 720. I may be wrong idk but try that. Im fully confident in that answer

Final answer:

To calculate the total number of crayons in a carton, multiply the number of crayons in a small box by the number of boxes in a package, and then by the number of packages in a carton. This results in 720 crayons per carton.

Explanation:

To find out how many crayons come in a carton, we need to do a series of multiplications. We start at the smallest unit, which is the crayon, and work our way up to the carton.

Therefore, there are 720 crayons in a carton.

Answer:i have no idea but go back to your math book and lesson and check :p

Step-by-step explanation:

Answer:

84, 91, 98, 105

Step-by-step explanation:

7x + 7 (x+1) + 7(x+2) + 7(x+3) = 378

28x + 42 = 378

28x = 336

x = 12

7x12, 7x13, 7x14, 7x15   i.e. 84, 91, 98, 105

check: 84 + 91 + 98 + 105 = 378

Answer:

Nolan took 100 seconds.

Step-by-step explanation:

Given:

Kong took 15%, percent fewer seconds than Nolan took to complete his multiplication timed test.

Kong took 85 seconds.

Now, to find the number of seconds Nolan take to complete the test.

Let the number of seconds Nolan take be [tex]x.[/tex]

Kong took = 85 seconds.

As, given Kong took 15%, percent fewer seconds than Nolan took.

Now, to get the number of seconds Nolan took:

[tex]x-15\%\ of\ x=85[/tex]

[tex]x-\frac{15}{100} \times x=85[/tex]

[tex]x-0.15x=85[/tex]

[tex]0.85x=85[/tex]

Dividing both sides by 0.85 we get:

[tex]x=100.[/tex]

Therefore, Nolan took 100 seconds.

Answer:

100 seconds

Step-by-step explanation:

easy math

Answer: x=6

Step-by-step explanation:

3x+7+x=31

4x+7=31

-7 -7

4x=24

24/4= 6

When you divide the same value raised to different powers keep the value and subtract the powers.

A^15 / a^5 = a ^(15-5) = a^10

Answer:

a^10

Step-by-step explanation:

Answer:

0.5 miles/min

Step-by-step explanation:

average speed = total distance / total time

= 15 miles / 30 min

= 0.5 miles/min

Answer:

x = 84

Step-by-step explanation:

The sum of the interior angles of a polygon is

sum = 180° (n - 2) ← n is the number of sides

Here n = 5, thus

sum = 180° × 3 = 540°

Sum the interior angles and equate to 540 for x

131 + 108 + 107 + 110 + x = 540, that is

456 + x = 540 ( subtract 456 from both sides )

x = 84

Answ

this is slope intercept form

Step-by-step explanation: