Answer:
x = 5
Step-by-step explanation:
The interior angles of a triangle <em>always</em> have to add up to 180 degrees.
This means you can form an equation with the three angles you have:
(10x - 4) + (8x + 3) + 91 = 180
Then, solve:
combine like terms
subtract 90 from both sides
divide both sides by 18
√(x+7) = x + 1
Squaring on both sides,
x + 7 = (x + 1)²
x + 7 = x² + 2x + 1
x² + x - 6 = 0
x² + 3x - 2x - 6 = 0
x(x + 3) - 2(x + 3) = 0
(x - 2)(x + 3) = 0
x = 2 or -3
Hope this helps!
<h3>
Answer: y = -2x+8</h3>
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Explanation:
Parallel lines have equal slopes, but different y intercepts. The given line y = -2x+4 has a slope of -2. Any line parallel to this will also have a slope of -2.
So m = -2
The unknown line goes through the point (x,y) = (2,4). Which means x = 2 and y = 4 pair up together.
Plug m = -2, x = 2, y = 4 into y = mx+b and solve for b
y = mx+b
4 = -2(2)+b
4 = -4+b
4+4 = b ... adding 4 to both sides
8 = b
b = 8
Since m = -2 and b = 8, we go from y = mx+b to y = -2x+8
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Side note: the y intercept of the original equation is 4 while the y intercept of the new equation is 8
You sure seem to be asking a lot of questions lately. I'd like to see that you've been trying with these problems at least because if you can't get that first one it's almost like you missed the whole lesson.
1. 20 = 4b + 7 + 5
Add the 7 and 5.
20 = 4b + 12
Subtract 12 from each side.
8 = 4b
Divide each side by 4.
2 = b
2. 7 = 6k - 7k
6k - 7k = -1k. (the k acts as a sort of unit)
7 = -1k
Divide each side by -1.
-7 = k
3. 3.23 - 2m = 3 - 2(5m - 2)
Distribute the ×-2 to each term inside the parentheses.
3.23 - 2m = 3 - 10m + 4
Add the 3 and 4.
3.23 - 2m = 7 - 10m
Add 10m to each side.
3.23 + 8m = 7
Subtract 3.23 from each side.
8m = 3.77
Divide by 8.
m = 0.47125
4. -88/45=1/3r+2/5r
To get rid of the fractions, let's multiply everything by 45.
-88 = 15 + 18r
Subtract 15 from each side.
-103 = 18r
Divide by 18.
-103/18 = r
As a mixed number, r = -5 and 13/18
As a decimal, r = -5.7222...