Mathematics, 12.11.2020 06:40, biaxialpower789

please help! the approximate path of a projectile launched from 100 m above the ground is given by f(×)= -5×^2+40+100, where f(×) represents the height × seconds after it is released into the air. use the info to answer the questions below. 1. what is the factored form of the equation? 2 how long will it take the projectile to reach the ground?

Answers: 2

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Answers

answered: Buttercream16

Part 1) f(x)=-5(x-10)(x+2)

Part 2) After 10 seconds.

Step-by-step explanation:

We have the function:

f(x)=-5x^2+40x+100

Where f(x) represents the height x seconds after it is released into the air.

Part 1)

First, let's distribute a -5 out of the function:

f(x)=-5(x^2-8x-20)

Now, let's factor. We want to pick two number that multiplies to -20 and adds to -8.

We can use -10 and 2. So:

f(x)=-5(x^2+2x-10x-20)

Factor:

$\begin{aligned}f(x)&=-5(x^2+2x-10x-20) \\ f(x)&=-5(x(x+2)-10(x+2)) \\ f(x)&=-5(x-10)(x+2) \end{aligned}$

Hence, our factored form is:

f(x)=-5(x-10)(x+2)

Part 2)

We want to find after how many seconds does it take for the projectile to reach the ground.

If it reaches the ground, the height above the ground, f(x), will be 0.

So, we can set f(x) equal to 0 and solve for x. Instead of using the original equation, we can use the factored form. So:

0=-5(x-10)(x+2)

Zero Product Property:

$x-10=0\text{ or } x+2=0$

Solve for x:

$x=10 \text{ or } x=-2$

Since x measures time, -2 does not make sense in this context.

Therefore, our solution is x=10.

So, after 10 seconds, the projectile will hit the ground.

answered: Guest

answer: 0+0=0

step-by-step explanation:

that is the only answer that can make 0

answered: Guest

x= 1

step-by-step explanation: convert 5\frac{11}{12}5

to improper fraction. use this rule: a \frac{b}{c}=\frac{ac+b}{c}a

ac+b

3.25+0.5x+1\frac{1}{3}+\frac{5}{6}x=\frac{5\times 12+11}{12}3.25+0.5x+1

5×12+11

2 simplify 5\times 125×12 to 6060

3.25+0.5x+1\frac{1}{3}+\frac{5}{6}x=\frac{60+11}{12}3.25+0.5x+1

60+11

3 simplify 60+1160+11 to 7171

3.25+0.5x+1\frac{1}{3}+\frac{5}{6}x=\frac{71}{12}3.25+0.5x+1

4 simplify \frac{5}{6}x

x to \frac{5x}{6}

3.25+0.5x+1\frac{1}{3}+\frac{5x}{6}=\frac{71}{12}3.25+0.5x+1

5 convert 1\frac{1}{3}1

to improper fraction. use this rule: a \frac{b}{c}=\frac{ac+b}{c}a

ac+b

3.25+0.5x+\frac{1\times 3+1}{3}+\frac{5x}{6}=\frac{71}{12}3.25+0.5x+

1×3+1

6 simplify 1\times 31×3 to 33

3.25+0.5x+\frac{3+1}{3}+\frac{5x}{6}=\frac{71}{12}3.25+0.5x+

3+1

7 simplify 3+13+1 to 44

3.25+0.5x+\frac{4}{3}+\frac{5x}{6}=\frac{71}{12}3.25+0.5x+

8 simplify 3.25+0.5x+\frac{4}{3}+\frac{5x}{6}3.25+0.5x+

to \frac{13.75}{3}+\frac{4x}{3}

13.75

\frac{13.75}{3}+\frac{4x}{3}=\frac{71}{12}

13.75

9 simplify \frac{13.75}{3}

13.75

to 4.5833334.583333

4.583333+\frac{4x}{3}=\frac{71}{12}4.583333+

10 subtract 4.5833334.583333 from both sides

\frac{4x}{3}=\frac{71}{12}-4.583333

−4.583333

11 simplify \frac{71}{12}-4.583333

−4.583333 to \frac{4}{3}

\frac{4x}{3}=\frac{4}{3}

12 multiply both sides by 33

4x=\frac{4}{3}\times 34x=

×3

13 simplify \frac{4}{3}\times 3

×3 to \frac{12}{3}

4x=\frac{12}{3}4x=

14 simplify \frac{12}{3}

to 44

4x=44x=4

15 divide both sides by 44

x=1

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