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4 years ago

Refer to the figures below to complete the following problem.

Mathematics

2 answers:

xxTIMURxx [149]4 years ago

7 0

Answer:

Step-by-step explanation:

Klio2033 [76]4 years ago

4 0

Answer:

120°

Step-by-step explanation:

they are parallel to each other also meaning they equal each other

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3.1 Find the equation of the line passing through (4, 5) and parallel to the line 3x – 2y = 4.

valentinak56 [21]

$\rule{50}{1}\large\blue\textsf{\textbf{\underline{Question:-}}}\rule{50}{1}$

<em>Find the equation of the line passing through (4, 5) and parallel to </em>

<em />

<em> </em> $\rule{50}{1}\large\blue\textsf{\textbf{\underline{Answer and how to solve:-}}}\rule{50}{1}$

First of all, We need to convert this equation from standard form (ax+by=c) into slope-intercept form (y=mx+b).

$\rightarrow$ First, add 2y on both sides:-

$\Large\textsf{3x+2y=4}$

$\rightarrow$ Now, subtract 3x on both sides:-

$\Large\textsf{2y=-3x+4}$

$\rightarrow$ Divide by 2 on both sides

$\Large\text{$y=-\displaystyle\frac{3}{2}x +2$}$

$\rule{300}{3}$

Now, let's find the equation of the line that's parallel to the given line.

Remember, if lines are parallel to each other, then their slope's the same.

So the slope of the line that's parallel to the line whose equation we just found, is

$\Large\text{$-\displaystyle\frac{3}{2}$}$

Now let's write the equation in point-slope form:-

$\hookrightarrow\sf{y-y_1=m(x-x_1)}$

Replace numbers with letters, as follows:-

$\sf{y-5=-\displaystyle\frac{3}{2} (x-4)}$

The equation above is the equation in point-slope form.

Incase you need it converted to slope intercept form, refer to the steps below ~

Multiply -3/2 times x and -4:-

$\hookrightarrow\sf{y-5=-\displaystyle\frac{3}{2} x-6}$

Now, Add 5 on both sides:-

$\hookrightarrow\sf{y=\displaystyle\frac{3}{2} x+1}$

$\Uparrow\sf{Our\:equation\:in\:slope\;intercept\;form}$

<h3>Good luck with your studies.</h3>

#TogetherWeGoFar

$\rule{300}{1}$

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[^2 meaning squared]

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Which of the following expressions is equivalent to (x5 y3 z2) (x4 y3 z6) for all real values of x y, and z ?

leonid [27]

The product of the expressions (x⁵y³z²) and (x⁴y³z⁶) is equivalent to the expression option is A x⁹y⁶z⁸. Hence, the correct option is A.

<h3>What is a simplification of an expression?</h3>

Usually, simplification involves proceeding with the pending operations in the expression.

Simplification usually involves making the expression simple and easy to use later.

The expression is given as

(x⁵y³z²) and (x⁴y³z⁶)

Then, the product of the expression will be

= (x⁵y³z²) (x⁴y³z⁶)

= x⁵x⁴y³y³z²z⁶

= x⁵⁺⁴y³⁺³z²⁺⁶

= x⁹y⁶z⁸

Hence, the correct option is A x⁹y⁶z⁸.

More about the equivalent expression link is given below.

brainly.com/question/889935

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