First, we can factor an x out of this.
We're left with x(x^2 - 16)
We can use the difference of squares theorem here to factor this further.
<h3><u>We're left with (x)(x + 4)(x - 4)</u></h3>
Answer: m∠ABF = 120°
Concept:
Here, we need to know the idea of the <u>corresponding angle theorem </u>and <u>linear pair postulate</u>.
The corresponding angle theorem states that if a transversal cuts two parallel lines, their corresponding angles are congruent.
The linear pair postulate states that two angles that form a linear pair are supplementary.
Solve:
<u>Given information</u>
m∠ABF = m∠ABF = 2x + 3x
- According to the corresponding angle theorem, ∠ABF is congruent to ∠BCI which is 2x + 4x.
m∠BCH = 3x
Total angle = 180°
- ∠ABF and ∠BCH are linear pairs which means they form a supplementary angle.
<u>Given equation</u>
m∠ABF + m∠BCH = Total Angle
<u>Substitute values into the equation</u>
2x + 4x + 3x = 180
<u />
<u>Combine like terms</u>
9x = 180
<u>Divide 9 on both sides</u>
9x / 9 = 180 / 9
x = 20
m∠ABF = 2x + 4x = 2 (20) + 4 (20) = 40 + 80 = <u>120°</u>
Hope this helps!! :)
Please let me know if you have any questions
Answer:
Step-by-step explanation:
We are told that the perimeter is 48 = 2L + 2W. This reduces to
24 = L + W. Next, substitute, one by one, the 3 widths 10 cm, 3.6 cm and w cm:
a) If W = 10 cm, 24 = L + W becomes 24 = L + 10, or L = 14 cm
b) If W = 3.6 cm, 24 = L + W becomes 24 = L + 3.6, or L = 20.6 cm
c) If W = w, 24 L + W becomes 24 = L + w, so that L = (24 - w) cm
Answer:
Emma began her journey at 7:30 a.m., at 8 a.m. she was 20 miles away, she stayed for an hour and a half, she left at 10 a.m., she was 7.5 miles from her house at 11:45, she traveled 80 miles total
Answer:
1.94 & -1.94
Step-by-step explanation:
I took the test! Hope this helps :)