Directions: Multiply, divide, and simplify the following exponential expressions.
Pls help

Answer:

She went on the slide 8 times and on the roller coaster 4 times

Step-by-step explanation:

We convert each statements to a mathematical equation.

Firstly, let's represent the number of times she went on the coaster with R and the number of times on the slide with S. We know quite well she went on 12 rides. Hence the summation of both number of times yield 12.

Mathematically, R + S = 12. ........(i)

Now we also know her total wait time was 3hours. Since an hour equals 60 minutes, her total wait time would equal 180 minutes.

To get a mathematical representation for the wait time, we multiply the number of roller coaster rides by 25 and that of the slides by 10.

Mathematically, 25R + 10S = 180 .......(ii)

Here we now have two equations that we can solve simultaneously.

From equation 1 we can say R = 12 - S. We can then substitute this into equation 2 to yield the following:

25(12 - s) + 10s = 180

300 - 25s + 10s = 180

300 - 25s + 10s = 180

300 - 15s = 180

15s = 300 - 180

15s = 120

S = 120/15

S = 8

S = 8 , and R = 12 - S = 12 - 8 = 4

Answer:

C

Step-by-step explanation:

Answer:

The first one is -28x

Step-by-step explanation:

2^2x is 4x and 4x-32x is -28

Given:

The growth of a sample of bacteria can be modeled by the function

[tex]b(t)=100(1.06)^t[/tex]

where, b is the number of bacteria and t is time in hours.

To find:

The number of total bacteria after 3 hours.

Solution:

We have,

[tex]b(t)=100(1.06)^t[/tex]

Here, b(t) number of total bacteria after t hours.

Substitute t=3 in the given function, to find the number of total bacteria after 3 hours.

[tex]b(t)=100(1.06)^3[/tex]

[tex]b(t)=100(1.191016)[/tex]

[tex]b(t)=119.1016 [/tex]

Therefore, the number of total bacteria after 3 hours is 119.1016.

Answer:

8/21

Step-by-step explanation:

1- 2/7 - 1/3 = 21/21 - 6/21 - 7/21 = 8/21

Answer:

1

Step-by-step explanation:

Answer:

1

Step-by-step explanation:

if i am not wrong i think it is 1 bc u can only cut a verticle line in the middle, then i dont see any other ways.

Answer: z=2

Step-by-step explanation:

Answer:

6x+24

Step-by-step explanation:

The simplified form of the expression 6(x + 4) is 6x + 24.

We have,

To simplify the expression 6(x + 4), we can apply the distributive property of multiplication over addition.

The distributive property states that when we have a number multiplied by a sum of terms, we can distribute the multiplication to each term separately and then simplify.

In this case, we have 6 multiplied by the sum (x + 4). Applying the distributive property, we can multiply 6 by both x and 4:

6(x + 4) = 6 * x + 6 * 4

Simplifying further:

6x + 24

Therefore,

The simplified form of the expression 6(x + 4) is 6x + 24.

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Answer:One is 2 feet and one is 4 feet

Step-by-step explanation:

Answer:

a. 50 weeks

Step-by-step explanation:

Answer:

y=2

Step-by-step explanation:

Logarithmic Equations

The following equation is given:

[tex]log_y 8+ log_y 4=5[/tex]

Recall the property:[tex]log_b x+lob_b y=log_b (x.y)[/tex]

Applying: [tex]log_y 32=5[/tex]

Now recall the definition of the log:

If:

[tex]log_b a=x[/tex]

Then

[tex]b^x=a[/tex]

The equation becomes:

[tex]y ^5=32[/tex]

But 32=2^5, so:

[tex]y ^5=2^5[/tex]

Equating the bases:

y=2

the midpoint is x1 and y10.5

Answer:

(1, 10.5)

Step-by-step explanation:

X-  6 + -4 = 2/2 = 1

Y-   5 + 16 = 21/2 = 10.5

You add the x coordinates together then divide by 2, then do the same with the y coordinates.

Answer:

3/5

Step-by-step explanation:

all you have to do is get the fraction to its lowest point and you get 3/5.

Answer:

Step-by-step explanation:

Step-by-step explanation:

i think the answer must be like this (4)(x‒5)

i hope it helps you

Answer: 3/4

Step-by-step explanation:

Answer:

Step-by-step explanation:

easy flip them and make it into mixed fractions  hope it helps

Answer:

216

Step-by-step explanation:

.48 * 450 = 216

Answer:

There are 216 girls in that school.

Step-by-step explanation:

hope this helps! have a great day.

Answer:

The answer is 5

Step-by-step explanation:

3+2=5

Answer:

first option

Step-by-step explanation:

i think its self explanatory!!!

Answer:

The most number of layers he can afford is 2

Step-by-step explanation:

We automatically have a fee of 17 so we know we have 13 dollars remaining. Using this information, we know that one layer is 5 dollars which means we can get 2 layers which is equal to 10 dollars which turns our total fee to $27. Hope this helps!

Answer:

50

Step-by-step explanation:

1.25 - .05 = 1.20 made per balloon

60/1.2 = 50 balloons sold to recoup 60$ start up and break even

Answer:

+45

Step-by-step explanation:

a deposit is a sum of money placed or kept in a bank account, usually to gain interest

Answer:

what is the equation?

Step-by-step explanation:

Answer:

[tex]3\frac{11}{24}[/tex]

Step-by-step explanation:

Given parameters:

Leftover pizza from the Science club = [tex]1\frac{1}{4}[/tex]

Left over pizza from french club  = [tex]2\frac{5}{24}[/tex]

Unknown;

Total left over pizzas between the two clubs = ?

