Determine (without solving the problem) an interval in which the solution of the given initial value problem is certain to exist
1 answer:
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<h3>Answer: Choice B) x = 65, y = 10</h3>
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Work Shown:
The upper pair of angles 60 degrees and (2x-y) degrees are supplementary angles. This is because of the parallel lines. Note how they are same side interior angles. Therefore, (2x-y) and 60 combine to 180 degrees like so
(2x-y)+60 = 180
2x-y = 180-60 ... subtract 60 from both sides
2x-y = 120 ... call this equation 1
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Similarly, (2x+y) and 40 also combine to 180
(2x+y) + 40 = 180
2x+y = 180-40 ... subtract 40 from both sides
2x+y = 140 ... call this equation 2
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Line up equation 1 and equation 2. Then add straight down
That becomes 4x = 260 which solves to x = 65 when you divide both sides by 4.
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If x = 65, then,
2x-y = 120
2(65)-y = 120
130 - y = 120
-y = 120-130
-y = -10
y = 10
or
2x+y = 140
2(65)+y = 140
130+y = 140
y = 140-130
y = 10
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Either way end up with x = 65 and y = 10
Answer:
4/45
Step-by-step explanation:
Multiply the top by the top, and the bottom by the bottom:
4/45 cannot be reduced down anymore, therefore that is your answer.
<em>Hope this helps!!</em>
<em>- Kay :)</em>
Answer:
7 cm²
Step-by-step explanation:
First, find the area of the big circle with the formula A = r²
A = (3)²
A = 9
Now, we can find the areas of the smaller circles. Since they have the same radius, they are congruent (will have the same area)
A = r²
A = (1)²
A =
Now, we will subtract the areas of the smaller circles from the area of the big circle to find the area of the shaded region:
9 -
-
= 7
So, the area of the shaded region is 7 cm²