What is the answer to this??

A teenager who is 5 feet tall throws an object into the air. The quadratic function LaTeX: f\left(x\right)=-16x^2+64x+5f ( x ) =

tia_tia [17]

Answer:

At approximately x = 0.08 and x = 3.92.

Step-by-step explanation:

The height of the ball is modeled by the function:

$f(x)=-16x^2+64x+5$

Where f(x) is the height after x seconds.

We want to determine the time(s) when the ball is 10 feet in the air.

Therefore, we will set the function equal to 10 and solve for x:

$10=-16x^2+64x+5$

Subtracting 10 from both sides:

$-16x^2+64x-5=0$

For simplicity, divide both sides by -1:

$16x^2-64x+5=0$

We will use the quadratic formula. In this case a = 16, b = -64, and c = 5. Therefore:

$\displaystyle x=\frac{-b\pm\sqrt{b^2-4ac}}{2a}$

Substitute:

$\displaystyle x=\frac{-(-64)\pm\sqrt{(-64)^2-4(16)(5)}}{2(16)}$

Evaluate:

$\displaystyle x=\frac{64\pm\sqrt{3776}}{32}$

Simplify the square root:

$\sqrt{3776}=\sqrt{64\cdot 59}=8\sqrt{59}$

Therefore:

$\displaystyle x=\frac{64\pm8\sqrt{59}}{32}$

Simplify:

$\displaystyle x=\frac{8\pm\sqrt{59}}{4}$

Approximate:

$\displaystyle x=\frac{8+\sqrt{59}}{4}\approx 3.92\text{ and } x=\frac{8-\sqrt{59}}{4}\approx0.08$

Therefore, the ball will reach a height of 10 feet at approximately x = 0.08 and x = 3.92.

7 0

2 years ago

Please help! I mark brainliest :3

vladimir1956 [14]

no for a
yes for B
no for c
that what I think It is opinion could be wrong

3 0

3 years ago

f(x) = x2. What is g(x)?SIf(x)= x/g(x)(2,1)-5O A.06)-()O B. g(x) = 2x2O C. g(x)-9(x)=(*)O D. g(x)= x2

Andrew [12]

Explanation

As you can see all the possible answers have the same form:

$g(x)=ax^2$

By looking at the picture you'll notice that the graph of g(x) has to pass through the point (2,1). Remember that the points in the graph of g(x) have the form (x,g(x)). Since (2,1) is part of the graph of g(x) then we have the following:

$\begin{gathered} (2,1)=(x,g(x)) \\ x=2 \\ g(2)=1 \end{gathered}$

So let's evaluate the expression for g(x) that we wrote before at x=2. This way we'll obtain an equation for the number a:

$\begin{gathered} g(2)=1=a\cdot2^2 \\ 1=4a \end{gathered}$

Then we can divide both sides by 4:

$\begin{gathered} \frac{1}{4}=\frac{4a}{4} \\ a=\frac{1}{4} \end{gathered}$

Then we get:

$g(x)=\frac{1}{4}x^2=(\frac{1}{2}x)^2$ Answer

Then the answer is option A.

3 0

1 year ago

Which is the graph of the linear inequality 1/2 x-2y>-6 ?

larisa86 [58]

Answer:

<h2>Your Answer is C!!!!!!!!!</h2>

Steps:

$\frac{1}{2} x-2y>-6$

Add 2y to both sides:

$\frac{1}{2} x-2y+2y>-6+2y$

Simplify:

$\frac{1}{2}x>-6+2y$

Multiply both sides by 2:

2· $\frac{1}{2}x>-2$ ·6+2·2y

Simplify:

x>-12+4y

5 0

3 years ago

Dharmesh has a square garden with a perimeter of 132 feet. Is the area of the garden greater than 1,000 square feet?

Delvig [45]

Answer: Yes. The area is 1089 square feet.

Step-by-step explanation:

For a square, all the sides are equal: L = W

Hence, the perimeter of a square = 4 × L

Perimeter = 4L

132 = 4L

132 ÷ 4 = L

33 = L = W

Area of a square with 33 feet sides = L × L = 33 × 33 = 1089

1089 > 1000

3 0

3 years ago