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Mekhanik [1.2K]

2 years ago

14

Production increased from 8,200 units to 13,530 units; the percent increase was what?

1 answer:

mamaluj [8]2 years ago

6 0

(13530-8200)/8200 times 100

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1 2/3 + (2 1/2) = ?<br> pls help

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What is the differences in length between the shortest and longest crayons

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3 years ago

Are AB and CD parallel, perpendicular, or neither?*<br> 1. A(-4, 8), B(4, 10), C(1, 1), D(-2, 13)

ohaa [14]

Answer:

Perpendicular

<em />

Step-by-step explanation:

Given

$A = (-4, 8)$

$B = (4, 10)$

$C = (1, 1)$

$D = (-2, 13)$

Required

Is AB and CD parallel?

First, we need to calculate the slope (m) of AB and CD

$m = \frac{y_2 - y_1}{x_2 - x_1}$

For AB:

$A (x_1,y_1)= (-4, 8)$

$B(x_2,y_2) = (4, 10)$

So:

$m = \frac{y_2 - y_1}{x_2 - x_1}$

$m = \frac{10 - 8}{4 - (-4)}$

$m = \frac{10 - 8}{4 +4}$

$m = \frac{2}{8}$

$m = \frac{1}{4}$

For CD:

$C(x_1,y_1) = (1, 1)$

$D(x_2,y_2) = (-2, 13)$

So:

$m = \frac{y_2 - y_1}{x_2 - x_1}$

$m = \frac{13 - 1}{-2 - 1}$

$m = \frac{12}{-3}$

$m = -4$

For Lines to be parallel, the slope must be equal:

i.e. $m_1 = m_2$

This condition is not true because:

$\frac{1}{4} \neq -4$

For Lines to be perpendicular, the slope must be:

$m_1 = -\frac{1}{m_2}$

This implies:

$\frac{1}{4} = -\frac{1}{-4}$

$\frac{1}{4} = \frac{-1}{-4}$

$\frac{1}{4} = \frac{1}{4}$

<em>Hence, the lines are perpendicular</em>

6 0

3 years ago

What is |18x + 9| + 1 > 64 put into an interval notation and on a graph?

Gnoma [55]

$\bf |18x+9| + 1 > 64\implies \pm(18x+9)+1>64 \\\\[-0.35em] ~\dotfill\\\\ +(18x+9)+1>64\implies 18x+10>64\implies 18x > 54 \\\\\\ x >\cfrac{54}{18}\implies \boxed{x > 3} \\\\[-0.35em] ~\dotfill\\\\ -(18x+9)+1>64\implies -18x-9+1>64\implies -18x-8>64 \\\\\\ -8>64+18x\implies -72 > 18x\implies \cfrac{-72}{18}=x\implies \boxed{-4>x}$

Check the picture below.

4 0

3 years ago