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4 years ago

What is the equation of the line that is parallel to the line 5x + 2y = 12 and passes through the point (-2, 4)?

Mathematics

1 answer:

Aneli [31]4 years ago

7 0

Answer: 5x + 2y = -2

Step-by-step explanation:

Change 5x+2y=12 to slope intercept: 2y = 12 - 5x, y = -5x/2 + 6

A parallel line has the same slope, so the line we try to find is y = -5x/2 + b.

Substitute (-2, 4) in and get 4=5+b, so b = -1.

Therefore the answer is y = -5x/2 - 1, or if you want it in the original form it would be 2y = -5x - 2 ---> 5x+2y = -2.

Hope that helped,

-sirswagger21

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How do you solve this?

vagabundo [1.1K]

You would add up all of the sides by combining like terms. Let me know if you want the answers for it.

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3 years ago

Graph the linear equation find three points that solves the equation 2y=5x+11

Julli [10]

Answer:

<h3>Attachment</h3>

Step-by-step explanation:

Convert to the slope-intercept form (<em>y = mx + b</em>):

$2y=5x+11$ <em>divide both sides by 2</em>

$\dfrac{2y}{2}=\dfrac{5x}{2}+\dfrac{11}{2}\\\\y=\dfrac{5}{2}x+\dfrac{11}{2}$

We choose any three x values and calculate the y value:

for x = -1

$y=\dfrac{5}{2}(-1)+\dfrac{11}{2}=-\dfrac{5}{2}+\dfrac{11}{2}=\dfrac{6}{2}=3\to A(-1,\ 3)$

for x = 1

$y=\dfrac{5}{2}(1)+\dfrac{11}{2}=\dfrac{5}{2}+\dfrac{11}{2}=\dfrac{16}{2}=8\to B(1,\ 8)$

for x = -3

$y=\dfrac{5}{2}(-3)+\dfrac{11}{2}=-\dfrac{15}{2}+\dfrac{11}{2}=-\dfrac{4}{2}=-2\to C(-3,\ -2)$

Mark the points on the coordinate plane and draw a line through the given points.

6 0

3 years ago

HELP!! ASAP PLEASE!! WILL GIVE BRAINLIEST!!

patriot [66]

Answer:

6^-4 ÷ 3^-4

6^-4/3^-4

Since their powers are negative

Flip them both so the negative index is lost.

It now becomes

3^4/6^4

81/1296

=1/16

6 0

3 years ago

Electric charge is distributed over the disk x2 + y2 ≤ 16 so that the charge density at (x, y) is rho(x, y) = 2x + 2y + 2x2 + 2y

professor190 [17]

Answer:

Required total charge is $256\pi$ coulombs per square meter.

Step-by-step explanation:

Given electric charge is dristributed over the disk,

$x^2=y^2\leq 16$ so that the charge density at (x,y) is,

$\rho (x,y)=2x+2y+2x^2+2y^2$

To find total charge on the disk let Q be the total charge and $x=r\cos\theta,y=r\sin\theta$ so that,

$Q={\int\int}_Q\rho(x,y) dA$ where A is the surface of disk.

$=\int_{0}^{2\pi}\int_{0}^{4}(2x+2y+2x^2+2y^2)dA$

$=\int_{0}^{2\pi}\int_{0}^{4}(2r\cos\theta+2r\sin\theta+2r^2 \cos^{2}\theta+2r^2\sin^2\theta)rdrd\theta$

$=2\int_{0}^{2\pi}\int_{0}^{4}r^2(\cos\theta+\sin\theta)drd\theta+2\int_{0}^{2\pi}\int_{0}^{4}r^3drd\theta$

$=\frac{2}{3}\int_{0}^{2\pi}(\sin\theta+\cos\theta)\Big[r^3\Big]_{0}^{4}d\theta+2\int_{0}^{2\pi}\Big[\frac{r^4}{4}\Big]d\theta$

$=\frac{128}{3}\int_{0}^{2\pi}(\sin\theta+\cos\theta)d\theta+128\int_{0}^{2\pi}d\theta$

$=\frac{128}{3}\Big[\sin\theta-\cos\theta\Big]_{0}^{2\pi}+128\times 2\pi$

$=\frac{128}{3}\Big[\sin 2\pi-\cos 2\pi-\sin 0+\cos 0\Big]+256\pi$

$=256\pi$

Hence total charge is $256\pi$ coulombs per square meter.

3 0

3 years ago

You roll a number cube 20 times. Which scenario is least likely?

BigorU [14]

Answer:

you won't roll the same number 5 times

7 0

3 years ago