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3 years ago

30 points please help with steps

Mathematics

2 answers:

lesya [120]3 years ago

8 0

The answer is 6. 2(x+1)^2+q. 2(x^2+2x+1)+q. 2x^2+4x+1+q. So, q is 6 as the only number without x that we have is 1 so, to get 7 we need 6.

earnstyle [38]3 years ago

5 0

Answer: 6. 2

Explanation:

(x+1)^2+q

2(x^2+2x+1)+q

2x^2+4x+1+q.

q must be 6, because the only number that does not have x that is in the equation is 1; therefore for us to get 7 we need 6.

Hope this helped! :)

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The hypotenuse of a right triangle is 37 units long. Find the other two sides if the perimeter of the triangle is 84 units. Sepa

taurus [48]

Answer:

The lengths of the legs are 12 and 35 units

Step-by-step explanation:

Let c represent the hypotenuse and a and b represent the legs. Then the Pythagorean Theorem requires that a^2 + b^2 = c^2 = 37^2 = Hypotenuse^2

Also: a + b + c = Perimeter = 84 units.

Since c = 37 units, a + b + 37 units = 84 units, or a + b = 47 units, or a = 47 - b.

Then a^2 + b^2 = 37^2 becomes (47 - b)^2 + b^2 = 37^2, or 1369. Therefore:

2209 - 94b + b^2 + b^2 = 1369.

Simplifying by combining like terms, we get:

840 - 94b + 2b^2 = 0, which is a quadratic equation in standard form.

Reducing all terms by division by 2, we get:

420 - 47b + b^2 = 0. Here the coefficients are a = 1, b = -47 and c = 420.

The discriminant is therefore b^2 - 4ac, or 529, whose square root is ± 23.

Then the b values of this quadratic in b are

47 ± 23

b = -------------- , so that b is either 35 or 12

and then side a has length a = 47 - b = 12 or 35.

Thus, a = 12 and b = 35, and c is given: 37.

Check: Is 12^2 + 35^2 = 37^2 true? Is 144 + 1225 = 1369? YES

The lengths of the legs are 12 and 35 units.

7 0

3 years ago

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Mrrafil [7]

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