A. 199
b. -71
c. -2.25
d. 30
e. -18
f. -4
g. 4
h. 7
i. 0
Since BD bisects angle ABC, that means angle ABD and angle CBD are equal to each other. With that set up the equation to solve for x like this:
-4x+33 = 2x+81
-2x -2x
————————
-6x +33 = 81
-33 -33
————————
-6x = 48
————- (divide by -6)
-6
x = -8
Now substitute that to ABD
-4(-8) +33
32 +33
=65
here’s CBD
2(-8) + 81
-16 + 81
=65
Finally angle ABC will be double the amount of ABD or CBD so 65 times 2 is 130.
ANSWERS: (angles)
ABD and CBD: 65
ABC: 130
Answer:
3x-526
Step-by-step explanation:
the 3x would go in the beginning. then you subtract (-4-522)= -526.
Answer:
(1) 2π - x² = 0 (2) x = 2.5 cm (3) perimeter = 10 cm
Step-by-step explanation:
(1)The area of the circular coin without the inner square removed is πr² where r = 3 cm is the radius of the coin. So, the area of the coin without the inner square removed is πr² = π(3 cm)² = 9π cm²
The area of the square of x sides removed from its center is x².
The area A of the each face of the coin is thus A = 9π - x²
Since the area of each face of the coin A = 7π cm²,
then
7π = 9π - x²
9π - 7π - x² = 0
2π - x² = 0
(2) Solve the equation 2π - x² = 0
2π - x² = 0
x² = 2π
x = ±√(2π)
x = ± 2.51 cm
Since x cannot be negative, we take the positive answer.
So, x = 2.51 cm
≅ 2.5 cm
(3) Find the perimeter of the square
The perimeter of the square, p is given by p = 4x
p = 4 × 2.51 cm
= 10.04 cm
≅ 10 cm
