A bacteria population increases exponentially at a rate of r% each day. After
32 days, the population has increased by 309%. Find the value of r.

Answer:

f(6)=2

f(2)=4

f(0)=7

f(5)=1.5

Step-by-step explanation:

Answer:

7 × 1 = 7  7 × 10 = 70  7 × 12 = 84

Step-by-step explanation:

Answer:

7.68912

Step-by-step explanation:

Answer:

6

Step-by-step explanation:

Because 17/12=6

Answer:

vertical....

Step-by-step explanation:

NawfSide 38 Baby

Answer:

B vertical compression

Step-by-step explanation:

edge :)

Answer:

21 quarters and 19 dimes

Step-by-step explanation:

Create a system of equations where q is the number of quarters and d is the number of dimes.

0.25q + 0.1d = 7.15

q + d = 40

Solve by elimination by multiplying the bottom equation by -0.25

0.25q + 0.1d = 7.15

-0.25q - 0.25d = -10

Add them together and solve for d:

-0.15d = -2.85

d = 19

Then, plug in 19 as d into the second equation to solve for q:

q + d = 40

q + 19 = 40

q = 21

So, there are 21 quarters and 19 dimes

Answer:

21 Quarters, 19 Dimes.

Step-by-step explanation:

21 x .25 = 5.25

19 x .10 = 1.90

5.25 + 1.90 = 7.15

Answer:

7 x 10^-5

Step-by-step explanation:

0.00001 is 1 x 10^-5 so multiply that by 7

Answer:

B. 7 x [tex]10^5[/tex] or not here

Step-by-step explanation:

if B. is [tex]10^5[/tex] then it is B. if it is 105 then it is not here

Hope this helped!!

Answer:

1st picture: (0,4)

The lines intersect at point (0,4).

2nd picture: Graph D

2x ≥ y - 1

2x - 5y ≤ 10

Set these inequalities up in standard form.

y ≤ 2x + 1

-5y ≤ 10 - 2x → y ≥ -2 + 2/5x → y ≥ 2/5x - 2

When you divide by a negative number, you switch the inequality sign.

Now you have:

y ≤ 2x + 1

y ≥ 2/5x - 2

Looking at the graphs, you first want to find the lines that intersect the y-axis at (0, 1) and (0, -2).

In this case, it is all of them.

Next, you would look at the shaded regions.

The first inequality says the values are less than or equal to. So you look for a shaded region below a line. The second inequality says the values are greater than or equal to. So you look for a shaded region above a line.

That would mean Graph B or D.

Then you look at the specific lines. You can see that the lower line is y ≥ 2/5x - 2. You need a shaded region above this line. You can see the above line is y ≤ 2x + 1. You need a shaded region below this line. That is Graph D.

Answer:

  A) (-4, 1)

  B) graph C

Step-by-step explanation:

A) The point that is in the doubly-shaded area is the solution. The point at (0, 4) is on the dashed line, so is NOT a solution. See the first attachment.

__

B) Look at the given inequalities. You are looking for two things:

Here, you can identify which line goes with which equation a couple of ways. One way is to look at the x- or y-intercept. To find the x-intercept, set y=0 and solve for x. For the first equation, that gives ...

  2x ≥ -1

  x ≥ -1/2

The steep line, the one that intersects the top of the graph, is the one that has an x-intercept at x = -1/2. You will also note that the solution x ≥ -1/2 means the shading is to the right of that line. (Only graphs C and D have shading to the right of that line.)

For determining which side of the line is shaded, it is useful to pick a variable term with a positive coefficient. For the second inequality, that is 2x. Considering only that term and the relationship in the inequality, we see that we have 2x ≤. This means values of x that are in the solution set are less than (or equal to) those on the boundary line. In other words, shading is to the left of the line with the shallow slope. This is true only for graphs A and C. We have already eliminated graph A, so the desired graph is C.

See the second attachment for what we're talking about here.

Answer:

The volume of the rectangular prism is 512 inches³

Step-by-step explanation:

Any cube has 6 square faces

Area of any square = L × L, where L is a length of each side

The volume of the cube = L × L × L

∵ The area of the top face of a cube = 16 inches²

→ Find which number multiply by itself = 16

∵ 16 = L × L

∵ 16 = 4 × 4

∴ L = 4 inches

Let us find the volume of 1 cube

∵ The volume of the cube = L × L × L

∵ L = 4 inches

∴ The volume of each cube = 4 × 4 × 4

∴ The volume of each cube = 64 inches³

∵ We will use 8 of this cube to make a rectangular prism

→ That means the volume of the rectangular prism is 8 times

   the volume of 1 cube

∴ The volume of the prism = 8 × volume of 1 cube

∵ The volume of each cube = 64 inches³

∴ The volume of the prism = 8 × 64

∴ The volume of the prism = 512 inches³

The volume of the rectangular prism is 512 inches³

Answer:

(fog)(x) = f(x)g(x) = x^2 * 1/x = x

Answer:

x = 15/8

Step-by-step explanation:

x/3 = 5/8

Using cross products

8x = 3*5

8x = 15

Divide each side by 8

8x/8 = 15/8

x = 15/8

X= 1 7/8

Step-by-step explanation:

Answer: i think it is 109.51

Step-by-step explanation:

Answer:

30.30

Step-by-step explanation:

solve on the calculator

Answer:

Time in hours (x) ==> distance in miles (y)

1 ==> 610

2 ==> 1,220

2.5 ==> 1,525

Note: constant of proportionality is same all through = 610

Step-by-step explanation:

Constant of proportionality = [tex] \frac{y}{x} = \frac{915}{1.5} = 610 [/tex]

To get the y-values (miles) for each given x-value (hours), multiply each x-value by the constant of proportionality, 610. Constant of proportionality is same all through.

