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3 years ago

Find an equation of the line perpendicular to the graph of 10x - 5y = 8 that passes through the point at (-4, 7)

1 answer:

vladimir2022 [97]3 years ago

5 0

We need to swap the numerator and denominator, and change the sign of one of them to get a perpendicular slope.5x + 10y = c. Now subtract the point.
5(-4) + 10(7) = -20 + 70 = 50 = c
5x + 10y = 50 is an equation. If we want, we can divide everything by 5 to get x + 2y = 10.The more usual way to do these is put the equation in slope-intercept form by solving for y. 10x-5y=8 -5y = -10x + 8 y = 2x - 8/5 Now you have the slope of the original line, 2. Any line perpendicular to this one must have a slope that is the negative reciprocal of this one, -1/2 So this new line must be y = -1/2 x + c .Now subtract in point to solve for c.
7 = (-1/2)(-4) + c 7 = 2+c
5 = c
y = -1/2 x + 5
The first time we solved we got this.
x + 2y = 10 but, if we divide everything by 2, we get 1/2 x + y = 5 So... subtract 1/2 x from both sides and you have identical equations. So the two are equivalent. The answer is y = -1/2 x + 5
Hope this helped!

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liubo4ka [24]

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3 years ago

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A has the coordinates (–4, 3) and B has the coordinates (4, 4). If DO,1/2(x, y) is a dilation of △ABC, what is true about the im

loris [4]

Answer:

Coordinates of Vertices of triangle ABC are A (-4,3) , B(4,4) and C(1,1).

As, DO is Dilation of Δ ABC by Scale factor of $\frac{1}{2}$ .

Vertices of A' B'C' are

$A'=(\frac{-4}{2},\frac{3}{2})=(-2,\frac{3}{2}), B'=(\frac{4}{2},\frac{4}{2})=(2,2), C'=(\frac{1}{2},\frac{1}{2})$

So, Image Δ A'B'C' will be smaller than the Pre image Δ ABC.

The two triangles will be congruent.

AO is Dilated by a factor of half , so A'O' will be half of AO.

So, correct Statements are

1. AB is parallel to A'B'.

2.DO,1/2(x, y) =

The distance from A' to the origin is half the distance from A to the origin.

$OA=\sqrt{(-4)^2+3^2}=\sqrt{25}=5\\\\ O'A'=\sqrt{2^2+(\frac{3}{2})^2}=\frac{5}{2}=2.5$

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3 years ago

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when buying lemonade mix , Cece spend $0.72 on a 6- ounce packet and $0.27 on a 3- ounce packet . Use unit rates to determine if

siniylev [52]

6- ounce packet rate = $0.72 .

In order to find the one ounce rate, we need to divide $0.72 by 6.

On dividing 0.72 by 6, we get $0.12.

<em>Therefore, first unit rate is $0.12 per ounce.</em>

3- ounces packet rate = $0.27.

In order to find the one ounce rate, we need to divide $0.27 by 3.

On dividing 0.27 by 3, we get $0.09.

<em>Therefore, second unit rate is $0.09 per ounce.</em>

<h3>So, we can say that each pair of rates is not equivalent. </h3>

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3 years ago

Assume the random variable x has a binomial distribution with the given probability of obtaining a success. Find the following.

borishaifa [10]

Answer:

P(x > 10) = 0.6981.

Step-by-step explanation:

Binomial probability distribution

The binomial probability is the probability of exactly x successes on n repeated trials, and X can only have two outcomes.

$P(X = x) = C_{n,x}.p^{x}.(1-p)^{n-x}$

In which $C_{n,x}$ is the number of different combinations of x objects from a set of n elements, given by the following formula.

$C_{n,x} = \frac{n!}{x!(n-x)!}$

And p is the probability of X happening.

In this question:

$n = 14, p = 0.8$

P(x>10)

$P(x > 10) = P(X = 11) + P(X = 12) + P(X = 13) + P(X = 14)$

In which

$P(X = x) = C_{n,x}.p^{x}.(1-p)^{n-x}$

$P(X = 11) = C_{14,11}.(0.8)^{11}.(0.2)^{3} = 0.2501$

$P(X = 12) = C_{14,12}.(0.8)^{12}.(0.2)^{2} = 0.2501$

$P(X = 13) = C_{14,13}.(0.8)^{13}.(0.2)^{1} = 0.1539$

$P(X = 14) = C_{14,14}.(0.8)^{14}.(0.2)^{0} = 0.0440$

$P(x > 10) = P(X = 11) + P(X = 12) + P(X = 13) + P(X = 14) = 0.2501 + 0.2501 + 0.1539 + 0.0440 = 0.6981$

So P(x > 10) = 0.6981.

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