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AleksAgata [21]
3 years ago
9

A system of linear equations includes the line that is created by the equation y = x+ 3, graphed below, and the line through the

points (3, 1) and (4, 3).
On a coordinate plane, a line goes through (0, 3) and (2, 5).
What is the solution to the system of equations?

Mathematics
1 answer:
frez [133]3 years ago
3 0

Answer:

  (8, 11)

Step-by-step explanation:

The 2-point form of the equation of a line is useful for the one where only points are given.

  y = (y2 -y1)/(x2 -x1)(x -x1) +y1

  y = (3 -1)/(4 -3)(x -3) +1

  y = 2(x -3) +1

We can equate this to the expression for y in the given equation.

  x +3 = 2(x -3) +1

  x +3 = 2x -5 . . . . . . eliminate parentheses

  8 = x . . . . . . . . . . . . add 5-x

Using the given equation, we can find y:

  y = x +3 = 8 +3

  y = 11

The solution to the system is (x, y) = (8, 11).

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Arte-miy333 [17]

Answer:

The z-score for the statistics test grade is of 1.11.

The z-score for the calculus test grade is 7.3.

Due to the higher z-score, the student performed better on the calculus test relative to the other students in each class

Step-by-step explanation:

Z-score:

In a set with mean \mu and standard deviation \sigma, the z-score of a measure X is given by:

Z = \frac{X - \mu}{\sigma}

The Z-score measures how many standard deviations the measure is from the mean. After finding the Z-score, we look at the z-score table and find the p-value associated with this z-score. This p-value is the probability that the value of the measure is smaller than X, that is, the percentile of X. Subtracting 1 by the p-value, we get the probability that the value of the measure is greater than X.

In this question:

The grade with the higher z-score is better relative to the other students in each class.

Statistics:

Mean of 79 and standard deviation of 4.5, so \mu = 79, \sigma = 4.5

Student got 84, so X = 84

The z-score is:

Z = \frac{X - \mu}{\sigma}

Z = \frac{84 - 79}{4.5}

Z = 1.11

The z-score for the statistics test grade is of 1.11.

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Mean of 69, standard deviation of 3.7, so \mu = 69, \sigma = 3.7

Student got 96, so X = 96

The z-score is:

Z = \frac{X - \mu}{\sigma}

Z = \frac{96 - 69}{3.7}

Z = 7.3

The z-score for the calculus test grade is 7.3.

On which test did the student perform better relative to the other students in each class?

Due to the higher z-score, the student performed better on the calculus test relative to the other students in each class

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