Answer:
Step-by-step explanation:
we know that
The area of the shaded region is equal to the area of triangle plus the area of semicircle
so
we have
Find the height of the right triangle applying the Pythagorean Theorem
The radius of the semicircle is half the height of triangle
substitute in the formula
Answer:
x=30, A=132
Step-by-step explanation:
These 2 angels are alternate interior angles so they are equal
5x-18=3x+42
Solve.
2x=60
x=30
Now substitute x into angle A
A=150-18
A=132
Answer:
a1 = 2
d = 3
an = 2 + (n - 1) * 3
a7 = 20
a59 = 176
Steps:
a1 is the initial value (when n equals 1), and since there are 2 crosses, it is 2.
d is the added value to each amount of crosses. And since the second amount is 5 and the third amount is 8, we can determine that each n is adding 3 crosses, therefore making d = 3.
The equation is simply plugging in the values for a1 and d.
A7 is simply plugging in 7 for n in the equation and solving for it. So;
a7 = 2 + (7 - 1) * 3
a7 = 2 + 6 * 3
a7 = 2 + 18
a7 = 20
And same thing as the last for 59 except substitute 59 in for where you put 7;
a59 = 2 + (59 - 1) * 3
a59 = 2 + 58 * 3
a59 = 2 + 174
a59 = 176
Answer:
<em>x = -10</em>
Step-by-step explanation:
(9/2)(8 - x) + 36 = 102 - (5/2)(3x + 24)
Multiply both sides by 2.
9(8 - x) + 2 * 36 = 2 * 102 - 5(3x + 24)
Distribute on both sides.
72 - 9x + 72 = 204 - 15x - 120
Combine like terms on each side.
144 - 9x = 84 - 15x
Subtract 144 from both sides. Add 15x to both sides.
6x = -60
Divide both sides by 6.
x = -10
