Problem 24
<h3>Answer: w = 120</h3>
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Work Shown:
We have an isosceles triangle. The angles opposite the congruent sides are congruent. These are the base angles each 30 degrees. The missing angle is w. The three angles add to 180
(angle1)+(angle2)+(angle3) = 180
30+30+w = 180
60+w = 180
60+w-60 = 180-60 ... subtract 60 from both sides
w = 120
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Problem 25
<h3>Answers:</h3><h3>x = 6.5</h3><h3>y = 5</h3>
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Work Shown:
The angle marks are all the same, so the three angles are congruent to one another. We consider this an equiangular triangle. Any equiangular triangle is also equilateral, meaning all three sides are the same length.
So,
2x-5 = 8
2x-5+5 = 8+5 ... add 5 to both sides
2x = 13
2x/2 = 13/2 ... divide both sides by 2
x = 6.5
and also,
y+3 = 8
y+3-3 = 8-3 ... subtract 3 from both sides
y = 5
4x - 24y = 72
First subtract 4x from each side
-24y = -4x + 72
Divide each side by -24 so y is by itself
y = -4/-24x + 72/-24
To simplify -4/-24, the greatest common factor they have is -4, so divide the numerator and denominator by -4
y = 1/6x + 72/-24
To simplify 72/-24, the greatest common factor is 24, so divide the numerator and denominator by 24
y = 1/6x - 3
This is now in slope intercept form
answer: x = 1
explanation:
remember: input = x values, output = y values.
so, the question is asking us, for which x value will x = y on both graphs?
we will notice that this is true for the third option, because if you look at x = 1, y also equals 1, but this won't be true on any of the other options. this means that x = 1 is your answer.
<em>i hope this helps, and have a great day! don't hesitate to ask if you need more help with this specific question! ♥ - eviezoom </em>
Answer:
x = π/6, 5π/6
Step-by-step explanation:
4 sin² x − 4 sin x + 1 = 0
(2 sin x − 1)² = 0
sin x = ½
x = π/6, 5π/6
