All categories

3 years ago

What is the slope of a line passing through (5, 9) and (7, 15)?

Mathematics

1 answer:

LenaWriter [7]3 years ago

6 0

Slope = change in y / change in x

= (15 - 9) / (7 - 5)

= 6 / 2

= 3

You might be interested in

6CO2 + 6H2O → C6H12O6 + 6O2=?

kramer

Answer:

Photosynthesis equation

Step-by-step explanation:

6 0

3 years ago

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 weekly wages for a person who earns $15 an hour and worked 8 hours from Monday through Sunday

Fudgin [204]

Answer:

840$

Step-by-step explanation:

4 0

3 years ago

PLEASE HELP ASAP! EXPLAIN THE ANSWER!

Stells [14]

Answer:

<h3>1863 m squared</h3>

Step-by-step explanation:

So, the goal here is to find the area of each block individually then add it all together. In other words, you're gonna look for a way to solve for the missing square in the total large rectangle. Keep in mind 23 + 23 + 23 = 69 (aka the length of the whole rectangle)

So:

12 x 23 = the missing square = 276

31 x 69 = rectangle with the square = 2139

Total area = 2139 - 276 = 1863

7 0

3 years ago

Find the coordinates of the midpoint of the segment whose endpoints are given.

Afina-wow [57]

You can think of midpoint as being an average.
Add the values and divide by 2.
(x1 + x2)/2, (y1 + y2)/2

(2 + 6)/2, (3 + 11)/2
(4,7) would be the midpoint

4 0

4 years ago

Read 2 more answers