Answer:
n = 9
Step-by-step explanation:
Step 1: Write equation
-4(9n + 9) = -12(4n - 6)
Step 2: Solve for <em>n</em>
<u>Distribute:</u> -36n - 36 = -48n + 72
<u>Add 48n to both sides:</u> 12n - 36 = 72
<u>Add 36 to both sides:</u> 12n = 108
<u>Divide both sides by 12:</u> n = 9
Step 3: Check
<em>Plug in n to verify if it's a solution.</em>
-4(9(9) + 9) = -12(4(9) - 6)
-4(81 + 9) = -12(36 - 6)
-4(90) = -12(30)
-360 = -360
Answer:
y = (1/3)x
Step-by-step explanation:
If this is truly a line, then we can find its equation using any two of the three given points. If we go from (3, 1) to (27, 9), x increases by 24 and y increases by 8. Thus, the slope of this line is m = rise / run = 8 / 24, or m = 1/3.
Using the point (3, 1) and the slope m = 1/3, the slope-intercept form y = mx + b becomes 1 = (1/3)(3) + b. Thus, b = 0, and the line is y = (1/3)x.
First one: x would be equal to 8 because the angles opposite sides 8 and x are congruent (isosceles triangle)
Second one: x is 75° because the sides opposite x and 75° are congruent (isosceles triangle)
Third one: This is an equilateral triangle since all the sides are equal. In equilateral triangles, every angle is 60° because 60*3=180. So both x and y are 60°
Fourth one: We know that all three angles in a triangle add to 180°. And we also know that the last unlabled angle would be equal to x because this is an isosceles triangle. So we can write
x+x+38=180 (combine like terms)
2x+38=180 (subtract 38 from both sides)
2x=142 (divide both sides by 2)
x=71°
Fifth one: This is an equilateral triangle so all the angles are congruent and add to 180. So we can write
3(4x+12)=180 (distribute)
12x+36=180 (subtract 36 from both sides)
12x=144 (divide both sides by 12)
x=12
Last one: Since the two given angles are opposite congruent sides, these angles are equal. Therefore, we can just make each of these angles 3x to solve for x first. And since we know the last angle is 90° we can write
3x+3x+90=180 (combine like terms)
6x+90=180 (subtract 90 from both sides)
6x=90 (divide both sides by 6)
x=15
So the angle 3x would be 3*15 or 45.
So we can set 45 equal to y+7 and solve for y
y+7=45 (subtract 7 from both sides)
y=38
Hope this helps<span />
Answer:
17
Step-by-step explanation:
55-15-18-5=17
