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2 years ago

Solve this equation for x in terms of y and z:

Mathematics

2 answers:

lora16 [44]2 years ago

6 0

Answer:

x = 5

Step-by-step explanation:

9x + 3y + 4z = 24

9x + 3(9) + 4(-12) = 24

9x + 27 + (-48) = 24

9x + 27 - 48 = 24

9x - 21 = 24

9x = 24 + 21

9x = 45

x = 45 ÷ 9

x = 5

Alex Ar [27]2 years ago

4 0

3y = 3 * 9 = 27
4z = 4 * -12 = -48
: -48 + 27 = -21
: -21 + x = 24
: X = 45.
I hope that makes sense.

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2 years ago

Prove that BUGS is a trapezoid with coordinates B(-2,-1), U(0,3), G(3,2) and S(4,-3).

telo118 [61]

Answer:

Proved

Step-by-step explanation:

Given

$B =(-2,-1)$

$U = (0,3)$

$G = (3,2)$

$S = (4,-3)$

Required

Prove BUGS is a trapezoid

Given the coordinates, to prove a trapezoid; all we need to do is to check if one pair of sides is parallel.

Taking BU and GS as a pair

First, we calculate the slope using:

$m = \frac{y_2 - y_1}{x_2 - x_1}$

For BU

$B =(-2,-1)$ --- $(x_1,y_1)$

$U = (0,3)$ --- $(x_2,y_2)$

So, we have:

$m = \frac{3 - -1}{0- -2}$

$m = \frac{4}{2}$

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For GS

$G = (3,2)$ --- $(x_1,y_1)$

$S = (4,-3)$ --- $(x_2,y_2)$

So, we have:

$m = \frac{-3-2}{4-3}$

$m = \frac{-5}{1}$

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The slope of BU and GS are not the same; hence, they are not parallel.

Taking BS and GU as a pair

Calculate the slope

For BS

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$S = (4,-3)$ --- $(x_2,y_2)$

So, we have:

$m = \frac{-3 - -1}{4- -2}$

$m = \frac{-2}{6}$

$m = -\frac{1}{3}$

For GU

$G = (3,2)$ --- $(x_1,y_1)$

$U = (0,3)$ --- $(x_2,y_2)$

So, we have:

$m = \frac{3-2}{0-3}$

$m = \frac{1}{-3}$

$m = -\frac{1}{3}$

The slope of BS and GU are the same; hence, they are parallel.

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