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Schach [20]
3 years ago
9

A 100 point test contains a total of 20 questions. The multiple choice questions are worth 3 points each and the short response

question are worth 8 points each. Write a linear system that represents this situation. How many multiple choice and short response questions are on the test?
Mathematics
1 answer:
JulsSmile [24]3 years ago
5 0

Answer: the number of multiple choice questions in the test is 12.

the number of short response questions in the test is 8.

Step-by-step explanation:

Let x represent the number of multiple choice questions in the test.

Let y represent the number of short response questions in the test.

The total number of questions in the test is 20. It means that

x + y = 20

The multiple choice questions are worth 3 points each and the short response question are worth 8 points each. The total number of points is 100. It means that

3x + 8y = 100 - - - - - - - - - - 1

Substituting x = 20 - y into equation 1, it becomes

3(20 - y) + 8y = 100

60 - 3y + 8y = 100

- 3y + 8y = 100 - 60

5y = 40

y = 40/5 = 8

x = 20 - y = 20 - 8

x = 12

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What is an equation of the line that passes through the point (8,-7)(8,−7) and is parallel to the line 5x+4y=165x+4y=16?
gizmo_the_mogwai [7]

Answer:

The equation of line that passes through the point (8,-7) and is parallel to the line 5x+4y=16 is  \mathbf{y=-\frac{5}{4}x+3}

Step-by-step explanation:

We need to write an equation of the line that passes through the point (8,-7) and is parallel to the line 5x+4y=16.

The equation will be of form y=mx+b where m is slope and b is y-intercept.

Finding slope of the line:

Since both the lines are parallel, and we know that parallel lines have same slope.

The slope of given line 5x+4y=16 can be found by writing in slope-intercept form y=mx+b

5x+4y=16\\4y=-5x+16\\y=-\frac{5}{4}x+16

Comparing with y=mx+b the slope m is: m=-\frac{5}{4}

So, the slope of required line is: m=-\frac{5}{4}

Now, finding y-intercept b

y-intercept can be found using slope m=-\frac{5}{4} and point (8,-7)

y=mx+b\\-7=-\frac{5}{4}(8)+b\\-7=-5(2)+b\\-7=-10+b\\b=-7+10\\b=3

So, we get y-intercept: b=3

Now, the equation of required line having slope m=-\frac{5}{4} and y-intercept b=3 is:

y=mx+b\\y=-\frac{5}{4}x+3

So, the equation of line that passes through the point (8,-7) and is parallel to the line 5x+4y=16 \mathbf{y=-\frac{5}{4}x+3}

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2 years ago
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