Answer:
C
Step-by-step explanation:
Given 2 secants intersect a circle from a point outside the circle, then
The product of the external part and the entire part of one secant is equal to the product of the external part and the entire part of the other secant, that is
x(x + 10 + x) = 6(6 + 10 + x)
x(2x + 10) = 6(16 + x) ← distribute parenthesis on both sides
2x² + 10x = 96 + 6x ← subtract 96 + 6x from both sides
2x² + 4x - 96 = 0 ← in standard form
Divide through by 2
x² + 2x - 48 = 0 ← factor the left side
(x + 8)(x - 6) = 0
Equate each factor to zero and solve for x
x + 8 = 0 ⇒ x = - 8
x - 6 = 0 ⇒ x = 6
However x > 0 ⇒ x = 6 → C
Answer:
If you were solving the right triangle, it would be:
m∠A = 46°
m∠B = 44°
m∠C = 90°
AB = 32
BC ≈ 23
AC ≈ 24
Step-by-step explanation:
To solve this right triangle, you can use trigonometric ratios to solve for the sides. To find the angle measures:
m∠A = 46° (given)
m∠B = x
m∠C = 90° (given)
180 - (46 + 90) = x
180 - 136 = x
44 = x
m∠B = 44°
To find the side measures, you can use tangent, sine, cosine, and the Pythagorean Theorem.
Recall that:
tangent = opposite side/adjacent side
sine = opposite side/hypotenuse
cosine = adjacent side/hypotenuse
So:
sin46 = BC/32
BC = 32 (sin46)
BC ≈ 23
tan46 = BC/AC
AC = BC/tan46
AC = (23.01887361...) (tan46)
AC ≈ 24
Answer:
4
Step-by-step explanation:
-2 + 6 = 4