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1 year ago

Are these lines parallel or not: L1: (1,2), (3,1), and L2: (0,-1), (2,0)

Mathematics

1 answer:

Phoenix [80]1 year ago

5 0

First find the slope of the first line

m = ( y2-y1)/(x2-x1)

m = ( 1-2)/(3-1)

= -1/2

Now find the slope of the second line

m= ( y2-y1)/(x2-x1)

= ( 0 - -1)/(2 -0)

= (0+1)/(2-0)

= 1/2

Parallel lines have the same slope

These lines do not have the same slope, they are different by a negative sign.

These lines are not parallel.

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4 years ago

What is the solution of the system of equations?

umka21 [38]

No solution of the system of equations y = -2x + 5 and -5y = 10x + 20 ⇒ 2nd answer

Step-by-step explanation:

Let us revise the types of solutions of a system of linear equations

One solution
No solution when the coefficients of x and y in the two equations are equal and the numerical terms are different
Infinitely many solutions when the coefficients of x , y and the numerical terms are equal in the two equations

∵ y = -2x + 5

- Add 2x to both sides

∴ 2x + y = 5 ⇒ (1)

∵ -5y = 10x + 20

- Subtract 10x from both sides

∴ -10x - 5y = 20

- Divide both sides by -5

∴ 2x + y = -4 ⇒ (2)

∵ The coefficient of x in equation (1) is 2

∵ The coefficient of x in equation (2) is 2

∴ The coefficients of x in the two equations are equal

∵ The coefficient of y in equation (1) is 1

∵ The coefficient of y in equation (2) is 1

∴ The coefficients of y in the two equations are equal

∵ The numerical term in equation (1) is 5

∵ The numerical term in equation (2) is -4

∴ The numerical terms are different

From the 2nd rule above

∴ No solution of the system of equations

No solution of the system of equations y = -2x + 5 and -5y = 10x + 20

Learn more:

You can learn more about the system of equations in brainly.com/question/6075514

#LearnwithBrainly

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4 years ago

What is (-7)^4 in scientific notation?

lutik1710 [3]

Answer:

2.401 * 10^3

Step-by-step explanation:

put -7 to the fourth power and then use scientific notation rules

6 0

4 years ago

How do you solve: f(x) = -x2e-x<br> +2xe-x , finding the zero's of f.

Maksim231197 [3]

Answer:

0 and 2

Step-by-step explanation:

$f(x) = -x^2e^{-x}+2xe^{-x}$

To find zeros set f(x)=0 and solve for x

$0 = -x^2e^{-x}+2xe^{-x}$

$0 = -e^{-x}(x^2-2x)$

now factor out x

$0 = -xe^{-x}(x-2)$

set each factor =0 and solve for x

$x=0$

$-e^{-x}=0$ no solution for x

$x-2=0, x=2$

zeros of f are 0 and 2

7 0

4 years ago