A crickets jump can be measured by the function h(x) = -4x^2 + 36x, where h(x) is the height in cm and x is the horizontal distance in cm. how far did the cricket jump?

A: 3 cm

B: 6 cm

C: 9 cm

D: 12 cm

Option C: 9 cm is the distance that the cricket jump

Explanation:

Given that the crickets jump can be measured by the function

Where h(x) is the height in cm and x is the horizontal distance in cm.

We need to determine the distance that the cricket jump.

Distance:

The distance that the cricket jump can be determined by substituting in the function

Thus, we have,

Switch sides, we get,

or

or

Thus, the value of x is 9

Hence, the cricket jump up to 9 cm

Therefore, Option C is the correct answer.

something that characterises a right triangle is the fact that we may use pythagoras' theorem to find any one of its sides given that we have the length of the other two sides. here, we have the length of the hypotenuse, √(87) yd, and one other side, √(23) yd, thus we can easily find the length of the remaining side using pythagoras' theorem as defined below:

c^2 = a^2 + b^2, where c is the length of the hypotenuse, and a and b are the lengths of the other two sides.

thus, given that c = √(87) and a = √(23), we may substitute these into the formula we defined above to get:

c^2 = a^2 + b^2

(√87)^2 = (√23)^2 + b^2 (substitute c = √87 and a = √23 into the equation)

87 = 23 + b^2 (evaluate (√87)^2 = 87 and (√23)^2 = 23 - remember that the square root of a number, squared will equal that very same number)

64 = b^2 (subtract 23 from both sides)

√64 = b (take the square root of both sides)

8 = b (evaluate √64 = 8)

therefor, the length of the unknown leg in the right triangle is 8 yd (first answer).

the answer is c. hope this !

step-by-step explanation: