Ashley is putting money into a savings account. She starts with $750 in the savings account, and each week she adds $70.
Let s represent the total amount of money in the savings account (in dollars), and let w represent the number of weeks Ashley has been adding money. Write an equation relating s to w. Then use this equation to find the total amount of money in the savings account after 18 weeks.

Part a: The data points appear to follow an exponential pattern. This is because the balance is increasing at a rate that is proportional to the current balance.

Part b: The equation of the best fit is y = 50(1.06)^x. This can be found using a variety of methods, including graphing the data points and fitting a curve to them, or using a statistical software package.

Part c: When x = 32, y = 50(1.06)^32 = $2,499.82.

Years since 1990, x 0 5 10 15 20 25 30

Balance, y $50 $62.31 $77.65 $96.76 $120.59 $150.27 $187.27 $2,499.82

The equation of the fitted curve is y = 50(1.06)^x.

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Answer:The fourth function

Step-by-step explanation:

You can never have repeating x-values. You can have repeating y-values though. Whenever determining whether something is a function, just look at whether it has repeating x-values or not. If it does, it is not a function. If it doesn't, it is a function.

Answer:

2km

Step-by-step explanation:

Distance = Speed ÷ Time

Distance = 3 ÷ 1.5 (as 1 hour and 30 minutes is an hour and a half)

Distance = 2km

Answer:

4.5 km

Step-by-step explanation:

it takes an hour to walk 3. 1 hour is 60 minutes cut that in half to get 30, so you have to cut the 3 in half as well. which is 1.5. add 3 and 1.5 to get your answer 4.5

Answer:

To mathematically prove that Marc hit the ball near the top of the tower, he could use the equation h(x) = -16x^2 + 120x, where h is the height of the ball and x is the number of seconds the ball is in the air.

First, Marc would need to determine the maximum height the ball reached during its flight. This can be found by using the vertex formula, which is x = -b/2a. In this case, a = -16 and b = 120, so x = -120/(2*-16) = 3.75 seconds.

Next, Marc can substitute this value back into the original equation to find the maximum height the ball reached. h(3.75) = -16(3.75)^2 + 120(3.75) = 135 feet.

Since the tower is 300 feet tall, Marc could conclude that if the ball hit near the top of the tower, it would have reached a height close to 300 feet. Since the ball reached a maximum height of 135 feet, it is unlikely that it hit the top of the tower.

However, this calculation assumes that the tower is directly in line with Marc's shot and that the ball did not have any horizontal movement. In reality, the tower could have been to the left or right of the shot, and the ball could have had some horizontal movement, which would affect its height at impact. Therefore, this calculation can only provide a rough estimate and cannot definitively prove whether or not the ball hit near the top of the tower.

Answer:

C

Step-by-step explanation:

Answer: 24

Step-by-step explanation: 24

Simply multiply all of the fractions with the total number of marbles

48(2/3)(3/4)

a) The ratios are proportional.

b) 156 people will need  30 pounds.

The ratios will be only if we can rewrite one into the other.

4/14 and 32/112

Let's take the second one and simplify it:

32/112 = 16/56 = 8/28 = 4/14

So yea, the ratios are equivalent.

b) We know that 5 pounds are enough for 26 people, then the amount that 156 people will need is:

(156/26)*5 pounds = 30 pounds.

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The price the supermarket can charge per egg that is between the prices of per egg for the two different-sized cartons is $0.245 per egg.

According to the question,

We have the following information:

Cost of 12 eggs in a carton = $3.00

Cost of 18 eggs in another carton = $4.32

Now, to find the charge per egg that is between the prices of per egg for these different-sized cartons, we will first find the charge per egg of both of them.

We know that to find the cost of 1 product we divide the given cost by the number of products.

Cost of 12 eggs in a carton = $3.00

Cost of 1 egg = $ (3.00/12)

Cost of 1 egg = $0.25

Cost of 18 eggs in another carton = $4.32

Cost of 1 egg = $(4.32/18)

Cost of 1 egg = $0.24

Now, we have to find the price of egg between 0.24 and 0.25.

