Becky has one piece of paper. She cuts the paper in half and then has two pieces. She cuts these in half to get four pieces. The process continues. Which describes how many pieces she has at each step? (a) p(1) = 1; p(n) = 2p(n-1), for n is greater than or equal to 2 (b) p(1) = 1; p(n) = 1/2p(n-1), for n is greater than or equal to 2 (c) p(1) = 1; p(n) = p (n-1) +1, for n is greater than or equal to 2

To add fractions 1/9 and 5/6, find the least common denominator, convert each fraction to have this denominator, then add the numerators while keeping the denominator the same. The resulting fraction is 17/18.

The first thing you need to do to add fractions 1/9 and 5/6 is to find a common denominator. Since we can only add numerators with the same denominator, we must convert these fractions so that they have the same bottom number. The least common denominator (LCD) for 9 and 6 is 18.

So, we convert 1/9 by multiplying both its numerator and denominator by 2, to get 2/18. Similarly, we convert 5/6 by multiplying both its numerator and denominator by 3, to get 15/18. Now we can add the numerators:

2/18 + 15/18 = 17/18

Remember, we never add the denominators; they remain the same. After finding a common denominator and converting each fraction, we add the numerators together to get the final result.

Final answer:

To add 1/9 and 5/6, find a common denominator, convert each fraction to an equivalent fraction with this denominator, and then add the numerators. The least common multiple of 9 and 6 is 18, leading to 1/9 + 5/6 = 17/18 after conversion and addition.

Explanation:

The first thing you need to do to add the fractions 1/9 and 5/6 is to find a common denominator. A common denominator is necessary because you can only add fractions directly when they share the same denominator. To find a common denominator, you can often multiply the denominators together, but it's better to find the least common multiple (LCM) of the two denominators to simplify the process.

Once the common denominator is found, you convert each fraction to an equivalent fraction with this common denominator. Then, you add the numerators while keeping the denominator the same. The denominators are never added together. If the result is an improper fraction, you may have to simplify it or convert it to a mixed number.
Using our given fractions, the LCM of 9 and 6 is 18. Therefore, 1/9 can be converted to 2/18 and 5/6 to 15/18. Adding these gives 2/18 + 15/18 = 17/18.

Answer:

[tex]2 a^3 b^4 (a^3 - 11 a b + 8 b^3)[/tex]

Step-by-step explanation:

The given expression is

[tex]16a^3b^7 + 2a^6b^4 -22a^4b^5[/tex]

We need to find the factored form of the given expression.

In the given expression [tex]2 a^3 b^4[/tex] is the greatest common factor of all terms.

Taking GCF we get.

[tex]2 a^3 b^4 (8 b^3+a^3 - 11 a b)[/tex]

In can be written as

[tex]2 a^3 b^4 (a^3 - 11 a b + 8 b^3)[/tex]

This expression is the complete factored form of the given expression because [tex]a^3 - 11 a b + 8 b^3[/tex] can not be factored further.

Therefore, the factor form of given expression is [tex]2 a^3 b^4 (a^3 - 11 a b + 8 b^3)[/tex].

Answer:

The given graph is : f(x) = [tex]3^x[/tex]

The  graph g(x) is transformation of graph f(x).

The curve g(x) passes through (-2,2) and (-1,4).

Let (a,b) be any point on f(x).After translation  new curve g(x) is obtained which is parallel to line, y=1 or asymptode is ,y=1 or when y becomes 1 the graph becomes parallel to x axis.

g(x)= y-1=[tex]3^{x+2}[/tex]

g(x) = y = [tex]3^{x+2} +1[/tex] is the graph of translated curve.

The two graph is depicted below.

The values of x in both equations are 1/26 and 1/50, respectively

The equations are linear equations.

So, the variable can be calculated by simply dividing both sides by the coefficient

Using the above as a guide, we have the following computations:

Part A: (26)x = 1

Divide both sides by 26

x = 1/26

Part B: (50)x = 1

Divide both sides by 50

x = 1/50

Hence, the values of x in both equations are 1/26 and 1/50, respectively

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Answer:

Step-by-step explanation:

Part A: If (26)x = 1, what is the value of x? Explain your answer. 

