Anyone able to help?
1 answer:
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Answer:
9
Step-by-step explanation:
<u>→You can use the Pythagorean Theorem to solve this, by plugging in the numbers, like so:</u>
<u />
<u>→Subtract </u><u> from both sides:</u>
<u>→Subtract 12x from both sides:</u>
<u />
<u>→Factor out x:</u>
<u />
<u>→Separate, set = to 0, and solve:</u>
<u /> → <u>Add 12 to both sides:</u>
→So we have 0 and 12, as our answers. However, we cannot have 0 as a side length, since this would not be possible.
→All we need to do is take 12, and plug it into the equation for the shortest leg.
Answer:
Step-by-step explanation:
We know that .
Then by CPCTC, ∠P≅∠C, ∠H≅∠N, and ∠S≅∠F.
Therefore, let’s solve for each of the angle relations.
∠P≅∠C:
We know that ∠P is 36°. ∠C is (4z-32)°. Therefore:
Solve for z:
So, the value of z is 17.
∠H≅∠N
∠H is (6x-29) and ∠N is 115. So:
Solve for x:
Therefore, the value of x is 24.
∠S≅∠F
We will need to find ∠S.
We already know that ∠P is 36.
∠H will be (6x-29). Substitute 24 for x to acquire: (6(24)-29)=144-29=115.
A triangle always totals 180°. Therefore, 115+36+∠S=180 or 151+∠S=180.
Therefore, ∠S=29.
∠F is (3y-1). So:
Solve for y:
Therefore, the value of y is 10.
So, x=24, y=10, and z=17.
And we are done!
Let x ft be the lenght of the fence and y ft be the width of the fence.
1. The length of the habitat should be at least 80 feet, then
2. The perimeter of the habitat should be no more than 300 feet. The perimeter of the fenceis 2x+2y ft, then
3. The system of inequalities that represent the model is
The graph of these inequalities is attached.
Two possible solutions are
- x=100 ft, y=20 ft (100≥80 and 2·100+2·20=240≤300);
- x=110 ft, y=30 ft (110≥80 and 2·110+2·30=280≤300).
