A bacterium in a petri dish multiplies by a factor of 31 every day. On day O,
there is 1 bacterium; on day 1, there are 31 bacteria; on day 2, there are
bacteria; on day 3, there are
bacteria, and so on.
What logarithmic equation can be used to find the number of days it takes for
a colony of 1 bacteria to develop?

Let's evaluate explicitly [tex]f(x+k)[/tex]:

[tex]f(x)=2x+4\iff f(x+k)=2(x+k)+4=2x+2k+4[/tex]

If this must equal [tex]2x+22[/tex], we have

[tex]2x+2k+4=2x+22 \iff 2k+4=22 \iff 2k=18 \iff k=9[/tex]

Answer:

For what values of does the equation (2 + 1)^2 + 2 = 10 − 6 have two real and equal roots?

Step-by-step explanation:

For what values of does the equation (2 + 1)^2 + 2 = 10 − 6 have two real and equal roots?

Answer:

18

Step-by-step explanation:

3/4 divided by 1/4 equals 3

3 times 6 equals 18

Answer:

She forgot to find the y intercept add it in the equation

y = .5x-6

Step-by-step explanation:

First we need to find the slope

m = (y2-y1)/(x2-x1)

   = (-5 - -7.5)/ (2 - -3)

   =(-5 +7.5)/( 2+3)

   = 2.5/5

   = 1/2

Substitute into the slope intercept form of the equation

y= mx+b

y= .5x +b

We need to determine b by substituting a point into the equation

-5 = .5(2) +b

-5 = 1+b

Subtract 1 from each side

-5-1 = 1-1+b

-6 = b

y = .5x-6

Answer:

She forgot the y-intercept

y = 0.5x - 6

Step-by-step explanation:

y = 0.5x + c

-5 = 0.5(2) + c

c = -6

Correct equation:

y = 0.5x - 6

Answer:

None are correct

Step-by-step explanation:

Because triangle ABC is the original as it says in the problem"Triangle ABC TO Triangle DEF" which means the answer should be Triangle DEF is 6 times larger than triangle ABC.

Answer:

Step-by-step explanation:

If the scale factor of the larger prims to the smaller prism is 3, that means each side is triple.

We know the a triangular prims has a volume defined by

[tex]V_{small} =\frac{b \times h_{1} }{2} \times h_{2}[/tex]

If we take that formula as the smaller prism, then the larer prism has a volum of

[tex]V_{large} =\frac{2b \times 2h_{1} }{2} \times 2h_{2}=8(\frac{b \times h_{1} \times h_{2} }{2} )[/tex]

If we compare, we can deduct that

[tex]V_{large}=8V_{small}[/tex]

In words, the volume of the larger prims is eight times greater than the smaller prism.

Answer:

Answer Choice 3

Step-by-step explanation:

on edge 2020

Answer:

I agree with Jose that the sum of the probability that a randomly selected pen will not be black and the probability that the pen will not be red is 1.

Step-by-step explanation:

If we sum the probability of not black and probability of not red, we will get 1.

The probability of not black means probability of red i.e 50/450

The probability of not red means probability of black i.e 400/450.

When we add the probability, we get 1.

50/450 + 400/450 = 450/450 = 1

Invariably, the statement is same as finding probability of black and probability of red; just that the value are interchanged.

Answer:

volume of tank = 2000 cm³

Step-by-step explanation:

given data

tank long = 25 cm

tank wide = 10 cm

tank deep = 8 cm

to find out

how many liters of water

solution

we get here volume of this tank that is express as

volume of tank = tank long × wide × deep    .......................1

put here value and we will get

volume of tank = 25 × 10 × 8

volume of tank = 2000 cm³

Answer:

M=(-8, -3.5)

Step-by-step explanation:

The midpoint formula for two points is [tex](\frac{x_1+x_2}{2},\frac{y_1+y_2}{2})[/tex]. Plugging in our numbers, you get [tex](\frac{-9-7}{2},\frac{-10+3}{2})=(-8, -3.5)[/tex]. Hope this helps!

Answer:

16 adults

Step-by-step explanation:

There were 3 times more children than adults at the park.

That means that dividing the number of children by 3 would give us the number of adults.

48 / 3 = 16

Answer:

16:48 Therefore, 16 adults

Step-by-step explanation:

Answer:

  47 seconds

Step-by-step explanation:

It takes 37 seconds to scan 37 items at the rate of 1 second per item. It takes an additional 10 seconds to process the payment. Then the total time is ...