Thus,

Time in hours (x) ==> distance in miles (y)

1 ==> 1*610 = 610

2 ==> 2*610 = 1,220

2.5 ==> 2.5*610 = 1,525

Answer:

0

Step-by-step explanation:

24z + 12 = 24z + 12

0z = 0

0

Answer:

many solutions or infinite solutions

Step-by-step explanation:

12(2z + 1) = 3(8z + 4)

ok simplify it

24z + 12 = 24z + 12

there's many solutions no matter what you do you'll end out in this

Answer:

90

Step-by-step explanation:

i did the math hope this helps you out

Answer:

$746.24

Step-by-step explanation:

3.2/100 = 0.032

5,830 X 4 = 23,320

23,320 X 0.032 = 746.24

Answer:

The domain is -oo < x < oo or (-oo,oo)

Step-by-step explanation:

Sometimes it helps if you draw this out on a number line or graph the equation! :)

Domain is how far x goes. As in this case x is infinite both ways.

======================================================

Work Shown:

B = amount Beth earned

P = amount Pam earned

amounts are in dollars

Pam earned $4 less than 3 times as much as Beth, so,

P = 3B-4

Together they earned $860, meaning

P+B = 860

Plug the first equation into the second. Solve for B

P+B = 860

3B-4+B = 860

4B-4 = 860

4B = 860+4

4B = 864

B = 864/4

B = 216

Use this to find P

P = 3B-4

P = 3*216-4

P = 648-4

P = 644

Beth earned $216 and Pam earned $644.

----------------------------------------

Check:

B+P = 860

216+644 = 860

860 = 860

First equation is true

P = 3B-4

644 = 3*216-4

644 = 644

Second equation is true

Both equations are true when (B,P) = (216,644) so the solutions have been confirmed.

Answer:

x = 7/3

Step-by-step explanation:

4x - 2 = x + 3 + 2

4x - 2 = x + 5

Rearranging the terms, we get,

4x - x = 5 + 2

3x = 7

x = 7/3

Hence, x = 7/3.

Answer:

Yes! if this was an option then this one would be correct

Step-by-step explanation:

In order to see if the ordered pair are a function you could graph them, or you could look at the x-values and see if there are any duplicates. in this case there are not.

High Hopes^^

Barry-

Answer:

C

Step-by-step explanation:

A, B, and D equal -4, while C equals 4.

A positive number times/divided by a negative number (or vice versa) is a negative number.  A negative number times/divided by a negative number (or vice versa) is a positive number.

Answer:   The equation of the line in slope-intercept form will be

y = (7/4)x + b

Since the line passes through the point (8,-2), plug in the values of the point into the equation to find b.

-2 = (7/4)(8) + b

-2 = 14 + b

-16 = b

The equation of the line is

y = (7/4)x - 16

In standard form,

-(7/4)x + y = -16

Multiply both sides of equation by -4.

7x - 4y = -64

Step-by-step explanation:   hope this helps :)

Answer:

A)

Less than $100

B)

[tex]B(21)=300[/tex]

For each day after Day 16, Ebony deposited $40.

Step-by-step explanation:

We know that on Day 16 she deposited $100 into her account.

And each day after Day 16, she made a deposit and each deposit were equal to each other.

So, let's answer each of the questions using the available information.

Part A)

Notice that the 5th Segment starts and ends with the 5th to the 6th Point. The 6th Point represents the 16th Day, where B(16)=100.

We want to know whether or not each of her deposits after Day 16 were less than, equal to, or greater than $100.

We can immediately conclude that it must be less than $100 because we can see that the slope of the 6th Segment is less steep than the slope of the 5th Segment.

Since it is less steep, this means that the unit rate of change from each day after Day 16 is less than the unit change on Day 16, which is $100/day.

So, the each of the deposits made after Day 16 is less than $100.

Part B)

We want to estimate B(21) in hundreds.

Remember that Ebony's maximum balance is $400.

Also, recall that the first point is $200.

B(21), the 7th Point, seems to be between the 2nd/3rd Point and the 1st Point.

So, it is reasonable to say that at the 21st Day, her account balance was (200+400)/2=600/2=$300.

We know that at Day 16, her account balance was $100. So, we have the point (16, 100).

And at Day 21, her account balance is $300. So, (21, 300).

Since each deposit after Day 16 is the same, it has a constant rate of change. So, we can use the slope formula:

[tex]m=\frac{y_2-y_1}{x_2-x_1}[/tex]

Let (16, 100) be (x₁, y₁) and let (21, 300) be (x₂, y₂). Substitute them into the slope formula. This yields:

[tex]m=\frac{300-100}{21-16}[/tex]

Subtract and divide. So:

[tex]m=\frac{\$200}{5\text{ days}}=\$40\text{/day}[/tex]

So, for each day after Day 16, Ebony deposited $40.

And we're done!

Answer:

425 miles

Step-by-step explanation:

65+.06m=48+.1m

65=48+.04m

17=.04m

425=m

Answer:

Since the points X , Y and Z are collinear:

For the diagram, you just have to draw a line and mark the end-points of the line as X and Z and mark the mid-point of the line as Y

Since we are given that XY = YZ,

We will replace with the provided values:

XY = YZ

4(x + 5) = 2(x + 11)

4x + 20 = 2x + 22

2x = 2

x = 1

Since x = 1 and XY = YZ,

We can say that:

XZ = XY + YZ

XZ = XY + XY   or       XZ = 2XY

Now, replacing the variables for the value of XZ

XZ = 2XY

XZ = 2(4x + 20)

XZ = 2(4 + 20)              (Since x = 1)

XZ = 48 units

Answer:

A

Step-by-step explanation:

Answer:

A

Step-by-step explanation: