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suter [353]
3 years ago
14

A student has a 90, 84, and an 86 on their first 3 tests. What possible scores would the student need

Mathematics
1 answer:
Ugo [173]3 years ago
4 0
The student would have to score 100% on their next test to brung their average up to 90. Here is why;
90+84+86=260
(260+?)/4=90
(260+100)/4=90
360/4=90
This is done to get the mean (or average) of a group of numbers by adding all the numbers and dividing by the amount of numbers you added together. Here it is divided by 4 because of the three tests he has taken and the test he will take.
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3x + 2y = 5 5x + 2y = 7 Based on the given system of equations, which of the following is not true? 2x = 2 8x = 12 4y = 4
weqwewe [10]
<h3>Answer:</h3>

8x = 12

<h3>Explanation:</h3>

Subtracting the first equation from the second, you get ...

... (5x +2y) -(3x +2y) = (7) -(5)

... 2x = 2 . . . . . the first answer choice is true

___

Multiplying this expression for x by 4, we get

... 8x = 8 . . . . . the second answer choice (8x=12) is false

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Adding thee first equation to the second, you get ...

... (3x +2y) +(5x +2y) = (5) +(7)

... 8x +4y = 12

... 8 + 4y = 12 . . . . . . use the value of 8x just computed

... 4y = 4 . . . . . . . . . . subtract 8; the third answer choice is true

_____

<em>Alternate approaches</em>

In short, if you solve the system by any of the methods available, you find x=1 and y=1, so the second answer choice is clearly the correct one:

... 8x ≠ 12

By Cramer's method:

... x = (2·7-2·5)/(2·5-2·3) = 4/4 = 1

... y = (5·5-7·3)/4 = 4/4 = 1

By graphing, see attached.

By substitution (for 2y):

... 5x +(5-3x) =7 . . . . . using 2y=5-3x

... 2x = 2 . . . . . . subtract 5

... x = 1 . . . . . . . .divide by 2

... 5 -3·1 = 2y = 2 . . . . substitute x into the expression for 2y

... y = 1 . . . . . . . divide by 2

By matrix methods, see the second attachment. (x, y) = (1, 1), found in the rightmost column of the result.

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