What is the x-intercept h=-16t^2+20t+6?

see explanation

Step-by-step explanation:

To find the intercepts equate h to zero, that is

- 16t² + 20t + 6 = 0 ← divide all terms by 2

- 8t² + 10t + 3 = 0 ← multiply through by - 1

8t² - 10t - 3 = 0 ← factor the quadratic

Consider the factors of the product of the coefficient of the t² term and the constant term which sum to give the coefficient of the t- term

product = 8 × - 3 = - 24 , sum = - 10

Factors are - 12 and + 2

Use these factors to split the middle term

8t² - 12t + 2t - 3 = 0 ( factor the first/second and third/fourth terms )

4t(2t - 3) + 1(2t - 3) = 0 ← factor out (2t - 3)

(2t - 3)(4t + 1) = 0

Equate each factor to zero and solve for t

2t - 3 = 0 ⇒ 2t = 3 ⇒ t =

4t + 1 = 0 ⇒ 4t = - 1 ⇒ t = -

Intercepts are (- , 0) abd (, 0)

7, and 7√2

Step-by-step explanation:

The angle ratios are 1.5 : 1.5 : 3, so there are

1.5 + 1.5 + 3 = 6 total parts.  There are 180° in a triangle, so we have

6x = 180

  x = 30

Each part is 30°,

1.5 becomes 45°  (30 plus half of 30)

3 becomes 90°

There are 2 angles with a ratio of 1.5, so we have a 45° - 45° - 90° triangle.  

The side opposite the smallest angle is 7, there are angels with the least measure, so there are 2 sides that are 7.  

The hypotenuse of a 45° - 45° - 90° triangle is larger than the legs by a factor of √2, so the hypotenuse is 7√2