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mafiozo [28]
3 years ago
8

David bought three DVDs in for books for $40 at a yard sale and I bought one DVD and six books for $18 how much did each DVD and

book cost
Mathematics
1 answer:
grandymaker [24]3 years ago
4 0

Answer: One DVD is $12 and one book is $1

Step-by-step explanation:

Let the DVD be d and the book be b.

Case 1:

3d + 4b = $40.......(1)

Case 2:

1d + 6b = $18........... (2)

In this equations above, I intend to eliminate variable d, so I'm going to multiply the coefficient of d in (1) to multiply (2)

3 × (1d + 6b = 18)

3d + 18b = 54........ .(3)

Then, subtract (1) from (3)

3d + 18b = 54

- ( 3d + 4b = 40)

3d - 3d + 18b - 4b = 54 - 40

0 + 14b = 14

b = 14/14

b = 1.

Then substitute 1 for b in (2)

1d + 6(1) = 18

d + 6 = 18

d = 18 - 6

d = 12.

(d,b) = (12,1)

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The average heights of x number of girls and 15 boys is 123. if the average heights of boys is 125 and that of girls is 120.find
mamaluj [8]

Answer:

x = 10. In other words, there number of girls is 10.

Step-by-step explanation:

The average of a number of measurements is equal to the sum of these measurements over the number of measurements.

\displaystyle \text{Average} = \frac{\text{Sum of measurements}}{\text{Number of measurements}}.

Rewrite to obtain:

\begin{aligned}& \text{Sum of measurements}= (\text{Number of measurements}) \times (\text{Average}) \end{aligned}.

For this question:

\begin{aligned}& \text{Sum of heights of boys} \\ &= (\text{Number of boys}) \times (\text{Average height of boys}) \\ &= 15 \times 125 = 1875\end{aligned}.

\begin{aligned}& \text{Sum of heights of girls} \\ &= (\text{Number of girls}) \times (\text{Average height of girls}) \\ &= x \times 120 = 120\, x\end{aligned}.

Therefore:

\begin{aligned}& \text{Sum of boys and girls} \\ &= \text{Sum of heights of boys} + \text{Sum of heights of girls}\\ &= 1875 + 120\, x\end{aligned}.

On the other hand, there are (15 + x) boys and girls in total. Using the formula for average:

\begin{aligned}& \text{Average height of boys and girls} \\ &= \frac{\text{Sum of heights of boys and girls}}{\text{Number of boys and girls}} \\ &= \frac{1875 + 120\, x}{15 + x}\end{aligned}.

From the question, this average should be equal to 123. In other words:

\displaystyle \frac{1875 + 120\, x}{15 + x} = 123.

Solve this equation for x to obtain:

1875 + 120\, x= 123\, (15 + x).

(123 - 120)\, x = 1875 - 123 \times 15.

x = 10.

In other words, the number of girls here is 10.

5 0
3 years ago
(Don’t send me a link pls just answer!) First 3 people to answer get lots of points pls do it by friday!
Natali5045456 [20]

Answer:

8835.73ft^3

Step-by-step explanation:

First:

Find area of the base circle.

Diameter is 15, so radius is 7.5

Area of the base circle is 56.25pi (use formula: A=pi(r)^2 ) (also ill convert pi into decimals only later)

next find the volume of the cylinder

height is 40 so volume = 56.25pi*40 = 2250pi

next find the volume of the dome at the top.

you know the radius is 7.5

Use volume of sphere formula below :

4 /3πr^3

=1767.15

alright now add the two bolded values

1767.15+2250pi

= 8835.73

hope this helps

7 0
3 years ago
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Find the equation of the line that contains the point (3,9) and is parallel to the line y=4x+1. Write the line in slope-intercep
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Y = 4x + 1....slope here is 4. A parallel line will have the same slope

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now we sub and find b, the y int
9 = 4(3) + b
9 = 12 + b
9 - 12 = b
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so ur parallel equation is : y = 4x - 3
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A restaurant is making hamburgers. The cooks use two thirds
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Identify 3 major arcs of circle that contain point A?
natita [175]

Answer:

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Semi Circle (three capital letters) Arcs that have a degree measure equal to 180 degrees.Step-by-step explanation:

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