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3 years ago

write an equation of the line with the same slope as the line given by 5x+2y=8 and as the same y-intercept as 3x-7y=10

2 answers:

5 0

The slope of the first equation would be -5/2 because
2y=-5x+8
y=-5x/2+4
The y intercept of the 2nd equation is when x=0, so -7y=10
y=-10/7
The equation of the line would be y=-5x/2-10/7
Or in standard form....
5x/2+y=-10/7
5x+27=-20/7

vampirchik [111]3 years ago

4 0

$5x+2y=8\ \ \Rightarrow\ \ 2y=-5x+8\ \ \Rightarrow\ \l_1:\ y=- \frac{5}{2}x+8\\ \\ l_2:\ y=ax+b\ \ \ and\ \ \ l_2\ ||\ l_1\ \ \ \Leftrightarrow\ \ \ a=- \frac{5}{2} \\ \\l_2:\ y=- \frac{5}{2}x+b\\ \\3x-7y=10\ \ \ and\ \ \ x=0 \ \ \ \Rightarrow\ \ \ 3\cdot0-7y=10 \ \ \Rightarrow\ \ \ y=- \frac{10}{7} \\ \\b=- \frac{10}{7}\ \ \ \Rightarrow\ \ \ l_2:\ y=- \frac{5}{2}x- \frac{10}{7}\\ \\ l_2:\ \frac{5}{2}x+y=- \frac{10}{7}\ \ /\cdot14\\ \\l_2:\ 35x+7y=-20$

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Solve. 4x−y−2z=−8 −2x+4z=−4 x+2y=6 Enter your answer, in the form (x,y,z), in the boxes in simplest terms. x= y= z=

ladessa [460]

Answer:

(-2, 4, -2)

x=-2, y=4, z=-2.

Step-by-step explanation:

So we have the three equations:

$4x-y-2z=-8\\-2x+4z=-4\\x+2y=6$

And we want to find the value of each variable.

To solve this system, first look at it and consider what you should try to do.

So we can see that the second and third equations both have an x.

Therefore, we can isolate the variables for the second and third equation and then substitute them into the first equation to make the first equation all xs.

Therefore, let's first isolate the variable in the second and third equation.

Second Equation:

$-2x+4z=-4$

First, divide everything by -2 to simplify things:

$x-2z=2$

Subtract x from both sides. The xs on the left cancel:

$(x-2z)-x=2-x\\-2z=2-x$

Now, divide everything by -2 to isolate the z:

$z=-\frac{2-x}{2}$

So we've isolated the z variable. Now, do the same to the y variable in the third equation:

$x+2y=6$

Subtract x from both sides:

$2y=6-x$

Divide both sides by 2:

$y=\frac{6-x}{2}$

Now that we've isolated the y and z variables, plug them back into the first equation. Therefore:

$4x-y-2z=-8\\4x-(\frac{6-x}{2})-2(-\frac{2-x}{2})=-8$

Distribute the third term. The -2s cancel out:

$4x-(\frac{6-x}{2})+(2-x)=-8$

Since there is still a fraction, multiply everything by 2 to remove it:

$2(4x-(\frac{6-x}{2})+(2-x))=2(-8)$

Distribute:

$8x-(6-x)+2(2-x)=-16\\8x-6+x+4-2x=-16$

Combine like terms:

$8x+x-2x-6+4=-16\\7x-2=-16$

Add 2 to both sides:

$7x=-14$

Divide both sides by 7:

$(7x)/7=(-14)/7\\x=-2$

Therefore, x is -2.

Now, plug this back into the second and third simplified equations to get the other values.

Second equation:

$z=-\frac{2-x}{2}\\ z=-\frac{2-(-2)}{2}\\z=-\frac{4}{2}\\z=-2$

Third equation:

$y=\frac{6-x}{2}\\y=\frac{6-(-2)}{2}\\y=\frac{8}{2}\\y=4$

Therefore, the solution is (-2, 4, -2)

3 0

3 years ago

Read 2 more answers

A reflection of shape I....

inn [45]

interestingifgihdfhguehr

6 0

2 years ago

PLEASE HELP step by step

Katen [24]

Answer:

The length of the line segment is 10 units.

Step-by-step explanation:

Let us call the given two points: (x₁, y₁) = (2, -3) and (x₂, y₂) = (8, 5).

The distance between two points, d = $\sqrt{(x_1 - x_2)^2 + (y_1 - y_2)^2} }$

Here, $(x_1, y_1) = (2, -3)$ and

$(x_2, y_2) = (8, 5)$

Therefore, distance, d = $\sqrt{(8 - 2)^2 + (5 - (-3))^2$

$= \sqrt{6^2 + 8^2}$

$= \sqrt{36 + 64}$

$= \sqrt{100}$

= 10 units.

Hence, the answer.

3 0

3 years ago

the legs of a scalene triangle are represented by (x+4),(x+8), and (2x - 3) which polynomial expression best represents the peri

AVprozaik [17]

perimeter means add the side

(x+4) +( x+8)+(2x-3) =P

x+x+2x+4+8-3=P

4x-9 =P

8 0

2 years ago

Read 2 more answers

1.)A rectangle has an area of 72 square centimeters and the length is twice the width. The perimeter of the rectangle

Greeley [361]

area = L x w = 72

L = 2w

72 = 2w*w = 2w^2

divide by 2

36 = w^2

w = sqrt(36) = 6

l = 2*6 =12

perimeter = 2L +2W = 2*12 + 2*6 = 24+12 = 36

sqrt(40)= 6.324555 cm ( round to 6.32 )

6.32 - 4 = 2.32 cm original length of a side

7 0

3 years ago