  37 +10 = 47 . . . seconds

Answer:

      1.reflection

     2. translation

     3. rotation

     4. rotation

      5. reflection

Step-by-step explanation:

Answer:

The exponential form is 49 to the power of one-half equals 7 ⇒ 4th answer

Step-by-step explanation:

The exponential equation of  [tex]log_{b}(m)=n[/tex]  is [tex]b^{n}=m[/tex] , where b is the base, n is the exponent of b and m is the value of [tex]b^{n}[/tex]

Ex: If  [tex]log_{3}(81)=4[/tex] , that means b = 3 , n = 4 and m = 81, then its exponential form is [tex]3^{4}=81[/tex]

Now let us solve the question

∵ The equation is  [tex]log_{49}(7)=\frac{1}{2}[/tex]

∴ The base is 49

∴ The exponent is [tex]\frac{1}{2}[/tex]

∴ The answer is 7

- Substitute them in the form of the exponential form

∴ The exponential form is [tex](49)^{\frac{1}{2}}=7[/tex]

The exponential form is 49 to the power of one-half equals 7

The given equation is log49(7) = 1/2. To convert it to exponential form, we can write it as 49^(1/2) = 7.

The given equation is:

log49(7) = 1/2

To convert this equation to exponential form, we need to remember that logarithms and exponentials are inverse functions. Therefore, we can write the equation as:

491/2 = 7

Hence, the exponential form of the given equation is 49 raised to the power of 1/2 equals 7.

Answer:

C. 24

Step-by-step explanation:

4!=24

Apply factorial rule: n! = 1 * 2 * 3 * ... * n

4! = 1 *2 * 3 * 4

1 *2 * 3 * 4 = 24

4! = 1 *2 * 3 * 4 = 24

4!=24

Answer:

1. 4

2.  6.4

3. 10.0828313253

Explanation:

2.

15/12=1.25

8/1.25=6.4

3. ill write explanation for 3 later im  occupied those are the correct answers

problably they want you to round to nearest tenth

Answer:

13 miles

Step-by-step explanation:

This problem can be represented as a right angle triangle (shown in the diagram).

The distance of the boat from the dock is the hypotenuse of the triangle, hence, we need to find the hypotenuse of the triangle. To do this, we apply Pythagoras theorem:

[tex]hyp^2 = opp^2 + adj^2[/tex]

where opp = side opposite angle of consideration = 12 miles

adj = side adjacent angle of consideration = 5 miles

Hence:

[tex]hyp^2 = 12^2 + 5^2\\\\\\hyp^2 = 144 + 25 = 169\\\\\\hyp = \sqrt{169}\\ \\\\hyp = 13 miles[/tex]

The boat is therefore, 13 miles from the dock.

Final answer:

To find the distance of the boat from the dock after traveling due south and then due west, apply the Pythagorean theorem to calculate the hypotenuse of a right-angled triangle, resulting in 13 miles.

Explanation:

The question involves finding the distance of the boat from the dock after it has traveled in a two-segment path: 5 miles due south and 12 miles due west. This problem can be solved by using the Pythagorean theorem, which is applied in the context of a right-angled triangle formed by the southward and westward paths of the boat as its legs.

Steps to Calculate Distance:

Represent the boat's journey as a right-angled triangle with the southward and westward paths forming the two legs.

Calculate the hypotenuse of the triangle, which represents the straight-line distance between the boat and the dock.

Use the Pythagorean theorem (a² + b² = c²) to find the distance.

For the distances given (5 miles and 12 miles), the calculation would be [tex]\sqrt{5² + 12²}[/tex]= [tex]\sqrt{169}[/tex] = 13  

Therefore, the boat is 13 miles away from the dock after traveling 5 miles due south and 12 miles due west.

Answer:

48π ≈ 150.72

Step-by-step explanation:

The volume formula is V = 1/3Bh

The base area formula would be πr²

Since 8 is the diameter, 4 would be the radius

Now plug that in, π (4²) = 16π

Now multiply that by the height, 9, and get 144π

Multiply again by 1/3 and you'll get 48π

Answer:

150.72 ft^3

Step-by-step explanation:

The volume of a cone is

V = 1/3 pi r^2 h

We need to get the radius

r = d/2 = 8/2 =4

V = 1/3 (3.14) (4)^2 *9

V = 1/3 (3.14) 16 *9

V =150.72

Rounding to the nearest hundredth

V = 150.72

Answer:

B. 1

Step-by-step explanation:

3x-1=2

3x=3

x=1

Answer:

24

Step-by-step explanation:

Answer:

the answer is 16mph

Step-by-step explanation:

Answer:

16 miles per hour

Step-by-step explanation:

Answer:

4x² - 9y²

General Formulas and Concepts:

Pre-Algebra

Algebra I

Step-by-step explanation:

Step 1: Define

Set up expression

12x² + 3xy - 5y² - (8x² + 3xy + 4y²)

Step 2: Simplify

Answer:

-3

Step-by-step explanation:

The equation is written in slope intercept form

y = mx+b  where m is the slope and b is the y intercept

y = 4x-3

4 is the slope and -3 is the y intercept

Answer:

net

Step-by-step explanation:

A two-dimensional shape has only two measurements and a three-dimensional shape has three measurements.

