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VikaD [51]
3 years ago
7

Find the equation of the line that is parallel to the line

0%2B%204" id="TexFormula1" title="y = -\frac{3}{2}x + 4" alt="y = -\frac{3}{2}x + 4" align="absmiddle" class="latex-formula"> and passes through the point (4, 0)
Work needs to be shown
Mathematics
2 answers:
nlexa [21]3 years ago
7 0

parallel lines have the same exact slope, so

\bf \begin{array}{|c|ll} \cline{1-1} slope-intercept~form\\ \cline{1-1} \\ y=\underset{y-intercept}{\stackrel{slope\qquad }{\stackrel{\downarrow }{m}x+\underset{\uparrow }{b}}} \\\\ \cline{1-1} \end{array}~\hspace{7em}\stackrel{slope}{y=\stackrel{\downarrow }{-\cfrac{3}{4}}x+4}


so we're really looking for a line whose slope is -3/4 and runs through (4,0),


\bf (\stackrel{x_1}{4}~,~\stackrel{y_1}{0})~\hspace{10em} slope = m\implies -\cfrac{3}{4} \\\\\\ \begin{array}{|c|ll} \cline{1-1} \textit{point-slope form}\\ \cline{1-1} \\ y-y_1=m(x-x_1) \\\\ \cline{1-1} \end{array}\implies y-0=-\cfrac{3}{4}(x-4)\implies y=-\cfrac{3}{4}x+3

ivann1987 [24]3 years ago
3 0

A line parallel to your equation has the same slope, so it should be in the form:


y = (-3/2)x + b


To figure what "b" has to be, plug in the point (4,0) and solve:

0 = (-3/2)*4 + b

0 = -6 + b

6 = b

So the equation of the line is:

y = (-3/2)x + 6

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3 years ago
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svetlana [45]

Answer:

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∠ 7 and ∠ 6

Step-by-step explanation:

Linear Pair:

A linear pair of angles is formed when two lines intersect.

Two angles are said to be linear if they are adjacent angles formed by two intersecting lines.

The measure of a straight angle is 180 degrees, so a linear pair of angles must add up to 180 degrees.

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∠ 1 and ∠ 2           ∠ 8 and ∠ 5 ,etc

Vertical Angles:

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Example

∠ 1 and ∠ 3           ∠ 8 and ∠ 6 ,etc

Supplementary Angles:

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All Linear pair are Supplementary angles

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∠ 7 and ∠ 6           ∠ 8 and ∠ 5 ,etc

3 0
3 years ago
Cynthia Besch wants to buy a rug for a room that is 24 ft wide and 33 ft long. She
qaws [65]
<h3>Answer:   16 ft by 25 ft</h3>

=========================================================

Explanation:

Refer to the diagram below.

The outer dimensions 24 ft and 33 ft shrink down to 24-2x ft and 33-2x ft respectively. This subtraction of 2x is due to subtracting two copies of x per side.

The carpet has area of (24-2x)(33-2x)

Cynthia can afford to buy 400 sq ft of carpet

So we set 400 equal to that previous expression and solve for x

(24-2x)(33-2x) = 400

24(33-2x) - 2x(33-2x) = 400

792-48x - 66x + 4x^2 = 400

4x^2 - 114x + 792 = 400

4x^2 - 114x + 792-400 = 0

4x^2 - 114x + 392 = 0

From here, use the quadratic formula to isolate x.

Plug in a = 4, b = -114, c = 392

x = \frac{-b\pm\sqrt{b^2-4ac}}{2a}\\\\x = \frac{-(-114)\pm\sqrt{(-114)^2-4(4)(392)}}{2(4)}\\\\x = \frac{114\pm\sqrt{6724}}{8}\\\\x = \frac{114\pm82}{8}\\\\x = \frac{114+82}{8} \ \text{ or } \ x = \frac{114-82}{8}\\\\x = \frac{196}{8} \ \text{ or } \ x = \frac{32}{8}\\\\x = 24.5 \ \text{ or } \ x = 4\\\\

The two possible solutions are x = 24.5 and x = 4

But if x = 24.5, then 24 - 2x = 24 - 2*24.5 = -25 which isn't possible. We cannot have a negative width or negative length for the carpet.

Luckily x = 4 does work since

24 - 2x = 24 - 2*4 = 16

33 - 2x = 33 - 2*4 = 25

Both results are positive.

Therefore, the carpet has dimensions of <u>16 ft by 25 ft</u>

Check: 16*25 = 400, so the answer is confirmed

5 0
2 years ago
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Step-by-step explanation:


7 0
3 years ago
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Lisa [10]
Your question would be clearer if written as "What is 145% of 6000?"

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8 0
3 years ago
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