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2 years ago

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To find the area of parallelogram RSTU, Juan starts by drawing a rectangle around it. Each vertex of parallelogram RSTU is on a

side of the rectangle he draws. On a coordinate plane, parallelogram R S T U has points (negative 4, negative 3,) (negative 5, 1), (4, 3), and (5, negative 1). Which expression can be subtracted from the area of the rectangle to find the area of parallelogram RSTU? 2 (18 + 4) One-half (18 + 4) (18 + 4) (18 - 4)

1 answer:

STatiana [176]2 years ago

6 0

Answer:

The value that can be subtracted from the area of the rectangle to give the area of the parallelogram = 1/2 × 4.1245 × 0.1085

Step-by-step explanation:

The given parameters are;

The coordinates of parallelogram RSTU are;

R(-4, -3), S(-5, 1), T(4, 3), U(5, -1)

The lengths of the sides are (using an online length calculator);

RS = 4.1231

RT = 10

ST = 9.2195

SU = 10.198

TU = 4.1231

UR = 9.2195

Therefore, by definition of a parallelogram, we have;

RS║TU and ST║UR

The slope of RS = (1 - (-3))/(-5 - (-4)) = -4

The slope of ST = (3 - 1)/(4 - (-5)) = 2/9

The equation of the line perpendicular to ST is therefore;

y - 1 = -9/2×(x - (-5))

y = -9x/2 - 43/2

The equation of RS = y - (-3) = 1/4×(x - (-4)) = x/4 + 1

y = x/4 - 2

The point where the two lines meet is therefore;

-9x/2 - 43/2 = x/4 - 2

x = -78/19

y = -115/38

The length of the side of the rectangle = 4.1245

The excess width of the rectangle = 0.1085

The value that can be subtracted from the area of the rectangle to give the area of the parallelogram = 1/2 × 4.1245 × 0.1085.

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Step-by-step explanation:

Problems of normally distributed samples can be solved using the z-score formula.

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In this problem, we have that:

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This is the pvalue of Z when X = 20000. So

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So this probability is 0.0392.

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This is the pvalue of Z when X = 30000 subtracted by the pvalue of Z when X = 20000.

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X = 20000

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$Z = \frac{20000 - 29858}{5600}$

$Z = -1.76$

$Z = -1.76$ has a pvalue of 0.0392.

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$1.645 = \frac{X - 29858}{5600}$

$X - 29858 = 5600*1.645$

$X = 39070$

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Answer:

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Step-by-step explanation:

* Lets revise the rules of the midpoint and the slope to prove the

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