Answer:
m∠C = 26°
m∠D = 108°
m∠E = 46°
Step-by-step explanation:
Set up the equation adding the expressions together to equal 180 (sum of all angles in a triangle)
(2x) + (x+3) + (5x-7) = 180
Remove the parentheses
2x + x+ 3 + 5x - 7 = 180
Add like terms
8x - 3 -7 = 8x -4 = 180
8x - 4 = 180
Add 4 on each side to cancel it out on the right
8x - 4 = 180
+4 = +4
8x = 184
Divide each side by 8 to get the variable by itself
8/8 =1 184/8 = 23
x = 23
Substitute x in eac expression
2x = 2(23) = 46°
x + 3 = 23 + 3 = 26°
5x - 7 = 5(23) - 7 = 115 -7 = 108
Chek it by adding all the degrees to make sure it equals 180
46 + 26 + 108 = 72 + 108 = 180
explanation:
The fastest way to find the missing endpoint is to determine the distance from the known endpoint to the midpoint and then performing the same transformation on the midpoint. In this case, the x-coordinate moves from 4 to 2, or down by 2, so the new x-coordinate must be 2-2 = 0. The y-coordinate moves from 4 to -5, or down by 9, so the new y-coordinate must be -5-9 = -14.
An alternate solution would be to substitute (4,4) for (x1,y1) and (2,-5) for (x,y) into the midpoint formula:
x=(x1+x2)/2
y=(y1+y2)/2
Solving each equation for (x2,y2) yields the solution (0,-14).
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Answer:
1/3
Step-by-step explanation:
There are 6 possible outcomes when rolling 1 die
1,2,3,4,5,6
P ( 1 or 5) = number of times 1 or 5 happens / total outcomes
= 2/ 6
= 1/3
Sum divided by count. Add up all the numbers and divide it by how many numbers it is.
