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3 years ago

Given that JKLM is a parallelogram, solve for x.

Mathematics

2 answers:

Olegator [25]3 years ago

7 0

Answer:

x = 4

Step-by-step explanation:

In a parallelogram, the opposite sides are equal/congruent. This means that KL and JM are equivalent.

In other words, $7x - 2 = 12x - 22$ , and we have to solve for x.

Step 1: Subtract 12x from both sides.

$7x-2-12x=12x-22-12x$
$-5x-2=-22$

Step 2: Add 2 to both sides.

$-5x-2+2=-22+2$
$-5x=-20$

Step 3: Divide both sides by -5.

$-5x/-5 = -20/-5$
$x = 4$

Therefore, x = 4.

Have a lovely rest of your day/night, and good luck with your assignments! ♡

Ilya [14]3 years ago

3 0

X = 4

set both sides equal to each other:

12x - 22 = 7x - 2

5x - 22 = -2

5x = 20

x = 4

hope that helps

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If cos() = − 2 3 and is in Quadrant III, find tan() cot() + csc(). Incorrect: Your answer is incorrect.

nydimaria [60]

Answer:

$\tan(\theta) \cdot \cot(\theta) + \csc(\theta) = \frac{5 - 3\sqrt 5}{5}$

Step-by-step explanation:

Given

$\cos(\theta) = -\frac{2}{3}$

$\theta \to$ Quadrant III

Required

Determine $\tan(\theta) \cdot \cot(\theta) + \csc(\theta)$

We have:

$\cos(\theta) = -\frac{2}{3}$

We know that:

$\sin^2(\theta) + \cos^2(\theta) = 1$

This gives:

$\sin^2(\theta) + (-\frac{2}{3})^2 = 1$

$\sin^2(\theta) + (\frac{4}{9}) = 1$

Collect like terms

$\sin^2(\theta) = 1 - \frac{4}{9}$

Take LCM and solve

$\sin^2(\theta) = \frac{9 -4}{9}$

$\sin^2(\theta) = \frac{5}{9}$

Take the square roots of both sides

$\sin(\theta) = \±\frac{\sqrt 5}{3}$

Sin is negative in quadrant III. So:

$\sin(\theta) = -\frac{\sqrt 5}{3}$

Calculate $\csc(\theta)$

$\csc(\theta) = \frac{1}{\sin(\theta)}$

We have: $\sin(\theta) = -\frac{\sqrt 5}{3}$

So:

$\csc(\theta) = \frac{1}{-\frac{\sqrt 5}{3}}$

$\csc(\theta) = \frac{-3}{\sqrt 5}$

Rationalize

$\csc(\theta) = \frac{-3}{\sqrt 5}*\frac{\sqrt 5}{\sqrt 5}$

$\csc(\theta) = \frac{-3\sqrt 5}{5}$

So, we have:

$\tan(\theta) \cdot \cot(\theta) + \csc(\theta)$

$\tan(\theta) \cdot \cot(\theta) + \csc(\theta) = \tan(\theta) \cdot \frac{1}{\tan(\theta)} + \csc(\theta)$

$\tan(\theta) \cdot \cot(\theta) + \csc(\theta) = 1 + \csc(\theta)$

Substitute: $\csc(\theta) = \frac{-3\sqrt 5}{5}$

$\tan(\theta) \cdot \cot(\theta) + \csc(\theta) = 1 -\frac{3\sqrt 5}{5}$

Take LCM

$\tan(\theta) \cdot \cot(\theta) + \csc(\theta) = \frac{5 - 3\sqrt 5}{5}$

6 0

3 years ago

Figure a is dilated by a scale factor of 1/2 to form figure b. What is the length of x?

PIT_PIT [208]

Answer:

The correct option is 3. The value of x is 8 inches.

Step-by-step explanation:

It is given that Figure A is dilated by a scale factor of 1/2 to form Figure B. It means both figure are similar and corresponding sides of similar figures are proportional.

$\text{scale factor}=\frac{\text{Side of image}}{\text{Side of preimage}}$

$\frac{1}{2}=\frac{x}{16}$

Multiply both sides by 16.

$\frac{16}{2}=x$

$8=x$

Since scale factor is 1/2, so we can directly say that the side length of image is half of the corresponding side of preimage.

The length of x is 8 inches. Therefore the correct option is 3.

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Bingel [31]

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Please help Determine whether y varies directly with x. If so, find the constant of variation k and write the equation.

dsp73

The linear equation:
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---------------------
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Soloha48 [4]

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