Find the value of x in each case. PLEASE SHOW WORK!!!

Mathematics

1 answer:

myrzilka [38]3 years ago

4 0

$m\angle BCA=180^o-5x$

$\angle CAB=\angle ACD\\\\m\angle CAB=33^o$

In the triangle ABC:

$m\angle ABC+m\angle BCA+m\angle CAB=180^o\\\\2x+180^o-5x+33^o=180^o\\\\-3x+213^o=180^o\ \ \ |-213^o\\\\-3x=-33^o\ \ \ |:(-3)\\\\x=11^o$

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Answer:

y = (4/3)x − 10

Step-by-step explanation:

Rewrite in slope-intercept form.

The slope-intercept form is y = mx + b, where m is the slope and b is they-intercept.

y = mx + b

Subtract 4x from both sides of the equation.

−3y = 8 − 4x

Divide each term by −3 and simplify.

Divide each term in −3y = 8 − 4x by −3.

(−3y/−3)= (8/−3) + (−4x/−3)

Cancel the common factor of −3.

y= (8/−3) + (−4x/−3)

Simplify (8/−3) + (−4x/−3)

y= (4x/3 - 8/3)

Reorder terms.

y= 4x/3 - 8/3

Using the slope-intercept form, the slope is 4/3

m = 4/3

To find an equation that is parallel, the slopes must be equal. Find the parallel line using the point-slope formula.

Use the slope 4/3 and a given point (6, −2) to substitute for $x_{1}$ and $y_{1}$ in the point-slope form. $y$ − $y_{1}$ = $m$ ( $x$ − $x_{1}$ ) which is derived from the slope equation $m=$ ( $y_{2}$ − $y_{1}$ )/( $x_{2}$ - $x_{1}$ )