Answer:
x = 8
y = 21
Step-by-step explanation:
(7x + 12)° and (12x - 28)° are alternate interior angles. Alternate interior angles are congruent. Therefore:
(7x + 12)° = (12x - 28)°
Solve for x
7x + 12 = 12x - 28
Collect like terms
7x - 12x = - 12 - 28
-5x = -40
Divide both sides by -5
-5x/-5 = -40/-5
x = 8
(12x - 28)° + (9y - 77)° = 180° (linear pair)
To find y, plug in the value for x = 8.
12(8) - 28 + 9y - 77 = 180
96 - 28 + 9y - 77 = 180
Combine like terms
- 9 + 9y = 180
Add 9 to both sides
-9 + 9y + 9 = 180 + 9
9y = 189
Divide both sides by 9
9y/9 = 189/9
y = 21
This is the answer to the problem. Hope it helps
Answer:
Step-by-step explanation:
In order to write the equation of the line in point-slope form that goes through those points, we need to know the slope of that line. Therefore,
So the slope is 2. Now we'll pick a point and use it to write an equation in point-slope form. I'll use the first point given to see if that's the one used in any of the answers : (10, 5)
y - 5 = 2(x - 10). That's choice B. Let's see, just in case there are 2 answers to this, what the equation would be using the other point (4, -7):
y - (-7) = 2(x - 4) and simplified:
y + 7 = 2(x - 4) is the other equation. Since that's not a choice, the only answer is B
Answer:
Explanation:
In this problem, the amount of wood refers to the length of the frame, modeling it as a long piece of wood.
Thus, the amount of wood is equal to the perimeter of a rectangle with dimensions <em>width = 8 inches</em>, and l<em>ength = 3×8 inches = </em>24 inches.
The perimeter of a rectangles is 2 × width + 2 × length:
- 2 × 8 inches + 2 × 24 inches = 16 inches + 48 inches = 64 inches.
