What is the zero of the function: y = 15x + 30

The function h(t) = −16t2 + 18t models the height, in feet, reached by a leopard t seconds after it jumps. What is the approxima

S_A_V [24]

9514 1404 393

Answer:

5 1/16 ft

Step-by-step explanation:

h(t) = -16t(t -18/16) . . . . put in intercept form

The function describes a parabola that opens downward. It has zeros at t=0 and t=9/8. The maximum height will be found at the vertex of the parabola, halfway between these zeros.

f(9/16) = (-16)(9/16)² +18(9/16) = 81/16 = 5 1/16 . . . . feet

The approximate maximum height of the leopard is 5 1/16 feet.

5 0

3 years ago

at the movies, la quinta paid for drinks and popcorn for herself and her two children. she spend twice as much on popcorn as on

jarptica [38.1K]

Answer:

Step-by-step explanation:

let the amount spent on popcorn be x and amount spent on drinks be y

If the total bill paid is $17.94, then x+y = $17.94

If she spend twice as much on popcorn as on drinks, then y = 2x

Substitute y = 2x into the original equation

x+y = $17.94

x + 2x = $17.94

3x = $17.94

x = $17.94/3

x = $5.98

Since y = 2x

y = 2($5.98)

y = $11.96

Therefore she spent $5.98 on popcorn and $11.96 on drinks

4 0

3 years ago

Brandon bought Snacks for his teams practice he bought a bag popcorn for 211 and a six pack of juice bottles of total cost befor

yawa3891 [41]

Answer: 2.11X=11.41

X=9.3

or

211x=1141

930

Step-by-step explanation:

3 0

2 years ago

Read 2 more answers

Given f(x) =

sergejj [24]

Answer:

A

Step-by-step explanation:

We are given the function:

$\displaystyle f(x) = \left\{ \begin{array}{ll} 2\cos(\pi x) \text{ for } x \leq -1 \\ \\ \displaystyle \frac{2}{\cos(\pi x)}\text{ for } x > -1 \end{array} \right.$

And we want to find:

$\displaystyle \lim_{x\to -1}f(x)$

So, we need to determine whether or not the limit exists. In other words, we will find the two one-sided limits.

Left-Hand Limit:

$\displaystyle \lim_{x\to-1^-}f(x)$

Since we are approaching from the left, we will use the first equation:

$\displaystyle =\lim_{x\to -1^-}2\cos(\pi x)$

By direct substitution:

$=2\cos(\pi (-1))=2\cos(-\pi)=2(-1)=-2$

Right-Hand Limit:

$\displaystyle \lim_{x\to -1^+}f(x)$

Since we are approaching from the right, we will use the second equation:

$=\displaystyle \lim_{x\to -1^+}\frac{2}{\cos(\pi x)}$

Direct substitution:

$\displaystyle =\frac{2}{\cos(\pi (-1))}=\frac{2}{\cos(-\pi)}=\frac{2}{(-1)}=-2$

So, we can see that:

$\displaystyle \displaystyle \lim_{x\to-1^-}f(x)=\displaystyle \lim_{x\to -1^+}f(x) =-2$

Since both the left- and right-hand limits exist and equal the same thing, we can conclude that:

$\displaystyle \lim_{x \to -1}f(x)=-2$

Our answer is A.

8 0

3 years ago

Help please! my teacher wants us to show how we got our answer

Mila [183]

Direct variation is when $\dfrac{y}{x}$ is the same for each coordinate.

Indirect variation is when x · y is the same for each coordinate.

11. Answer: Direct Variation

<u>Step-by-step explanation:</u>

$\begin {array}{c||c|c|c|c|c}x&12&18&23&29&34\\y&132&198&253&319&374\\\\\dfrac{y}{x}&\dfrac{132}{12}=11&\dfrac{198}{18}=11&\dfrac{253}{23}=11&\dfrac{319}{29}=11&\dfrac{374}{34}=11\\\end{array} \\\\\\\text{The coordinates x and y show a direct variation.}$

12. Answer: Indirect Variation

<u>Step-by-step explanation:</u>

$\begin {array}{c||c|c|c|c|c}x&4&6&8&8.4&12\\y&21&14&10.5&10&7\\x\cdot y&4\cdot 21=84&6\cdot 14=84&8\cdot 10.5=84&8.4\cdot 10=84&12\cdot 7=84\\\end{array} \\\\\\\text{The coordinates x and y show an indirect variation.}$

3 0

3 years ago