Note the difference between these two charges is 0.01.

We will divide it by 2 to find the exact middle charge:

0.01/2 = 0.005

We can add this in $0.24 or subtract it from$ 0.25.

$0.24 + $0.005 = $0.245

Hence, price the supermarket can charge per egg is $0.245.

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The length of the guy wire to the nearest foot would be = 10 ft.

The relationship between the tower, guy wire and pole forms the shape of a right angle triangle.

The distance from the stake to the pole (opposite) =a = 5 ft

The distance from the pole to the tower (adjacent) =b= 9ft

The length of the guy wire= c = X

Using the Pythagorean formula:

c² = a² + b²

c² = 5² + 9²

c² = 25+81

c² = 106

C = √106

C= 10 ft ( to the nearest foot)

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Complete question:

A guy wire runs from the top of a cell tower to a metal stake in the ground. Sophie places a 7 ft tall pole to support the guy wire. After placing the pole, Sophie measures the distance from the stake to the pole to be 5 ft. She then measures the distance from the pole to the tower to be 9 ft. Find the length of the guy wire, to the nearest foot.

Answer:

67.25

Step-by-step explanation:

Since they can each get 1/2 the jelly beans but need to eat it over 4 days they will be eating 1/2*1/4 jelly beans per day. This is equal to 1/8x where x is the total jelly beans. We know the total so we can plug 538 in for x and divide 538 by 8 to get 67.25

Answer: x > 7

    Step-by-step explanation:

Given:

\(\displaystyle \frac{1}{3}x- \frac{2}{7}x > \frac{1}{3}\)

Subtract:

\(\displaystyle \frac{1}{21}x > \frac{1}{3}\)

Divide both sides of the equation by \(\frac{1}{21}\):

\(\displaystyle x > 7\)

    What does this mean?

This means the x is equal to all values greater than 7.

-> 7.432421, 7.5, 8, 250, etc

Answer: D:(-1,4)

R:(-4,4)

Step-by-step explanation:

I hope that correct

The vertex of point A' in the dilated triangle A'B'C' is (6, 4.5).

1. Start by calculating the distance between the vertices of the original triangle ABC:

  - Distance between A(4, 3) and B(3, -2):

    Δx = 3 - 4 = -1

    Δy = -2 - 3 = -5

    Distance = √((-\(1)^2\) + (-\(5)^2\)) = √26

  - Distance between B(3, -2) and C(-3, 1):

    Δx = -3 - 3 = -6

    Δy = 1 - (-2) = 3

    Distance = √((-6)² + 3²) = √45 = 3√5

  - Distance between C(-3, 1) and A(4, 3):

    Δx = 4 - (-3) = 7

    Δy = 3 - 1 = 2

    Distance = √(7² + 2²) = √53

2. Apply the scale factor of 1.5 to the distances calculated above:

  - Distance between A' and B' = 1.5 * √26

  - Distance between B' and C' = 1.5 * 3√5

  - Distance between C' and A' = 1.5 * √53

3. Determine the coordinates of A' by using the distance formula and the given coordinates of A(4, 3):

  - A' is located Δx units horizontally and Δy units vertically from A.

  - Δx = 1.5 * (-1) = -1.5

  - Δy = 1.5 * (-5) = -7.5

  - Coordinates of A':

    x-coordinate: 4 + (-1.5) = 2.5

    y-coordinate: 3 + (-7.5) = -4.5

4. Thus, the vertex of point A' in the dilated triangle A'B'C' is (2.5, -4.5).

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Answer:

the surface area of the cube is 150 inches squared

Step-by-step explanation:

The computation of the surface area of the cube is shown below:

As we know that

The surface area of the cube is

= 6s^2

= 6(5)^2

= 150 inches squared

hence, the surface area of the cube is 150 inches squared

Answer:

C.

