In the figure shown, line AB is parallel to line CD. Part A: What is the measure of angle x? Show your work. (5 points)

Mathematics

1 answer:

gtnhenbr [62]2 years ago

4 0

a) ∠PQR=65° (alternate interior angles theorem)

∠PRQ = 60° (linear pair)

x = 55° (angles in a triangle add to 180°)

b) ∠APQ and ∠PQR are congruent alternate interior angles.

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The zeros of the function f(x)=(x+2)^2 - 25 are?

zloy xaker [14]

Zeros of the function
f(x) = (x + 2)² - 25
f(x) = (x + 2)(x + 2) - 25
f(x) = x(x + 2) + 2(x + 2) - 25
f(x) = x(x) + x(2) + 2(x) + 2(2) - 25
f(x) = x² + 2x + 2x + 4 - 25
f(x) = x² + 4x + 4 - 25
f(x) = x² + 4x - 21
x² + 4x - 21 = 0
x = -(4) +/- √((4)² - 4(1)(-21))
 2(1)
x = -4 +/- √(16 + 84)
 2
x = -4 +/- √(100)
 2
x = -4 +/- 10
 2
x = -2 + 5
x = -2 + 5 x = -2 - 5
x = 3 x = -7
f(x) = x² + 4x - 21
f(3) = (3)² + 4(3) - 21
f(3) = 9 + 12 - 21
f(3) = 21 - 21
f(3) = 0
(x, f(x)) = (3, 0)
or
f(x) = x² + 4x - 21
f(-7) = (-7)² + 4(-7) - 21
f(-7) = 49 - 28 - 21
f(-7) = 21 - 21
f(-7) = 0
(x, f(x)) = (-7, 0)

Vertex
X - Intercept
-b/2a = -(4)/2(1) = -4/2 = -2

Y - Intercept
y = x² + 4x - 21
y = (-2)² + 4(-2) - 21
y = 4 - 8 - 21
y = -4 - 21
y = -25
(x, y) = (-2, -25)

5 0

3 years ago

Read 2 more answers

Examine the diagram at right. The smaller triangle (inside of the larger triangle) is similar to larger triangle. How can you so

olchik [2.2K]

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In order to solve for x we can set up the proportion between the horizontal and vertical sides:

$28\div 11.2 = 27+x \div x$