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:sorry dude
Step-by-step explanation:I got nothing
Answer:
Step-by-step explanation:
By the triangle sum theorem, the sum of angles in a triangle is equal to 180°. Therefore, m∠A + m∠B + m∠C = 180°. Using the Substitution property
(6x)° + 90° + (x+6)° = 180°
To solve for x, first combine the terms to get (7x + 96) = 180°
Using the Subtraction property of equality,
7x = 84.
Then using the division property of equality x = 12.
To find the measure of angle A,
Use the subtraction property to get m∠A = 6(12)°.
Finally simplifying the expression gets m∠A = 72°.
A ratio of 5:7 means out of 12 books, 5 are in one category and 7 are in another. (The “category” isn’t specified in this problem.)
So here we’re STARTING with 36 books; we want to find a ratio that is equal to 5:7 and adds up to 36. Well 36 = 3(12), and so if we multiply each number in the ratio by 3 as well, we might get what we want. Doing that gives us 15:21, which adds up to 36 and is equal to 5:7. Boom, that’s the answer.
P.S. Here’s a question you can think about: why do ratios stay the same when you multiply each number by the same amount? (For example, why is 3:1 the same as 6:2?)
We want to find the coeficient of the y terms when added together so find all the y terms
+12y and +2y
we add them together
12y+2y=(12+2)y=(14)y=14y
coeficient is 14
the constant is the number that is set already or the number that doesn't have it multiplied by a placeholder exg. 4 is a constnat but 4x is not so find the constants
+5 and +8
we add
5+8=13
the constant is 13
y coeficient=14
constant=14