Step-by-step explanation:

Answer:

B) \(4i\sqrt{2}\)

Step-by-step explanation:

\(\sqrt{-2}=i\sqrt{2}\\\sqrt{-18}=i\sqrt{18}=i\sqrt{9*2}=3i\sqrt{2}\\\\\sqrt{-2}+\sqrt{-18}=i\sqrt{2}+3i\sqrt{2}=4i\sqrt{2}\)

Answer:

The perimeter of the triangle is 11x+1

The adjusted balance, considering the new account balance, payments/credits, new purchases, and finance charge, is $489.61.

To calculate the adjusted balance, we need to consider the new account balance, payments/credits, new purchases, and finance charges.

Starting with the new account balance of $435.92, we subtract the payments/credits of $68.50. This represents the amount that has been paid or credited to the account, reducing the balance.

Next, we add the new purchases of $118.49. These are additional charges made to the account, increasing the balance.

Finally, we add the finance charge of $3.70. This charge is typically applied as interest on the outstanding balance.

To calculate the adjusted balance, we can follow these steps:

Start with the new account balance: $435.92

Subtract the payments/credits: $435.92 - $68.50 = $367.42

Add the new purchases: $367.42 + $118.49 = $485.91

Add the finance charge: $485.91 + $3.70 = $489.61

Therefore, the amount of the adjusted balance is $489.61.

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Answer:

convert the lengths to meters

10dm=1m

1dm=0.1m

hence, firs ribbon

2m+0.1m=2.1m

Second Ribbon

3m and 9dm

convert 9dm into Metres we get 0.9m

hence, 3m+0.9m=3.9m

Third Ribbon

6m+0.4m=6.4m

Answer:

The y-intercept of the graph of the equation is -9. This means that the graph crosses the y-axis at the point (0, -9).

Step-by-step explanation:

To solve this question, we need to plug in x = 0 into the given equation and simplify. We get:

y = 6(0 - 1/2)(0 + 3) y = 6(-1/2)(3) y = -9

Therefore, the y-intercept of the graph of the equation is -9. This means that the graph crosses the y-axis at the point (0, -9).

Answer:

A, B, C, D

Step-by-step explanation:

If it is wrong, then remove the C because i am not too sure about that

Answer:

(f+g)(x)=4x+3

Step-by-step explanation:

Given the functions f and g defined above, their sum f+g is defined by (f+g)(x)=f(x)+g(x). Using algebra, we thus have (f+g)(x)=2x-1+2x+4=4x+3.

Answer:

D

Step-by-step explanation:

y= -4/3x+2/3

Answer:

Price of X is $24.81

Price of Y is $3.66

Price of Z is $11.36

Step-by-step explanation:

for person A, we know that earns $40, then we can write the equation:

-4*z + 3*x + 3*y = $40

For person B, we know that earns $50, then:

1*z + 2*x - 3*y = $50

For person C, we know that earns $130, then:

6*z - 1*x + 4*y = $130

Then we have a system of equations:

-4*z + 3*x + 3*y = $40

1*z + 2*x - 3*y = $50

6*z - 1*x + 4*y = $130

To solve the system, we need to isolate one of the variables in one of the equations.

Let's isolate z in the second equation:

z = $50 - 2*x + 3*y

now we can replace this in the other two equations:

-4*z + 3*x + 3*y = $40

6*z - 1*x + 4*y = $130

So we get:

-4*($50 - 2*x + 3*y) + 3*x + 3*y = $40

6*($50 - 2*x + 3*y) - 1*x + 4*y = $130

Now we need to simplify both of these, so we get:

-$200 + 11x - 9y = $40

$350 - 13*x + 28*y = $130

Now again, we need to isolate one of the variables in one of the equations.

Let's isolate x in the first one:

-$200 + 11x - 9y = $40

11x - 9y = $40 + $200 = $240

11x = $240 + 9y

x = ($240 + 9y)/11

Now we can replace this in the other equation:

$350 - 13*x + 28*y = $130

$350 - 13*($240 + 9y)/11 + 28*y = $130

Now we can solve this for y.