For example square, the triangle are two-dimensional shapes and cube, prism are three-dimensional shapes.

A 2 D image of a 3 D figure is most commonly know as a net.

A net is a two-dimensional pattern that can be folded to form the three-dimensional figure.

When you cut out the "net", fold it and stick it together you get a three-dimensional shape.

Answer:

30 minutes

Step-by-step explanation:

Just look at the minutes only. Since you need 4 o'clock to 4:30, its only 30 minutes.

Answer:

30 minutes

Step-by-step explanation:

All you have to do is subtract 4:30 and 4:00 and get 30 minutes.

Answer:

34.54 inches.

Step-by-step explanation:

The formula for the circumference of the circle is given as [tex]C=\pi d[/tex], where [tex]\pi[/tex] is rounded to 3.14 and d is the diameter of the circle, 11 inches. Simply plug these values into the equation for the circumference to get your answer:

[tex]C=\pi d\\C=(3.14)*(11)[/tex]

C = 34.54 inches

Answer:

34.54 inches

Step-by-step explanation:

C=πd

d=11

C = 11 * 3.14

C = 34.54 inches

Answer:

General form of the equation of the line:  y-2 = 0

Step-by-step explanation:

The general form of the equation is given by:

y = mx +b where m is the slope and b is the y-intercept.

y-intercepts of the line is the value of y at the point where the line crosses the y-axis(i.e x= 0)

From the given figure;

we can see that the line crosses the y-axis at y =2  and also here the slope is , m= 0

therefore, by definition of y-intercepts

y-intercept (b) = 2

Therefore, the equation of line as shoen in figure is:

y = (0)x + 2

or

y = 2

y-2 = 0

Therefore, the general form of the equation line as shown in the figure is:

y-2 =0

Answer:

23 units²

Step-by-step explanation:

height = 2

length = 4

width = 2.5

Formula = 2(wl + lh + hw) ⇒ 2 [(2.5 × 4) + (4 × 2) + (2 ×2.5)] = 23 units²

Hope this helps.

#FORTHEPUPPIES

The volume of water in the tank, with a length of 4 feet, width of 1.5 feet, and filled to within 4 inches of the top, is approximately 42.667 cubic feet.

To find the volume of water in the tank, we need to calculate the volume of the portion of the tank that is filled with water.

1. First, let's convert all the measurements to the same unit. Since the height of the tank is given in feet and the width is given in inches, let's convert the width to feet.

Given:

- Length = 4 feet

- Width = 18 inches

- Height = 3 feet

- Water level = 4 inches from the top

Converting width to feet:

1 foot = 12 inches

So, 18 inches = 18/12 = 1.5 feet

Now, we have:

- Length = 4 feet

- Width = 1.5 feet

- Height = 3 feet

- Water level = 4 inches from the top

2. Calculate the height of the water in the tank:

Total height of the tank = Height of tank - Distance from the top to the water level

Total height = 3 feet - 4 inches

Total height = 3 feet - (4/12) feet

Total height = 3 feet - 0.3333 feet

Total height = 2.6667 feet

3. Calculate the volume of water using the formula for the volume of a rectangular prism:

Volume = Length × Width × Height

Volume = 4 feet × 1.5 feet × 2.6667 feet

Volume ≈ 16 feet³ × 2.6667

Volume ≈ 42.667 feet³

So, the volume of water in the tank is approximately 42.667 cubic feet.

Answer:

Having a deadbolt lock installed on the exteriors of a building would affect the price of Insurance.

The principles of insurance require that the Insurance Policy Holder or Insured should act as if uninsured. This means that even with an Insurance Policy in place, the owner of this house is required to ensure that all reasonable steps have been taken to secure the house.

This may include having a properly installed lock in place.

The price or insurance premium of a homeowner may go up very significantly if there is no lock installed, that is if the risk is accepted for coverage by the insurance company.

It (the premium that is) may or may not come down if there is a deadbolt lock in place. It all depends on the extent to which the deadbolt lock has reduced the exposure of the Insurance company. Where the deadbolt lock has very significantly reduced the risk, the policyholder may press for a reduction in insurance premium.

In most Homeowners Insurance policy, for a claim concerning theft of insured home items, the policyholder has to provide evidence of forceful entry or exit, showing that the house was reasonably secured to warrant a breaking in or breakout.

Cheers!