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4 years ago

Find the equation of the line that contains the point (4, -2) and is perpendicular to the line y= -2x+5

Mathematics

1 answer:

Firlakuza [10]4 years ago

7 0

Answer:

y +2 = (1/2)(x -4)

Step-by-step explanation:

The given line's equation is in the slope-intercept form ...

y = mx + b

where m is the slope and b is the y-intercept. Matching your equation to this one, you see that m = -2. That is, the slope of the given line is -2.

The slope of the perpendicular line will be the opposite of the reciprocal of this slope, so will be ...

-1/(-2) = 1/2

We can use the desired slope and given point in the point-slope form of the equation of a line:

y -k = m(x -h) . . . . . . . line with slope m through point (h, k)

Filling in the values we want, m=1/2, (h, k) = (4, -2), gives us the equation ...

y +2 = (1/2)(x -4) . . . . the equation of your line

This can be rearranged to any of several other forms

y = 1/2x -4 . . . . . slope-intercept form

x -2y = 8 . . . . . . standard form

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3 years ago

Which of the lines below is a line of symmetry?

natulia [17]

Answer:

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Step-by-step explanation:

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3 years ago

Of 200 youthful gamers (under 18) who tried the new Z-Box-Plus game, 160 rated it "excellent," compared with only 144 of 200 adu

beks73 [17]

Answer:

Correct option is (c). 1.873.

Step-by-step explanation:

The hypothesis can be defined as:

<em>H</em>₀: There is no difference between the two proportions.

<em>H</em>ₐ: There is a difference between the two proportions.

Given:

$X_{1} = 160,\ n_{1}=200\\X_{2} = 144,\ n_{2}=200$

The sample proportion of youthful gamers who tried the new Z-Box-Plus game and rated it "excellent," is:

$\hat p_{1}=\frac{X_{1}}{n_{1}} =\frac{160}{200} =0.80$

The sample proportion of adult gamers who tried the new Z-Box-Plus game and rated it "excellent," is:

$\hat p_{2}=\frac{X_{2}}{n_{2}} =\frac{144}{200} =0.72$

The population proportion of gamers who rated the game as "excellent" is:

$P=\frac{X_{1}+X_{2}}{n_{1}+n_{2}} =\frac{160+144}{200+200}= 0.76$

The test statistic is:

$z=\frac{\hat p_{1}-\hat p_{2}}{\sqrt{P(1-P)[\frac{1}{n_{1}}+\frac{1}{n_{2}} ]} } =\frac{0.80-0.72}{\sqrt{0.76(1-0.76)[\frac{1}{200}+\frac{1}{200} ]} }=1.873$

Thus, the value of the test statistic is 1.873.

The correct option is (c).

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3 years ago

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3 years ago

the area of a rectangle is x-16/x. If the width of a rectangle is x/4+1, find an expression to represent the length.

lakkis [162]

Answer:

The expression to represent the length

$length=\frac{4\left(x-4\right)}{x}$

Step-by-step explanation:

Given

Area = x-16/x

Width = x/4+1

Length =?

We know that The formula for the area of the rectangle is:

Area = Length x Width

Thus, the length of a rectangle

Length = Area ÷ Width

$=\frac{x-\frac{16}{x}}{\frac{x}{4}+1}$

$=\frac{x-\frac{16}{x}}{\frac{x+4}{4}}$

$=\frac{\frac{x^2-16}{x}}{\frac{x+4}{4}}$

$\mathrm{Divide\:fractions}:\quad \frac{\frac{a}{b}}{\frac{c}{d}}=\frac{a\cdot \:d}{b\cdot \:c}$

$=\frac{\left(x^2-16\right)\cdot \:4}{x\left(x+4\right)}$

$=\frac{\left(x+4\right)\left(x-4\right)\cdot \:4}{x\left(x+4\right)}$

Cancel the common factor: (x+4)

$=\frac{4\left(x-4\right)}{x}$

Thus, the expression to represent the length

$length=\frac{4\left(x-4\right)}{x}$

7 0

3 years ago