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nexus9112 [7]
2 years ago
6

Solve the following equation for x. 3x - 9 = -42

Mathematics
1 answer:
r-ruslan [8.4K]2 years ago
3 0

Answer:

x = -11

Step-by-step explanation:

Add 9 to both sides of the equation

3 − 9 = −42

3 − 9 + 9 = −42 + 9

Simplify

Add the numbers

3 = −33

Divide both sides of the equation by the same term

3 = −33

3/3 = −33/3

Simplify

Cancel terms that are in both the numerator and denominator

Divide the numbers

= −11

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prove that the quadrilateral whose vertices are the points A(-1,1), B(-3,4), C(1,5) and D(3,2) is a parallelogram.
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Answer:

Since \overrightarrow{AB} = \overrightarrow{DC} and \overrightarrow{AD} = \overrightarrow{BC}, then the quadrilateral ABCD is a parallelogram.

Step-by-step explanation:

First, we label each point of the quadrilateral with the help of a graphing tool. If the quadrilateral ABCD is a parallelogram, then \overrightarrow{AB} = \overrightarrow{DC} and \overrightarrow{AD} = \overrightarrow{BC}. If we know that A(x,y) =(-1, 1), B(x,y) =(-3,4), C(x,y) = (1,5) and D(x,y) = (3,2), then the measure of each vector is, respectively:

\overrightarrow{AB} = (-3,4)-(-1,1)

\overrightarrow{AB} = (-2, 3)

\overrightarrow{DC} = (1,5)-(3,2)

\overrightarrow{DC} = ( -2,3)

\overrightarrow{AD} = (3,2)-(-1,1)

\overrightarrow{AD} = (4, 1)

\overrightarrow{BC} = (1,5)-(-3,4)

\overrightarrow{BC} = (4, 1)

Since \overrightarrow{AB} = \overrightarrow{DC} and \overrightarrow{AD} = \overrightarrow{BC}, then the quadrilateral ABCD is a parallelogram.

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Answer:

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Step-by-step explanation:

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