The value of x is 0. Anything to the 0 power = 1. So I had to figure out what times 6 would = 0. Anything times 0 = 0. Hence x = 0 because 6 x 0 = 0 and 2^0 =1.

Part B: If (50)x = 1, what are the possible values of x? Explain your answer.

X could be any number because anything times 0 = 0. In order for the answer to be 1, I had to figure out how to keep 5 to the 0 power. Since anything times 0 = 0, it doesn't matter what number x is, because anything times 0 =0. 

Answer: 24 Units squared

Step-by-step explanation:

On simplification of inequality x + 10 > 2, we get x>-8.

The given question is related to algebra and inequalities.

To solve the inequality 'x + 10 > 2', we need to isolate x.

Subtract 10 from both sides: x + 10 - 10 > 2 - 10.

This simplifies to: x > -8.

The reflection of the point (-2,5) across the x-axis results in the point (-2,-5), as reflecting a point across the x-axis involves changing the sign of the y-coordinate while keeping the x-coordinate the same.

In mathematics, reflecting a point across the x-axis involves changing the sign of the y-coordinate while keeping the x-coordinate the same. To find the reflection of the point (-2,5) across the x-axis, we simply change the sign of the y-coordinate from positive 5 to negative 5, while keeping the x-coordinate -2 the same. Thus, the point (-2,5) reflects across the x-axis to (-2,-5).

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Answer: B) 5, −3, 1 over 2 are the zeros of f(x).

Step-by-step explanation:

Given function f(x)=[tex]2x^3-5x^2-28x+15[/tex]

If a is a zero of f(x) then f(a)=0

Let's check all the options

[tex]f(5)=2(5)^3-5(5)^2-28(5)+15\\=2(125)-5(25)-28(5)+15=250-125-140+15=0[/tex]

[tex]f(-3)=2(-3)^3-5(-3)^2-28(-3)+15\\=2(-27)-5(9)-28(-3)+15=-54-45+84+15=0[/tex]

[tex]f(\frac{-1}{2})=2\frac{-1}{2}()^3-5(\frac{-1}{2})^2-28(\frac{-1}{2})+15\\=2(\frac{-1}{8})-5(\frac{-1}{4})+14+15=\frac{-1}{4}-\frac{5}{4}+29=\frac{110}{4}=\frac{55}{2}\neq 0[/tex]

Therefore , 5 and -3 are zeroes of f(x).but -1/2 is not.

[tex]f(\frac{1}{2})=2\frac{1}{2}()^3-5(\frac{1}{2})^2-28(\frac{1}{2})+15\\=2(\frac{1}{8})-5(\frac{1}{4})-14+15=\frac{1}{4}-\frac{5}{4}-14+15=0[/tex]

⇒ 1/2 isthe third zero of f(x).

Here we got our three zeroes as 5,-3,1/2,rest other will not satisfy f(a)=0

Therefore B represents the zeroes of f(x).

Total time driving to and from beach: 12.3 hours; averaging 58 mph there, 65 mph returning home.

To find the total time Paul's family spent driving to and from the beach, we can calculate the time for each leg of the trip and then add them together.

1. Time taken for the trip to the beach:

[tex]\[ \text{Time}_1 = \frac{\text{Distance}_1}{\text{Speed}_1} \][/tex]

2. Time taken for the return trip:

[tex]\[ \text{Time}_2 = \frac{\text{Distance}_2}{\text{Speed}_2} \][/tex]

Given:

[tex]- Distance to the beach, \( \text{Distance}_1 = 377 \) miles\\- Speed to the beach, \( \text{Speed}_1 = 58 \) mph\\- Speed returning home, \( \text{Speed}_2 = 65 \) mph[/tex]

Let's calculate:

[tex]1. \[ \text{Time}_1 = \frac{377}{58} \][/tex]

[tex]2. \[ \text{Time}_2 = \frac{377}{65} \][/tex]

Now, let's compute:

[tex]\[ \text{Time}_1 = \frac{377}{58} \approx 6.5 \text{ hours} \]\[ \text{Time}_2 = \frac{377}{65} \approx 5.8 \text{ hours} \][/tex]

Finally, to find the total time spent driving to and from the beach, we add these times:

[tex]\[ \text{Total time} = \text{Time}_1 + \text{Time}_2 \]\[ \text{Total time} \approx 6.5 + 5.8 \]\[ \text{Total time} \approx 12.3 \text{ hours} \][/tex]

So, Paul's family spent approximately 12.3 hours driving to and from the beach.

