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3 years ago

Which of these factored expressions are equivalent to 15x+45? Select all that apply

Mathematics

1 answer:

mario62 [17]3 years ago

5 0

Answer:

A, B, C

Step-by-step explanation:

15x+45

3 (5x + 15)

5(3x +9)

15(x + 3)

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A number r divided by 82

Natalija [7]

Answer:

574 is a number that can be divided by 82

6 0

3 years ago

The measure of central angle XYZ is StartFraction 3 pi Over 4 EndFraction radians. What is the area of the shaded sector? 32Pi u

Tems11 [23]

Answer:

<em>96π units²</em>

Step-by-step explanation:

Find the diagram attached

Area of a sector is expressed as;

Area of a sector = θ/2π * πr²

Given

θ = 3π/4

r = 16

Substitute into the formula

area of the sector = (3π/4)/2π * π(16)²

area of the sector = 3π/8π * 256π

area of the sector = 3/8 * 256π

area of the sector = 3 * 32π

<em>area of the sector =96π units²</em>

5 0

3 years ago

Read 2 more answers

-4.8f+6.4=-8.48 what is f?

dalvyx [7]

Answer: The answer for f= 3.1

3 0

4 years ago

A rectangle is 4 times as long as it is wide. The perimeter of a rectangle is 50 cm. What are the dimensions of the rectangle?

marissa [1.9K]

We use the equation 2x+8x=50.

10x=50
x=5

The rectangle will be 20 cm long and 5 cm wide.

Hope this helps!

7 0

3 years ago

Read 2 more answers

A population of bees is decreasing. The population in a particular region this year is 1,250. After 1 year, it is estimated tha

8_murik_8 [283]

To model this situation, we are going to use the decay formula: $A=Pe^{rt}$
where
$A$ is the final pupolation
$P$ is the initial population
$e$ is the Euler's constant
$r$ is the decay rate
$t$ is the time in years

A. We know for our problem that the initial population is 1,250, so $P=1250$ ; we also know that after a year the population is 1000, so $A=1000$ and $t=1$ . Lets replace those values in our formula to find $r$ :
$A=Pe^{rt}$
$1000=1250e^{r}$
$e^{r}= \frac{1000}{1250}$
$e^{r}= \frac{4}{5}$
$ln(e^{r})=ln( \frac{4}{5} )$
$r=ln( \frac{4}{5} )$
$r=-02231$

Now that we have $r$ , we can write a function to model this scenario:
$A(t)=1250e^{-0.2231t}$ .

B. Here we are going to use a graphing utility to graph the function we derived in the previous point. Please check the attached image.

C.
- The function is decreasing
- The function doe snot have a x-intercept
- The function has a y-intercept at (0,1250)
- Since the function is decaying, it will have a maximum at t=0:
$A(0)=1250e^{(-0.2231)(0)$
$A_{0}=1250e^{0}$
$A_{0}=1250$
- Over the interval [0,10], the function will have a minimum at t=10:
$A(10)=1250e^{(-0.2231)(10)$
$A_{10}=134.28$

D. To find the rate of change of the function over the interval [0,10], we are going to use the formula: $m= \frac{A(0)-A(10)}{10-0}$
where
$m$ is the rate of change
$A(10)$ is the function evaluated at 10
$A(0)$ is the function evaluated at 0
We know from previous calculations that $A(10)=134.28$ and $A(0)=1250$ , so lets replace those values in our formula to find $m$ :
$m= \frac{134.28-1250}{10-0}$
$m= \frac{-1115.72}{10}$
$m=-111.572$
We can conclude that the rate of change of the function over the interval [0,10] is -111.572.

7 0

3 years ago