Phillip wrote an integer that is less than -2 and greater than -3.5. Which integer did he write?
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<h3>Answer: D) 70</h3>
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Explanation:
Label a new point E at the intersection of the diagonals. The goal is to find angle CEB. Notice how angle AED and angle CEB are vertical angles, so angle AED is also x.
Recall that any rectangle has each diagonal that is the same length, and each diagonal cuts each other in half (aka bisect). This must mean segments DE and AE are the same length, and furthermore, triangle AED is isosceles.
Triangle AED being isosceles then tells us that the base angles ADE and DAE are the same measure (both being 55 in this case).
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To briefly summarize so far, we have these interior angles of triangle ADE
- A = 55
- D = 55
- E = x
For any triangle, the three angles always add to 180, so,
A+D+E = 180
55+55+x = 180
110+x = 180
x = 180-110
x = 70
9514 1404 393
Answer:
x ≈ {-2.80176, -0.339837}
Step-by-step explanation:
Write in terms of sine and cosine:
sec(x) -5tan(x) -3cos(x) = 0 . . . . . . given, subtract 3cos(x)
1/cos(x) -5sin(x)/cos(x) -3cos(x) = 0
Multiply by cos(x). (Note, cos(x) ≠ 0.)
1 -5sin(x) -3cos(x)² = 0
Use the trig identity to write in terms of sin(x).
1 -5sin(x) -3(1 -sin²(x)) = 0
3sin(x)² -5sin(x) -2 = 0 . . . . . . . . quadratic in sin(x)
(sin(x) -2)(3sin(x) +1) = 0 . . . . . . factor the quadratic
Values of sin(x) that make this true are ...
sin(x) = 2 . . . . . true only for complex values of x
sin(x) = -1/3
Then the possible values of x are ...
x = arcsin(-1/3), -π -arcsin(-1/3)
x ≈ {-2.80176, -0.339837} . . . . . rounded to 6 sf
