The answer is A to the question
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
Answer:
Step-by-step explanation:
4 goes into 64 sixteen times. 64/4 = 16 16 x 4 = 64
Answer:
17.84875
Step-by-step explanation:
5.45 x 3.275 = 17.84875
Simplify both sides of the equation.
<span><span><span><span>3/5</span>n </span>+ 15 </span>= <span><span><span>2/5</span>n </span>+ 10
</span></span>Subtract 2/5n from both sides.
<span><span><span><span><span>3/5</span>n </span>+ 15 - </span><span><span>2/5</span>n </span></span>= <span><span><span><span>2/5</span>n </span>+ 10 - </span><span><span>2/5</span>n</span></span></span><span><span><span><span>15</span>n </span>+ 15 </span>= 10
</span>Subtract 15 from both sides.
<span><span><span><span><span>1/5</span>n </span>+ 15 - </span>15 </span>= <span>10 - 15</span></span><span><span><span>1/5</span>n </span>= -<span>5
</span></span>Multiply both sides by 5.
<span><span>5 </span></span>× (1/5n) = (5) × (−5)<span>n = -<span><span>25
Answer: n is -25.</span></span></span>