- 13*($240 + 9y)/11 + 28*y  = $130 - $350 = -$220

-13*$240  - (13/11)*9y + 28y = - $220

y*(28 - (9*13/1) ) = -$220 + (13/11)*$240

y = ( (13/11)*$240 - $220)/(28 - (9*13/1) ) = $3.66

We know that:

x = ($240 + 9y)/11

Replacing the value of y, we get:

x = ($240 + 9*$3.66)/11  = $24.81

And the equation of z is:

z = $50 - 2*x + 3*y = $50 - 2* $24.81 + 3*$3.66 = $11.36

Then:

Price of X is $24.81

Price of Y is $3.66

Price of Z is $11.36

Answer:

About 7.1 cups.

Step-by-step explanation:

Recipe requires 2 cups per 28 cookies.

28 divided by 2=14.

So 1 cup per 14 cookies.

100 divided by 14 equals 7.142....

Rounded to the tenths place is 7.1.

Answer:

it does

Step-by-step explanation:

i did this assignment yesterday

Answer:

(1) The slope of the line having y = 5 as its equation is zero ⇒ (C)

(2) The slope of the line having x = -4 as its equation is undefined ⇒ (B)

Step-by-step explanation:

Let us use the rules above to solve the question

(1)

∵ The equation of the line is y = 5

→ That means the line is horizontal

∴ The line is a horizontal line

∵ The slope of the horizontal line = zero

∴ The slope of the line having y = 5 as its equation is zero

(2)

∵ The equation of the line is x = -4

→ That means the line is vertical

∴ The line is a vertical line

∵ The slope of the vertical line is undefined

∴ The slope of the line having x = -4 as its equation is undefined

The product of the two complex number c₁c₂ is thus 10 + 9i.

Let c₁ = a + ib and c₂ = c + id. Also z₁ represent 2 + 2i and z₂ represent 5 + i. The length of side of the equilateral triangle formed can be obtained by

|z₁ - z₂| = r = √((5 - 2)² + (1 - 2)² = √10

a² + b² - 4a - 4b + 8 = 10

a² + b² - 10a - 2b + 26 = 10

So 6a - 2b = 18 that is 3a - b = 9

Thus b = 3a - 9

Similarly c² + d² - 4c - 4d + 8 = 10

c² + d² - 10c - 2d + 26 = 10

So 3c - d = 9, that is d = 3c - 9

Midpoint of line joining c₁ and c₂ is same as that of z₁ and z₂, so

(c + a)/2 = ( 5 + 2)/ 2 and (d + b)/2 = (1 + 2)/2

So midpoint is 3.5 + 1.5i

Altitude of equilateral triangle of side a is √3a/2

That is √(a - 3.5)² + (b - 1.5)² = √3×√10/2

√(a - 3.5)² + (3a - 9 - 1.5)² = √30 /2

a² - 7a + 12.25 + 9a² - 63a + 110.25 = 30/4

On solving a = (7 ± √3)/ 2

So a = (7 - √3)/ 2, c = (7 + √3)/ 2

b = 3a - 9 = (3 - 3√3)/ 2, d = (3 + 3√3)/2

So c

c₁ = (7 - √3)/2 + i (3 - 3√3)/ 2

c₂ = (7 + √3)/2 + i (3 + 3√3)/ 2

So the product c₁c₂ is

= ((7 - √3)/ 2) * ((7 + √3)/ 2) - ((3 - √3)/ 2) * ((3 + √3)/ 2) + i (((7 - √3)/ 2) * ((3 + √3)/ 2) + ((7 + √3)/ 2) * ((3 - √3)/ 2))

= 10 + 9i

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Answer:

36 < (x - 2)² + (y + 3)² and 16 > (x - 4)² + y²

Step-by-step explanation:

This is because the shaded area is inside the first circle (centered at (4, 0) with a radius of 4) but outside the second circle (centered at (2, -3) with a radius of 6). The inequalities reflect these conditions by setting the inequality signs accordingly. The inequality with "<" for the first circle ensures that the shaded area is within the circle, and the inequality with ">" for the second circle ensures that the shaded area is outside the circle.