Kate made 180 ounces of punch for a party. She serves the punch in 8-ounce cups.

Volume of a cube = s³

Therefore, s³ = 512, meaning that s = 8.

The question asks what the resulting volume would be if all sides of the cube were divided by 4.

The current side measures 8, and we know that 8/4 = 2.

Thus, the resulting volume = s³ = 2³ = 8 cubic mm.

6 0

3 years ago

A biologist has been observing a tree's height. This type of tree typically grows by 0.22 feet each month. Fifteen months into t

Lyrx [107]

Data:

x: number of months

y: tree's height

Tipical grow: 0.22

Fifteen months into the observation, the tree was 20.5 feet tall: x=15 y=20.5ft (15,20.5)

In this case the slope (m) or rate of change is the tipical grow.

m=0.22

To find the line's slope-intercep equation you use the slope (m) and the given values of x and y (15 , 20.5) in the next formula to find the y-intercept (b):

$\begin{gathered} y=mx+b \\ 20.5=0.22(15)+b \\ 20.5=3.3+b \\ 20.5-3.3=b \\ 17.2=b \end{gathered}$

Use the slope(m) and y-intercept (b) to write the equation:

$\begin{gathered} y=mx+b \\ \\ y=0.22x+17.2 \end{gathered}$ A) This line's slope-intercept equation is: y=0.22x+17.2

B) To find the height of the tree after 29 months you substitute in the equation the x for 29 and evaluate to find the y:

$\begin{gathered} y=0.22(29)+17.2 \\ y=6.38+17.2 \\ \\ y=23.58 \end{gathered}$ Then, after 29 months the tree would be 23.58 feet in height

C) In this case as you have the height and need to find the number of moths you substitute the y for 29.96feet and solve the equation for x, as follow:

$\begin{gathered} 29.96=0.22x+17.2 \\ 29.96-17.2=0.22x \\ 12.76=0.22x \\ \frac{12.76}{0.22}=x \\ \\ 58=x \end{gathered}$ Then, after 58 months the tree would be 29.96feet tall

3 0

1 year ago

SERIOUSLY HELPPPPPPPP

AlekseyPX

9514 1404 393

Answer:

B.

as x increases, f(x) decreases;
as x decreases,f(x) decreases

Step-by-step explanation:

The function is of even degree with a negative leading coefficient. f(x) will tend toward negative infinity as x gets larger or smaller. That is ...

as x increases, f(x) decreases;
as x decreases,f(x) decreases

_____

<em>Even degree</em> means the end behaviors are the same for both large and small x. <em>Negative leading coefficient</em> means the function value decreases for larger x.

8 0

3 years ago