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3 years ago

12

A tire shop had to fill 2 1 ⁄2 tires with air. It took a small air compressor 2 1 ⁄2 seconds to fill them up. How long would it

take to fill 8 tires?

1 answer:

Brums [2.3K]3 years ago

6 0

Let 2_1/2 = 5/2.

Let t = time to fill 8 tires

(5/2)/8 = (5/2)/t

8(5/2) = (5/2)t

20 = (5/2)t

20 ÷ 5/2 = t

20 • 2/5 = t

8 seconds = t

Done.

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3 years ago

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4 years ago

Write an equation (a) in slope-intercept form and (b) in standard form for the line passing through (-3,5) and parallel to x + 4

Dmitry [639]

Answer:

$\boxed{\sf Standard-form :x + 4y -17=0 }\\$

$\boxed{\sf Slope-intercept\ form :y =\dfrac{-1}{4}x +\dfrac{17}{4}}$

Step-by-step explanation:

Here a equation of the line is given to us and we need to find out the equation of line which passes through the given point and parallel to the given line , the given equation is ,

$\longrightarrow x + 4y = 7\\$

Firstly convert it into <em>s</em><em>l</em><em>o</em><em>p</em><em>e</em><em> </em><em>i</em><em>n</em><em>t</em><em>e</em><em>r</em><em>c</em><em>e</em><em>p</em><em>t</em><em> </em><em>f</em><em>o</em><em>r</em><em>m</em><em> </em>of the line which is <u>y</u><u> </u><u>=</u><u> </u><u>m</u><u>x</u><u> </u><u>+</u><u> </u><u>x</u><u> </u>, as ;

$\longrightarrow 4y = -x + 7 \\$

$\longrightarrow y =\dfrac{-x}{4}+\dfrac{7}{4}\\$

On comparing it to <em>y</em><em> </em><em>=</em><em> </em><em>m</em><em>x</em><em> </em><em>+</em><em> </em><em>c</em><em> </em>, we have ,

$\longrightarrow m =\dfrac{-1}{4}\\$

$\longrightarrow c =\dfrac{7}{4}\\$

Now as we know that the <em>s</em><em>l</em><em>o</em><em>p</em><em>e</em><em> </em><em>o</em><em>f</em><em> </em><em>t</em><em>w</em><em>o</em><em> </em><em>p</em><em>a</em><em>r</em><em>a</em><em>l</em><em>l</em><em>e</em><em>l</em><em> </em><em>l</em><em>i</em><em>n</em><em>e</em><em>s</em><em> </em><em>i</em><em>s</em><em> </em><em>s</em><em>a</em><em>m</em><em>e</em><em> </em>. Therefore the slope of the parallel line will be ,

$\longrightarrow m_{||)}=\dfrac{-1}{4}\\$

Now we may use <em>p</em><em>o</em><em>i</em><em>n</em><em>t</em><em> </em><em>s</em><em>l</em><em>o</em><em>p</em><em>e</em><em> </em><em>f</em><em>o</em><em>r</em><em>m</em><em> </em>of the line as ,

$\longrightarrow y - y_1 = m(x-x_1) \\$

On substituting the respective values ,

$\longrightarrow y - 5 =\dfrac{-1}{4}\{ x -(-3)\}\\$

$\longrightarrow y -5=\dfrac{-1}{4}(x+3)\\$

$\longrightarrow 4(y -5 ) =-1(x +3) \\$

$\longrightarrow 4y -20 = - x -3 \\$

$\longrightarrow x + 4y -20+3=0\\$

$\longrightarrow \underset{Standard \ Form }{\underbrace{\underline{\underline{ x + 4y -17=0}}}} \\$

Again the equation can be rewritten as ,

$\longrightarrow y - 5 = \dfrac{-1}{4}(x +3) \\$

$\longrightarrow y = \dfrac{-1}{4}x -\dfrac{3}{4}+5 \\$

$\longrightarrow y = \dfrac{-1}{4}x -\dfrac{20-3}{4} \\$

$\longrightarrow \underset{Slope-Intercept\ form }{\underbrace{\underline{\underline{ y =\dfrac{-1}{4}x +\dfrac{17}{4}}}}}\\$

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2 years ago

Identify the graphical solution to the inequality

NeTakaya

Answer:

A

Step-by-step explanation:

to solve absolute value inequalities you must solve it for when the absolute value is positive and then when it is negative

example, |4| = 4 and -4

first solution will be when we're solving for the positive value:

+(-4x+7) ≥ 27

-4x + 7 ≥ 27

-4x ≥ 20

x ≤ -5 [reverse the symbol when mult or div by a negative]

-(-4x+7) ≥ 27

4x - 7 ≥ 27

4x ≥ 34

x ≥ 34/4 or x ≥ 8 1/2

solution: x ≤ -5 or x ≥ 8.5

5 0

3 years ago