Math help xoxox?

Question

1.) the hypotenuse of a right triangle is 210. If one leg is 42 more than half of the other leg what is the length of the shorter leg?

2.) The product of two consecutive odd integers is 5775. What is the proper quadratic equation to find the numbers?

3.) A TV manufacturer designed a tv containing a screen with a length of 16 inches less than twice the width. If the screen area is 1536 inches squared, what is the quadratic equation that could be used to find the diemnsions of the screen?

4.) A grandmother is 2 more than 7 times the age of her grandchild. The addition of the square of their ages is 3428. Which quadratic formula could be used to find the age of the grandchild?

Answer 1

1) Call the short leg s.

s² + (s+42)² = 210²

2s² + 84s + 1764 = 44100

2s² + 84s - 42336

Quadratic equation gives answers:

s = -168 or s = 126

(ignore the negative solution).

Answer: 126

2) (2n+1)(2n+3) = 5775

or

4n² + 8n - 5772 = 0

3) L = 2W-16

A = LW = 1536

W(2W-16) = 1536

2W² - 16W - 1536 = 0

4) M = 2+7C

M² + C² = 3428

(2+7C)² + C² = 3428

50C² + 28C + 4 = 3428

50C² + 28C - 3424 = 0

Answer 2

1. Basic eqtn. h^2= a^2 + b^2
h = 210. Let a the leg we want to solve for.
Then b = (a/2)+42
Substitute and solve.
2. If the smaller odd digit is m, the larger odd digit it m+2. Then m*(m+2) = 5775

3. Area = width x length. Let w be width. Then length= 2*w - 16.

4. Let the grandchild age be gc
Then grandma's age is 7*gc + 2
And gc^2 + (7*gc +2)^2 = 3428

Answer 3

1. let x be one leg. Other leg: x/2 + 42
Equation: x² + (x/2 + 42)² = 210². Solve for x.

2. x=odd integer ; next odd: x+2
Equation: x(x+2) = 5775

3. Length : 2w-16 . Width: w.
Equation: w(2w-16) = 1536.

4. grandchild's age: x ; grandmother: 7x+2.
Equation: x² + (7x+2)² = 3428

d:

Answer 4

1) 210^2 = x^2 + (x/2 +42)^2

2) (2x+1)(2x+3) = 5775

3)x(2x-16) = 1536

4)g = 7c+2
g^2 +c^2=3428
(7c+2)^2+c^2=3428

Answer 5

1.) The shorter leg is 126
2.) x^2+2x-5775=0
3.) 2x^2-16x-1536=0
4.)50x^2+28x-3424=0