<h3>
Answer:</h3>
∠C = 40°
∠D = 75°
<h3>
Step-by-step explanation:</h3>
AB ║ CD, so AD and BC are transversals. The angle pairs (A, D) and (B, C) are "alternate interior angles", hence congruent.
∠C = ∠B = 40°
∠D = ∠A = 75°
If <em>x</em> + 1 is a factor of <em>p(x)</em> = <em>x</em>³ + <em>k</em> <em>x</em>² + <em>x</em> + 6, then by the remainder theorem, we have
<em>p</em> (-1) = (-1)³ + <em>k</em> (-1)² + (-1) + 6 = 0 → <em>k</em> = -4
So we have
<em>p(x)</em> = <em>x</em>³ - 4<em>x</em>² + <em>x</em> + 6
Dividing <em>p(x)</em> by <em>x</em> + 1 (using whatever method you prefer) gives
<em>p(x)</em> / (<em>x</em> + 1) = <em>x</em>² - 5<em>x</em> + 6
Synthetic division, for instance, might go like this:
-1 | 1 -4 1 6
... | -1 5 -6
----------------------------
... | 1 -5 6 0
Next, we have
<em>x</em>² - 5<em>x</em> + 6 = (<em>x</em> - 3) (<em>x</em> - 2)
so that, in addition to <em>x</em> = -1, the other two zeros of <em>p(x)</em> are <em>x</em> = 3 and <em>x</em> = 2
Answer:
y = 
(x - 5)² - 2
Step-by-step explanation:
The equation of a parabola in vertex form is
y = a(x - h)² + k
where (h, k) are the coordinates of the vertex and a is a multiplier
Here (h, k) = (5, - 2), thus
y = a(x - 5)² - 2
To find a substitute (7, 0) into the equation
0 = a(7 - 5)² - 2
0 = 4a - 2 ( add 2 to both sides )
2 = 4a ( divide both sides by 4 )
a = 
=
y = (x - 5)² - 2 ← in vertex form
G(x) = F(x + 4) + 2
Addition of a number to x indicates a shift towards left. Since 4 is being added to x, this means function is shifted to left by 4 units.
Addition of a number to the function represent an upward shift. Since 2 is being added to the function value, this mean function is shifted up by 2 units.
So, G(x) is obtained by shifted F(x) 4 units to left and 2 units up.
Thus, option C is the correct answer
Answer:
Step-by-step explanation:
A
