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3 years ago

Which ratios are not equivalent to 10 : 25

Mathematics

1 answer:

Leni [432]3 years ago

7 0

What is 333
$333 \times 3$

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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

I need help plz with this

madam [21]

Answer:

a) 390

b)108

I hope this answer was helpfull for you

5 0

3 years ago

All the info is in the pictures

Hunter-Best [27]

Bearing in mind that an absolute value expression is in effect a piece-wise function with two cases, thus

$\bf |-n|=
\begin{cases}
+(-n)\\
-(-n)
\end{cases}\implies 
\begin{cases}
-n\\
n
\end{cases}
\\\\\\
n|-n|=2n\implies 
\begin{cases}
n-n=2n\implies 0=2n\implies &0=n\\
n+n=2n\implies 2n=2n\impliedby &inconsistent
\end{cases}$