The equation to model Exponential Growth is: y=a(1+r)t y= total amount a= starting amount r= the growth rate as a decimal t= number of growth periods Question 4 A sample of bacteria cells in a petri dish increases by 50% every hour. A scientist starts with a sample of 30 bacteria cells. Write an equation that can be used to determine the number of cells after x hours.

Call the number : a

We have : [tex]a^{2} - 15 = 2a[/tex]
[tex]- > a^{2} - 2a = 15 - > a(a-2) = 15[/tex]

Now, we list all the numbers that can be multiplied to get 15 :

1 x 15 (and reverse)
3 x 5 (and reverse)

-1 x (-15) (reverse)
-3 x (-5) (a l s o r e v e r s e)

We substitute in :

If a = 1 -> a(a-2) = 1 x (-1) = -1 (not equal 15)
If a = 3 -> a(a-2) = 3 x 1 = 3 (not equal 15)
If a = -1 -> a(a-2) = -1 x (-3) = -3 (also not equal 15)
And if a = -3 -> a(a-2) = -3 x (-5) = 15 (satisfied)

So, the number is -3

Recheck : -3(squared) - 15 = 9 - 15 = -6
Twice of -3 = -6

[tex]========================================[/tex]

First of all, let the unknown number be z.

Then, "the square of z" means "z squared" which is the same as "z times z" or just z².

Now, "fifteen less than the square of z" means we subtract 15 from z²:

z²-15

Then, this equals twice the number, or 2 times z:

z²-15=2z

[tex]========================================[/tex]

:-)

well, we know she paid a total after tax of $68.37, we also know that each game had a tax of $1.29, so 3 games that'll be 3 * 1.29 = 3.87.

so if we take out the tax from 68.37, that'll be 68.37 - 3.87 = 65 bucks.

we know each game cost the same amount so 65 ÷ 3 ≈ 21.67 before tax.

Tiana bought 3 video games at a cost of $22.36 each, before tax. The total amount paid after tax was $68.37.

Given that,

Tiana bought 3 video games.

The cost of each video game was the same.

The tax on each video game was $1.29.

Tiana paid a total of $68.37 after tax.

To find the price of each video game before tax,

Start by subtracting the total tax from the total amount paid.

Tiana paid a total of $68.37 after tax and the tax on each video game was $1.29.

So, subtract the tax from the total amount to get the price before tax.

$68.37 - $1.29 = $67.08.

Since Tiana bought 3 video games,

Divide the total price before tax by 3 to find the price of each video game.

$67.08 ÷ 3 = $22.36.

Hence, the price of each video game before tax was $22.36.

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The logarithm value of log 1/2 462 to four decimal places is  –8.8517.

The logarithm is the mathematical inverse function to exponentiation.

The logarithm of a number x is the exponent to another fixed term.

It is given the log of 462 to a base of 1/2.

[tex]log_{0.5} 462 = \frac{log462}{log0.5}[/tex]

 = –8.8517

Therefore, the logarithm value of log 1/2 462 to four decimal places is  

–8.8517.

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Answer:

  8 11/20 ft³

Step-by-step explanation:

For dilated figures, the ratio of volumes is the cube of the ratio of corresponding linear dimensions.

  Vn/Vm = (Hn/Hm)³

  Vn = Vm(Hn/Hm)³ = (68 2/5 ft³)((2 3/8 ft)/(4 3/4 ft))³

  Vn = (342/5 ft³)((19/8)/(19/4))³ = (342/5 ft³)(1/2)³ = 342/40 ft³

  Vn = 8 11/20 ft³

The volume of Prism N is 8 11/20 ft³.

Answer:

The answer is 8 11/20.

Answer:

so how do i find the earea

Step-by-step explanation:

Answer:

[tex]\displaystyle [3, -2][/tex]

Explanation:

All you do is substitute three in for [tex]\displaystyle x[/tex]to get the y-coordinate of [tex]\displaystyle -2.[/tex]This means that these equations meet at the ordered pair of [tex]\displaystyle [3, -2].[/tex]

I am joyous to assist you at any time.

Answer:

Hope it helps u

Step-by-step explanation:

1.7

1.749

1.75

1.775

1.796

1.84

Answer:

the order would go 1.7, 1.749, 1.75, 1.775, 1.796, then 1.84.

Step-by-step explanation:

becuase if you ignore how long the numbers are, and focus on numerical order like 1, 2, 3, and apply that to this, this becomes the order.

Answer:

Step-by-step explanation:

Both data sets have a median of 3 and gave similar means, 3.19 and 2.57, so the answer should be B.

Answer:

Step-by-step explanation:

It is 1.645. My calculator is a little off though; see attached picture.

Answer: 9.06

Step-by-step explanation:

Do; 3.02+3.02+3.02

This adds up to 9.06

Pythagorean Theorem: a^2 + b^2 = c^2

a = 23 m

b = 11 m

c^2 = (23 m)^2 + (11 m)^2 = 650 m^2

c = sqrt(650 m^2) = 25.5 (rounded to nearest tenth)

Answer:

base: 1/4 * 12^2 * √3 = 36√3

each face: 1/2 * 12 * 8 = 48

Now finish it off

Step-by-step explanations:

Answer:

Step-by-step explanation:

A corresponds to angle P, so angle P measues 70 degrees.

Similarly, angle Q measures 60 degrees and angle R measures 50 degrees.

Answer: Nearly all thermal energy on Earth originates from the sun and radiates to the surface of our planet, traveling in the form of electromagnetic waves, such as visible light. Materials on Earth then absorb these waves to be used for energy or reflect them back into space. In an energy transformation, energy changes form.

