Answer:
3a) The value of x = 56
3b) The measure of ∠ H T M = 90°
3c) The radius of the circle = 53
Step-by-step explanation:
3a) ∵ A F is a tangent to the circle O at point F
∵ Secant AH intersects circle O at point T
∴ (A F)² = (A T)(A H)
∴ 7( x + 7) = (21)² ⇒ ÷ 7
∴ x + 7 = 63
∴ x = 63 - 7 = 56
3b) ∵ HM is a diameter
∴ The measure of the arc HM = 180° ⇒ semi-circle
∵ ∠ H T M is inscribed angle subtended by the arc HM
∴ m ∠ H T M = half the measure of arc HM
∴ m ∠ H T M = 180° ÷ 2 = 90°
3c) ∵ Δ H T M is a right angle triangle at T
∴ (H M)² = (M T)² + (H T)² ⇒ Pythagorean theorem
∴ (H M)² = (90)² + (56)²
∴ (H M)² = 11236
∴ HM = 
= 106
∴ OM = 106 ÷ 2 = 53
∵ OM is the radius of the circle O
∴ The radius = 53
I think it’s either b or c. But I’m leaning more towards c
n + n - 0.18n
We can rewrite it as
2n - 0.18n
And if we solve it
(2 - 0.18)n = 1.82n
So the equivalente expression is B.
Answer:
x = 37/3 = 12.333
Step-by-step explanation:
Step 1 :
Pulling out like terms :
1.1 Pull out like factors :
15x - 185 = 5 • (3x - 37)
Equation at the end of step 1 :
Step 2 :
Equations which are never true :
2.1 Solve : 5 = 0
This equation has no solution.
A a non-zero constant never equals zero.
Solving a Single Variable Equation :
2.2 Solve : 3x-37 = 0
Add 37 to both sides of the equation :
3x = 37
Divide both sides of the equation by 3:
x = 37/3 = 12.333
14.5% = 0.145
Step-by-step explanation:
The term 'percent' (%) actually means per 100. So when you say 14.5% it means 14.5 per 100. So when you put that into an equation it actually means:
So when you solve it, 14.5% is actually 0.145 and not 14.5.
Your friend is then incorrect because:
14.5% ≠ 14.5
