What is the reciprocal of 1 and 1/9

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

Identify the linear inequality from the graph

Dovator [93]

Answer:

B) y < 3/4x -2

Step-by-step explanation:

First, to eliminate 2 options let's see what sign we should use. The ≤ is a solid line where < is a dotted line. Next, you need to know which way to flip the sign. If it is under the line it is the < symbol.

5 0

3 years ago

A friend has a 83% average before the final exam for a course. That score includes everything but the final, which counts for 25

Klio2033 [76]

Answer:

$\mathrm{Best\:course\:grade\:possible:\:}87.25\%,\\\mathrm{Minimum\:score\:on\:final\:to\:earn\:at\:least\:a\:75\%\:for\:the\:course:\:}51\%$

Step-by-step explanation:

Assuming the maximum score for the final is $100\%$ , we can multiply each score by its respective course weight and add them together to give a final score. If your friend did receive this maximum score of $100\%$ , their overall grade for the course would be:

$83(1-0.25)+100(0.25)=\fbox{$87.25\%$}$ .

To find the minimum score they need to earn a 75% for the course, we set up the following equation:

$83(1-0.25)+x(0.25)=75$ , where $x$ is the minimum score she needs.

Solving, we get:

$62.25+x(0.25)=75,\\x(0.25)=12.75,\\x=\fbox{$51\%$}$ .

8 0

3 years ago

PLEASE I NEED HELP

notka56 [123]

You would transform 5x + 2x into the same term with the associative property, adding like terms. If you subsitute the different values into the expressions you notice that both have a rate of change of 7 like an arithmetic sequence. To see if any value will make the two expressions equal you make them equal to each other.

5x + 2x = 7x -1

7x = 7x - 1

0 = -1

No they will never have be a solution to both expressions to make them equal because they're parallel to each other.

7 0

4 years ago

Problem Page A table of values of a linear function is shown below. x −1 0 1 2 3 y −6 −8 −10 −12 −14 Find the slope and y -inter

Ivenika [448]

When x=0, y=-8, so that is the y-intercept.

When x increases by 1, y decreases by 2, so the slope is -2.

The equation of the function is
.. y = -2x -8

3 0

3 years ago