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2 years ago

The endpoints of GE are located at G(–6, –4) and E(4, 8). Using slope-intercept form, write the equation of GE.

1 answer:

4 0

Answer:
Equation of the line is:
y = 1.2x + 3.2

Explanation:
The general form of the linear equation is:
y = mx + c
where:
m is the slope
c is the y-intercept

1- getting the slope:
The slope of the line can be calculated using the following formula:
m = $\frac{y2 - y1}{x2 - x1}$

We are given the points:
(-6,-4) representing (x1,y1)
(4,8) representing (x2,y2)
Substitute with the given points in the above equation to get the slope as follows:
m = $\frac{8--4}{4--6} = 6/5$

The equation of the line now is:
y = 1.2x + c

2- getting the y-intercept:
To get the value of the c, we will use any of the given points, substitute in the equation and solve for c.
I will use the point (4,8) as follows:
y = 1.2 x + c
8 = 1.2(4) + c
c = 16/5 = 3.2

Therefore, the equation of the line is:
y = 1.2x + 3.2

Hope this helps :)

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Type the correct answer for each.

xxTIMURxx [149]

If point $\left(x,\ \frac{\sqrt{7}}{3}\right)$ is on the unit ircle, then:

$x^2+\left( \frac{ \sqrt{7} }{3} \right)^2=1 \\ \\ \Rightarrow x^2+ \frac{7}{9} =1 \\ \\ \Rightarrow x^2=1- \frac{7}{9} = \frac{2}{9} \\ \\ \Rightarrow x= \sqrt{ \frac{2}{9} } = \frac{ \sqrt{2} }{3}$

Since, the point is in the second quadrant, x is negative.

Thus, $(x,\ y)=\left(x,\ \frac{\sqrt{7}}{3}\right)=\left(-\frac{ \sqrt{2} }{3},\ \frac{\sqrt{7}}{3}\right)$

Part A:

$3 \sqrt{7} =6\left( \frac{ \sqrt{7} }{2} \right) \\ \\ =6\left( \frac{ \sqrt{7} }{3} \cdot \frac{3}{ \sqrt{2} } \right) \\ \\ =6\left( \frac{ \frac{ \sqrt{7} }{3} }{ \frac{ \sqrt{2} }{3} } \right)=-6\left( \frac{ \frac{ \sqrt{7} }{3} }{ -\frac{ \sqrt{2} }{3} } \right) \\ \\ =-6\left( \frac{y}{x} \right)=-6\tan\theta$

Therefore, $-6\tan\theta=3\sqrt{7}$ .

Part B:

$- \frac{ \sqrt{7} }{2} =- \frac{ \sqrt{7} }{3} \cdot \frac{3}{ \sqrt{2} } \\ \\ =- \frac{ \frac{ \sqrt{7} }{3} }{ \frac{ \sqrt{2} }{3} } = \frac{ \frac{ \sqrt{7} }{3} }{ -\frac{ \sqrt{2} }{3} } = \frac{y}{x} \\ \\ =\tan\theta$

Therefore, $\tan\theta=- \frac{ \sqrt{7} }{2}$

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3 years ago

QUICKKKKKKKK<br> EXPERTS/ACE/TRUSTED HELPERS

olchik [2.2K]

What are the answer choices???

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3 years ago

Find the minimum or maximum value of the function g(x)=−3x2−6x+5

polet [3.4K]

Step-by-step explanation:

g(x) = ax²+bx+c

g(x)=−3x²−6x+5

a = -3, b= -6, c = 5

since a <0 , the function has only maximum value.

=> g'(x) = 0

-6x -6 = 0

-6x = 6

x = -1

the maximum value => g(-1) =

-3(-1)²-6(-1)+5 = -3+6+5 = 9

the domain : {x | x € Real numbers}

the range : {y| y ≤ 9, y € Real numbers}

the function is increasing for x < -1

the function is decreasing for x > -1

4 0

2 years ago

Could someone help?<br> I’m confused

andre [41]

He will only need to sell one

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3 years ago

Carl wants to plant a garden that is 1 1/2 yards long and has an area of 3 1/2 yd.² how wide should the Garden be

lesya692 [45]

L= length= 1 1/2 yards
A= area= 3 1/2 yards^2
w= width

Area= length * width
plug in numbers you know
3 1/2= (1 1/2)(w)
convert to improper fractions
(3*2+1)/2= ((1*2+1)/2)(w)
7/2= 3/2w
divide both sides by 3/2
7/2 ÷ 3/2= w
to divide fractions, multiply by the reciprocal/inverse of 3/2
7/2 * 2/3= w
(7*2)/(2*3)= w
14/6= w
reduce by 2
7/3= width as improper fraction
OR
2 1/3= width as mixed fraction

ANSWER: The width should be 2 1/3 yards wide (or 7/3 yards wide).

Hope this helps! :)

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2 years ago