Now to solve problem, simply add the leftover from the science club and the french club together;

      Total left over pizza  = [tex]1\frac{1}{4}[/tex]   + [tex]2\frac{5}{24}[/tex]  

                                         = [tex]\frac{5}{4} + \frac{53}{24}[/tex]  

                                         =  [tex]\frac{83}{24}[/tex]

                                         = [tex]3\frac{11}{24}[/tex]

The total left over pizza between the two clubs is [tex]3\frac{11}{24}[/tex]

present age of charlie is  45 years

present age of priya is  25 years

Step-by-step explanation:

Let start from five years ago

Let at that age of Priya was x years

given that

Charlie was twice older than Priya

age of Charlie = 2x

_____________________________________________

present age of charlie = age 5 years ago + 5 years = 2x + 5

present age of priya = age of priya  5 years ago + 5 years x + 5 = x + 5

_________________________________________________

age of charlie 3 years from now = present age of charlie + 3 years

age of charlie 3 years from now =2x + 5 + 3 = 2x + 8

age of priya 3 years from now = present age of priya + 3 years

age of priya 3 years from now =x + 5 + 3 = x + 8

Given that

in 3 years the sum of their ages will be 76

thus

sum of their ages in 3 years from now = x + 8 + 2x + 8 = 76

=> 3x + 16 = 76

=> 3x = 76-16 = 60

=> x = 60/3 = 20

Thus,

present age of charlie =  2x + 5 = 2*20 + 5 = 45 years

present age of priya = x + 5 = 20 + 5 = 25 years

Answer:

y = 1

Step-by-step explanation:

3(7) - 2y = 19y

21 - 2y = 19y

21 = 21y

y = 1

Answer:

Step-by-step explanation:

let the apprentice duration of work be x hours

so that the electrician worked (x+4)hours

53*(x+4)+22*x=624.50

opening the bracket we have

53x+212+22x=624.50

collect like terms we have

53x+22x+212=624.50

75x+212=624.50

75x=624.50-212

75x=412.5

divide both sides by 75 we have

x=412.5/75

x=5.5

The electrician worked a total of (x+4)

5.5+4=9.5 hours or 9hours 30min

given that the electrician earns $53 per hour

then,for the work he would make 53*9.5=$503.5

Answer:

So ummmm..... I personally think that all of your answers on the first page should be flipped.

Second page:

#9: domain= [0,6] range=[-6,6]

#10: Domain= (-infinity, infinity) range: (-infinity, infinity)

#11: Domain= (-infinity, infinity) range: [-2, infinity)

Thats all I have time for

(Write infinity as the sideways 8)

A function is a relationship between input values and output values such that each input has exactly one output

The correct values are;

First page

11. A skateboarder motion

Second page

9. The square is not a function

10. Domain; -∞ < x < ∞

Range; -∞ < x < ∞

11. Domain of the graph is; -∞ < x < ∞

Range is; 2 ≤ y < ∞

12. A circle is not a function

13. Domain is; -∞ < x < ∞

Range; -2 ≤ y ≤ 4

14. Domain; -∞ < x < ∞

Range; y = 2

15. The relationship is a function

16. The relationship is not a function

17. The relationship is not a function

18.The given relationship is not a function

19. The relationship is a function

20. The relationship is not a function

21. The relationship is a function

22. The relationship is not a function

Reason:

First page;

11. The given graph can be described by the following real life situation;

Second page;

The domain and range of a

The domain of a function is set values of the input to the function where the function is defined

The range of a function are is the set of the output values of the function

9. The given figure of a square is not a function

10. The graph extends to infinity towards the top right, and the bottom left

11. The graph of the function extends infinity at the top left and top right

The graph has a minimum at y = 2, while it extends to infinity as the y-values increases, therefore;

12. The graph of a circle is not a function

13. The end behavior of the graph is as follows;

The graph is repeating and extending to infinity at the left and right ends

Therefore;

The maximum y-value is y = 4, the minimum y-value is y = -2, therefore;

14. The graph of the function is an horizontal line, y = 1, extending to infinity to the left and right, therefore;

Therefore;

15. The given data are; {(-2, 6), (2, 0), (3, 0), (4, -1), (5, 3)}

The relationship is a function

16. The given data values are presented as follows;

{(-3, 2), (-2, 2), (1, 2), (-3, 1), (0, 3)}

The relationship is not a function

17. The given data are presented as follows;

[tex]\begin{array}{|c|cc|}\mathbf{x}&&\mathbf{y}\\-2&&-3\\-1&&0\\5&&5\\4&&3\\-1&&7\end{array}\right][/tex]

The x-value, -1, has two different outputs, 0, and 7, therefore, the data is not a function

The relationship is not a function

18. In the given data, the x-value, 6, has two y-values, 3 and 5, therefore, the given relationship is not a function

19. The given graph is a function because each vertical line drawn from the horizontal axis, crosses the data points only once

The relationship is a function

20. The given graph is not a function because each vertical line crosses the graph only once

The relationship is not a function

21. The graph of is a function because each vertical line drawn from the horizontal axis crosses the graph at one point only

The relationship is a function

22. The graph is not a function because it has several points on the side that is vertical to the y-axis

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Answer:

x²-11x+24

(x -8) * (x -3) =0

x = 8 and x =3

Step-by-step explanation: