Answer:
(5, 2)
Step-by-step explanation:
Given the following system of equations;
2x - 2y = 6 ......equation 1.
4x + 4y = 28 ......equation 2.
To get an equivalent equation, we would multiply eqn 1 by 2;
2 * (2x - 2y = 6) = 4x - 4y = 12
The new equivalent system of equations are;
4x - 4y = 12
4x + 4y = 28
Adding the equivalent system of equations, we have;
(4x + 4x) + (-4y + 4y) = (12 + 28)
8x + 0 = 40
8x = 40
x = 40/8
<em>x = 5</em>
Next, we would find the value of y;
2x - 2y = 6
Substituting the value of x, we have;
2(5) - 2y = 6
10 - 2y = 6
Rearranging the equation (collecting like terms), we have;
2y = 10 - 6
2y = 4
y = 4/2
<em>y = 2</em>
<em>Therefore, the solutions to the new system of equations are 5 and 2.</em>
<u>Check:</u>
2x - 2y = 6
Substituting the values, we have;
2(5) - 2(2) = 6
10 - 4 = 6
6 = 6
Answer:
Step-by-step explanation:
Answer:
0.08 g/cm³
Step-by-step explanation:
We are given;
- Mass of the liquid = 2 pounds
But; 1 pound = 453.592 g
Therefore, mass = 907.184 g
- Volume of the liquid = 3 gallons
But; 1 gallon = 3785.41 cm³
Thus, volume = 11356.23 cm³
We are required to determine the density of the liquid;
We need to know that;
Density = Mass ÷ Volume
Therefore;
density of the liquid = 907.184 g ÷ 11356.23 cm³
= 0.0799 g/cm³
= 0.08 g/cm³
Thus, the volume of the liquid is 0.08 g/cm³
Answer:
4. A
5. B
Step-by-step explanation:
4. I'll solve question four first:
The two marked points on the line are (-2, -3)&(2, 5). Using the formula to find slope(y2-y1/x2-x1), substitute in the points.
5--3/2--2 or 8/4;simplified to 2/1 or 2.
Now use point-slope form: y-y1 = m(x-x1)
y--3 = 2(x--2): Substitute in the values of y1, m, and x1.
y+3 = 2x + 4: Distribute.
y = 2x + 1: Subtract three from both sides.
5. Do the same for question 5.
The first point is (-4, 2), the second point is (4, -1).
-1-2/4--4; -3/8.
Now use point-slope form:
y-2 = -3/8x -12/8: Substitute in the values of x1, y1, m, and distribute the slope to the parentheses.
y = -3/8x + 1/2