Step-by-step explanation:

Answer:

yes they are

Step-by-step explanation:

Answer:The solution is in the attached file

Step-by-step explanation:

The wholesale price that the store paid for the Y-Box game is $150.

When the price of an item is marked up, it means that the price of the item was increased by a certain percentage. The good then becomes more expensive.

Wholesale price = selling price / ( 1 + percentage mark up)

$207 / (1+ 38)

$207 / (1.38) = $150

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Answer: Fish A: 9 inches ; Fish B: 6 inches

Step-by-step explanation:

This can be turned into a systems of equation, where x equals the length of fish A and y equals the length of fish B:

3x + 2y = 39 → -3x - 2y = -39

3x + 4y = 51 → 3x +4y = 51

Combine: 0 + 2y = 12 → y = 6 inches.

Plug back in: 3x + 2(6) = 39 → 3x = 27 → x = 9 inches.

Answer:

b

Step-by-step explanation:

i just think so correct me if im wrong

Answer:

I know the answer but you may select me as Brainliest

Number 2 is incorrect :

[tex]\frac{-25x^{3}+15x }{5x} = \frac{-25x^{3}}{5x} + \frac{15x}{5x} = -5x^{2} + 3[/tex]

Number 1 :

[tex](-5)^{3} . 13^{-2} . (-5) .13^{9} = -125 . \frac{1}{13^{2}} .(-5).13^{9} = 625 . \frac{13^{9}}{13^{2}} = 625 . 13^{7}[/tex] (i dont think we can bare calculate this cause it;s too big ;-;)

Answer: A=a+b

 2h=95  

2·13.5=675

Step-by-step explanation:

Answer:

D 57.5

Step-by-step explanation:

9.5 + 13.5 = 23

23 x 5 = 115

115 divided by 2 is 57.5

Answer:

I think 10

letter C.

Step-by-step explanation:

divide *2

Answer:

x = 3

Step-by-step explanation:

A only 1 solution

B

4(2x - 5) = 4 ( divide both sides by 4 )

2x - 5 = 1 ( add 5 to both sides )

2x = 6 ( divide both sides by 2 )

x = 3

Answer:

Step-by-step explanation:

Isolate it by the term of x from one side of the equation.

First, divide by 4 from both sides.

[tex]\sf{\dfrac{4\left(2x-5\right)}{4}=\dfrac{4}{4}}[/tex]

Then, solve.

4/4=1

Rewrite the problem down.

2x-5=1

Add by 5 from both sides.

[tex]\sf{2x-5+5=1+5}[/tex]

Solve.

1+5=6

2x=6

Divide by 2 from both sides.

2x/2=6/2

Solve.

Divide the numbers from left to right.

6/2=3

x=3

I hope this helps you! Let me know if my answer is wrong or not.

Answer:

5(7b+3c-2)

Step-by-step explanation:

Common factor of 5

35b/5= 7b
15c/5= 3c
-10/5= -2

Take the common factor and multiply it by the quotients
5(7b+3c-2)

Answer:

x=2

Step-by-step explanation:

2(x)+5 =9
2(2)+5=9

Answer: The number is 2

Creating an Equation:

     The underlined portion of the sentence becomes a part of our mathematical equation in the next line.

           2 times some number plus 5 equals 9

           2 times n plus 5 equals 9

           2n plus 5 equals 9

           2n + 5 equals 9

           2n + 5 = 9

Solving our Equation:

     I will take the equation we created, and isolate variable n to solve.

           2n + 5 = 9

           2n + 5 - 5 = 9 - 5

           2n = 4

           (2n ) / 2 = (4) / 2

           n = 2

This is closed under addition because the sum of the polynomial produces another polynomial.

A polynomial is an expression that involves the addition, subtraction and multiplication of variables.

Polynomials will be closed under an operation if the operation produces another polynomial.

(3x⁴ + 5x - 7) + (2x - (2x)² + 4x - 1) + [(-8x)⁻² - (3x)³ + 7]

= 3x⁴ - 27x³ - 4x² + 9x - 1 + (-8x)⁻²

This is closed under addition because the sum of the polynomial produces another polynomial.

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Using exponential function concepts, it is found that that the y-intercept and the horizontal asymptote are given by, respectively:

(0, 3); y = 4

It is modeled by:

[tex]y = ab^x + c[/tex].

In which:

In this problem, the equation is:

[tex]y = 4^x + 3[/tex].

Hence the horizontal asymptote is y = 3, and the y-intercept is y when x = 0, hence:

[tex](0,y) = (0, 4^0 + 3) = (0, 4)[/tex]

Which means that the first option is correct.

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Answer:

B. (0, 4) ; y = 3

Step-by-step explanation:

I took the exam for algebra 2

Answer:

[tex]\boxed{\text{Slope = 5}}[/tex]

[tex]\boxed{\text{y-intercept = 1}}[/tex]

Step-by-step explanation:

To find the slope of the line, we must pick any two points on the line. Using those two points, we will calculate the Rise and the Run. Then, we will use the slope formula (Rise/Run) to find the slope. The y-intercept is the intersection of the point on the y-axis.

[tex]\text{My chosen points: (0,1) and (1,6)}[/tex]

[tex]\text{Rise = 5; Run = 1}[/tex]

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[tex]\text{Slope}= \dfrac{\text{Rise}}{\text{Run}}[/tex]

➡ [tex]\bold{Slope = \frac{5}{1} = \underline{5}} \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ [\text{Rise = 5; Run = 1}][/tex]

[tex]\underline{........................................................................................................................}[/tex]

[tex]\text{Intersection on y-axis:} \ (0,1)[/tex]

➡ [tex]\text{y-intercept} \rightarrow (0,\bold{ 1}) \rightarrow \bold{\underline{{1}}}}[/tex]

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