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balandron [24]
2 years ago
15

Ben and Alyssa play a game in which they earn the same number of points for each goal and lose the same number of points for eac

h penalty. Ben makes 7 goals and 2 penalties, ending the game with 21 points. Alyssa earns 10 goals and 8 penalties and ends the game with -6 points. How much does a penalty cost and how much does a goal give?
Mathematics
1 answer:
Nadya [2.5K]2 years ago
5 0

Answer:

Each goal gives 5 points and a penalty costs 7 points.

Step-by-step explanation:

Let a penalty cost = x points

And a goal gives = y points

Ben makes 7 goals and 2 penalties ending the game with 21 points,

7y - 2x = 21 --------(1)

Alyssa makes 10 goals and 8 penalties ending the game with (-6) points,

10y - 8x = -6

5y - 4x = -3 --------(2)

Equation (1) multiplied by 2, then subtracted from equation (2),

(5y - 4x) - 2(7y - 2x) = -3 - 2(21)

5y - 4x - 14y + 4x = -3 - 42

-9y = -45

y = 5

From equation (1)

7(5) - 2x = 21

35 - 2x = 21

2x = 35 - 21

2x = 14

x = 7

Therefore, each goal gives 5 points and a penalty costs 7 points.

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Step-by-step explanation:

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2 years ago
At how many points does the graph of the function below intersect the X axis?
masha68 [24]
The answer would be C.2
6 0
3 years ago
Heather measured a swimming pool and made a scale drawing. In real life, the pool is 45 meters long. It is 65 millimeters long i
oksano4ka [1.4K]
Greetings!

"<span>Heather measured a swimming pool and made a scale drawing. In real life, the pool is 45 meters long. It is 65 millimeters long in the drawing. What scale did Heather use for the drawing?"...

65mm=</span>45m<span>
Reduce to Simpliest Form.
</span>65/5=<span>45/5
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As a Representative Fraction (scale), it would look like: (in regards to mm)
13:9000

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4 0
3 years ago
The length of a rectangle is 4 yd less than three times the width, and the area of the rectangle is 55 ya? Find the dimensions o
inysia [295]

Answer:

length = 11 yard

width =  5 yard

Step-by-step explanation:

Area of a rectangle = L W

where A = 55 yard

           L = 3W - 4

find: Length

        width

solution:

A = L W

55 = (3W - 4) W

55 = 3W² - 4W

3W² - 4W - 55 = 0

use quadratic equation to solve for W:

W = <u> - (-4) ± √(-4)² - 4(3)-55 </u>

                    2(3)

W = 5,  W = -11/3

substitute W=5 to equation L = 3W - 4 to solve for L

L = 3W - 4

L = 3(5) - 4

L = 15 - 4

L = 11

therefore, the dimensions of a rectangle:

length = 11 yard

width =  5 yard

6 0
3 years ago
What is the y-intercept of this graph?
melisa1 [442]

Answer:

The Y-intercept is 0.

Step-by-step explanation:

5 0
2 years ago
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