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3 years ago

9

What is the area of the triangle ?

1 answer:

bezimeni [28]3 years ago

8 0

from the question, (-2,2) and (1,2) have the same y value so you can use that as your base and easily find the perpendicular height using the y axis since it's parallel to the x axis.

the third point, (0,-6), to the base is your height

use the sum of the positive of the y values to find your height (because height can't be negative): 6+2 = 8

area of a triangle = 1/2 bh = 1/2 x 3 x 8 = 12

Note: 1/2 bh only works because (-2,2) and (1,2) form a line parallel to the x axis

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3 years ago

Solve the following equation by factoring:9x^2-3x-2=0

olya-2409 [2.1K]

Answer:

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Step-by-step explanation:

Original quadratic equation is $9x^{2}-3x-2=0$

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$x^{2} - \frac{x}{3} - \frac{2}{9}=0$

Add $\frac{2}{9}$ to both sides to get rid of the constant on the LHS

$x^{2} - \frac{x}{3} - \frac{2}{9}+\frac{2}{9}=\frac{2}{9}$ ==> $x^{2} - \frac{x}{3}=\frac{2}{9}$

Add $\frac{1}{36}$ to both sides

$x^{2} - \frac{x}{3}+\frac{1}{36}=\frac{2}{9} +\frac{1}{36}$

This simplifies to

$x^{2} - \frac{x}{3}+\frac{1}{36}=\frac{1}{4}$

Noting that (a + b)² = a² + 2ab + b²

If we set a = x and b = $\frac{1}{6}\right)$ we can see that

$\left(x - \frac{1}{6}\right)^2$ = $x^2 - 2.x. (-\frac{1}{6}) + \frac{1}{36} = x^{2} - \frac{x}{3}+\frac{1}{36}$

So

$\left(x - \frac{1}{6}\right)^2=\frac{1}{4}$

Taking square roots on both sides

$\left(x - \frac{1}{6}\right)^2= \pm\frac{1}{4}$

So the two roots or solutions of the equation are

$x - \frac{1}{6}=-\sqrt{\frac{1}{4}}$ and $x - \frac{1}{6}=\sqrt{\frac{1}{4}}$

$\sqrt{\frac{1}{4}} = \frac{1}{2}$

So the two roots are

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4 years ago

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Answer:

The margin of error M.O.E = 2.5%

Step-by-step explanation:

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= 1 - 0.95

= 0.05

The critical value:

$Z_{\alpha/2} = Z_{0.05/2} \\ \\ Z_{0.025} = 1.96$ (From the z tables)

The margin of error is calculated by using the formula:

$M.O.E = Z_{\alpha/2} \times \sqrt{\dfrac{\hat p(1 -\hat p)}{n}}$

$M.O.E = 1.96 \times \sqrt{\dfrac{\hat 0.60(1 -0.60)}{1500}}$

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$M.O.E = 1.96 \times \sqrt{1.6 \times 10^{-4}}$

M.O.E = 0.02479

M.O.E ≅ 0.025

The margin of error M.O.E = 2.5%

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