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3 years ago

Given the following two points find the slope. p1(-2,3)and p2(1,0)

Mathematics

1 answer:

Aloiza [94]3 years ago

8 0

Answer

Slope(m) = -1

Step by step explanation

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

Here p1 = (-2, 3) and p2 (1, 0)

x1 = -2, y1 = 3, x2 = 1, y2 = 0

Now plug in the values in the slope formula, we get

m = (0 - 3) / (1 - (-2))

m = -3/(1 + 2)

m = -3/3

m = -1

Therefore, slope = -1

Thank you.

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19) Albert says that the two systems of equations shown have the same solutions.

k0ka [10]

Answer:

option A) Agree, because the solutions are the same is correct.

Step-by-step explanation:

FIRST SYSTEM

$6x + y= 2$

$-x-y=-3$

solving the system

$\begin{bmatrix}6x+y=2\\ -x-y=-3\end{bmatrix}$

$\mathrm{Multiply\:}-x-y=-3\mathrm{\:by\:}6\:\mathrm{:}\:\quad \:-6x-6y=-18$

$\begin{bmatrix}6x+y=2\\ -6x-6y=-18\end{bmatrix}$

adding the equation

$-6x-6y=-18$

$+$

$\underline{6x+y=2}$

$-5y=-16$

so the system becomes

$\begin{bmatrix}6x+y=2\\ -5y=-16\end{bmatrix}$

solve -5y for y

$-5y=-16$

Divide both sides by -5

$\frac{-5y}{-5}=\frac{-16}{-5}$

simplify

$y=\frac{16}{5}$

$\mathrm{For\:}6x+y=2\mathrm{\:plug\:in\:}y=\frac{16}{5}$

$6x+\frac{16}{5}=2$

subtract 16/5 from both sides

$6x+\frac{16}{5}-\frac{16}{5}=2-\frac{16}{5}$

$6x=-\frac{6}{5}$

Divide both sides by 6

$\frac{6x}{6}=\frac{-\frac{6}{5}}{6}$

$x=-\frac{1}{5}$

Therefore, the solution to the FIRST SYSTEM is:

$x=-\frac{1}{5},\:y=\frac{16}{5}$

SECOND SYSTEM

$2x-3y = -10$

$-x-y=-3$

solving the system

$\begin{bmatrix}2x-3y=-10\\ -x-y=-3\end{bmatrix}$

$\mathrm{Multiply\:}-x-y=-3\mathrm{\:by\:}2\:\mathrm{:}\:\quad \:-2x-2y=-6$

$\begin{bmatrix}2x-3y=-10\\ -2x-2y=-6\end{bmatrix}$

$-2x-2y=-6$

$+$

$\underline{2x-3y=-10}$

$-5y=-16$

so the system of equations becomes

$\begin{bmatrix}2x-3y=-10\\ -5y=-16\end{bmatrix}$

solve -5y for y

$-5y=-16$

Divide both sides by -5

$\frac{-5y}{-5}=\frac{-16}{-5}$

Simplify

$y=\frac{16}{5}$

$\mathrm{For\:}2x-3y=-10\mathrm{\:plug\:in\:}y=\frac{16}{5}$

$2x-3\cdot \frac{16}{5}=-10$

$2x=-\frac{2}{5}$

Divide both sides by 2

$\frac{2x}{2}=\frac{-\frac{2}{5}}{2}$

Simplify

$x=-\frac{1}{5}$

Therefore, the solution to the SECOND SYSTEM is:

$x=-\frac{1}{5},\:y=\frac{16}{5}$

Conclusion:

As both systems of equations have the same solution.

Therefore, we conclude that Albert is right when says that the two systems of equations shown have the same solutions.

Hence, option A) Agree, because the solutions are the same is correct.

8 0

3 years ago

What is the value of the digit 5 in the number 4,578.364

hichkok12 [17]

Answer:

500

have a nice day!

4 0

3 years ago

Read 2 more answers

Find the equation of the line with a slope of 12 that passes through the point (3, -1)

Anon25 [30]

Answer:

y = 12x - 37

Step-by-step explanation:

The equation of a line in slope- intercept form is

y = mx + c ( m is the slope and c the y- intercept )

here m = 12, thus

y = 12x + c ← is the partial equation

To find c substitute (3, - 1) into the partial equation

- 1 = 36 + c ⇒ c = - 1 - 36 = - 37

y = 12x - 37 ← is the equation of the line

3 0

3 years ago

Read 2 more answers

P+6/6+m*n; use m = 4, n = - 1, and p = -6 help plz i dont want to fail

Gemiola [76]

Answer:

The answer is Zero

Step-by-step explanation:

P+6/6+m*n

-6+6/6+4(-1)

0/-2

The answer is Zero

6 0

3 years ago

| x- ( - 18) | if x < - 18

aleksandrvk [35]

Answer:

well x-(-18) x+18 but the if part is x<-18 will stay the same

Step-by-step explanation:

6 0

2 years ago