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3 years ago

HELP!!!

Mathematics

1 answer:

ella [17]3 years ago

3 0

Answer:

120

Step-by-step explanation:

We are given that the function for the number of students enrolled in a new course is $f(x) = 4^{x}-1$ .

It is asked to find the average increase in the number of students enrolled per hour between 2 to 4 hours.

We know that the average rate of change is given by,

$A = \frac{f(x)-f(a)}{x-a}$ ,

where f(x)-f(a) is the change in the function as the input value (x-a) changes.

Now, the number of students enrolled at 4 = f(4) = $f(x) = 4^{4}-1$ = 255 and the number of students enrolled at 2 = f(2) = $f(x) = 4^{2}-1$ = 15

So, the average increase $A=\frac{f(4)-f(2)}{4-2}$ = $A=\frac{255-15}{4-2}$ = $A=\frac{240}{2}$ = 120.

Hence, the average increase in the number of students enrolled is 120.

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Which of these is a linear equation in standard form for the graph shown?

vampirchik [111]

Answer:

Step-by-step explanation:

Because the slope is a positive slope (goes through the positive quandrants on the graph), we can eliminate answer choices c. Now, if we solve a, b, and d and we can see if the slope + y-intercept matches the graph.

For A.) (solve for y to get a y=mx + b equation)

3x-2y=4

-2y= -3x + 4

y= 3/2 -2

For B.)

3x-2y= -4

-2y= -4-3x

y= 3/2 + 2

For D.)

2x+3y= 4

3y= 4-2x

y= -2/3x + 4/3

Now, if we look at D, the slope is negative so it cannot be D. That leaves us with A and B. The b in the y=mx + b equation stands for the y-intercept, so we can see that the y-intercept is 2. So, since the graph intersects the y-axis at (0,2), the answer is B! y=3/2 + 2 has a positive slope and 2 for the y-intercept!

4 0

3 years ago

You randomly choose two shapes from the bag, with replacement. Find the probability of choosing a star and then a circle. Write

vodka [1.7K]

Answer:

1/3

Step-by-step explanation:

3 0

3 years ago

Help ASAP I’ll mark you as brainlister

liraira [26]

Answer:

about 0.10 cents a unit

Step-by-step explanation:

If I'm wrong, I'm sorry!!

I hope you have a great day! Good luck with your math!

6 0

3 years ago

Identify the x-intercepts of the function below f(x)=x^2+12x+24

damaskus [11]

ANSWER:

x-intercepts of $\mathrm{x}^{2}+12 \mathrm{x}+24=0 \text { are }(-6+2 \sqrt{3}),(-6-2 \sqrt{3})$

SOLUTION:

Given, $f(x)=x^{2}+12 x+24$ -- eqn 1

x-intercepts of the function are the points where function touches the x-axis, which means they are zeroes of the function.

Now, let us find the zeroes using quadratic formula for f(x) = 0.

$X=\frac{-b \pm \sqrt{b^{2}-4 a c}}{2 a}$

Here, for (1) a = 1, b= 12 and c = 24

$X=\frac{-(12) \pm \sqrt{(12)^{2}-4 \times 1 \times 24}}{2 \times 1}$

$\begin{array}{l}{X=\frac{-12 \pm \sqrt{144-96}}{2}} \\\\ {X=\frac{-12 \pm \sqrt{48}}{2}} \\\\ {X=\frac{-12 \pm \sqrt{16 \times 3}}{2}} \\\\ {X=\frac{-12 \pm 4 \sqrt{3}}{2}} \\ {X=\frac{2(-6+2 \sqrt{3})}{2}, \frac{2(-6-2 \sqrt{3})}{2}} \\\\ {X=(-6+2 \sqrt{3}),(-6-2 \sqrt{3})}\end{array}$

Hence the x-intercepts of $\mathrm{x}^{2}+12 \mathrm{x}+24=0 \text { are }(-6+2 \sqrt{3}),(-6-2 \sqrt{3})$

8 0

3 years ago

Write multiplication expression to represent the change in temperature after the plane ascends 10,000 feet .... Above it says th

Allisa [31]

Answer:

1.3°F * 10 = 13°F

10.2°F

Step-by-step explanation:

Given that:

Temperature on the ground = - 2.8°F

Change in temperature per 1000 ft rise = 1.3°F

Change in temperature after the plane ascends 10000 ft

Change in temperature per 1000ft rise * (10000/1000)

1.3°F * 10 = 13°F

B.) Temperature at 10,000 feets

Temperature on ground + change in temperature at 10,000ft

-2.8°F + 13°F

= 10.2°F

5 0

3 years ago