Answer:

  (D)  3x +6 ≤ 3

Step-by-step explanation:

Since there is a solid dot at x=-1, the inequality must include "≤", which eliminates the first two choices.

You can check x=-1 in each of the remaining choices to see which results in the "equal to" case.

  2(-1) +5 ≤ 1 . . . . . choice C

  3 ≤ 1 . . . . . . . . . . .not true

__

  3(-1) +6 ≤ 3 . . . . . choice D

  3 ≤ 3 . . . . . . . . . . true; the "equal to" case we're looking for

to change the temperature from -13 on Saturday to -4 on Sunday, you would need to add 9 degrees ( -13 + 9 = -4 )

 so you need the equation that would also = 9

-4 + 13 = 9

-4 - (-13) = 9

-4 -13 = -17

4 +(-13)= -9

 there are 2 equations that equal the correct change in temperature, but since both temperatures are negative ( -13 & -4)

 the correct equation would also contain 2 negative numbers

 so correct equation should be: -4-(-13) =

The exact perimeter of pentagon JKLMN could not be calculated without the lengths of its sides. One would add the lengths of all sides for a polygon, while for a rectangle, such as a town square, the perimeter formula is twice the sum of its length and width.

To calculate the perimeter of a pentagon, you need to add the lengths of all its sides. Unfortunately, the specific lengths of the sides of pentagon JKLMN were not provided, so I cannot calculate the exact perimeter. However, I can explain how you would find the perimeter if the side lengths were known. If you have the coordinates of the vertices, you can use the distance formula to find the lengths of the sides between each pair of vertices. Then you would add those lengths together to find the total perimeter. On the other hand, if the pentagon is regular (all sides and angles are equal), you would just multiply the length of one side by 5.

You also provided an example of calculating the perimeter of a rectangle which has a formula of perimeter = 2(length + width). If we use this formula with the given dimensions of the town square, the perimeter would be 2(39.2 meters + 17.5 meters) = 2(56.7 meters) = 113.4 meters.

To find the approximate perimeter of pentagon JKLMN, we add up the given lengths of its sides. Using the information provided, we can estimate that the approximate perimeter of the pentagon is 840,000 km.

The perimeter of a polygon is the sum of the lengths of its sides. To find the approximate perimeter of pentagon JKLMN, we need to know the lengths of all its sides.

Since we are not given the lengths of the sides directly, it is not possible to compute the exact perimeter. However, we can use the information provided to find the approximate perimeter.

Using the given information, we know that the perimeter of the pentagon is approximately equal to 200,000 km + 100,000 km + 300,000 km + 240,000 km. Evaluating this expression gives us an approximate perimeter of 840,000 km.

Therefore, the correct answer is D. 40.62 units.

The solution of the equation 14 = 2c − 6 + 3c will be 4.

The distribution of weights to the variables involved that establishes the equilibrium in the calculation is referred to as a result.

Making anything easier to accomplish or comprehend, as well as making it less difficult, is the definition of simplification.

The equation is given below.

14 = 2c − 6 + 3c

Simplify the equation, then the value of the variable c will be

14 = 2c − 6 + 3c

20 = 5c

c = 20 / 5

c = 4

The solution of the equation 14 = 2c − 6 + 3c will be 4.

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Three of the numbers are correctly written in scientific notation. For the two that are not, we rewrite them correctly.

A. 4.51x10-2: This number is correctly written in scientific notation.

B. 0.789x105: This number is not correctly written in scientific notation. To rewrite it correctly, we move the decimal point to the right so that there is only one non-zero digit to the left of the decimal point. This gives us 7.89x104.

C. 31.5x102: This number is correctly written in scientific notation.

D. 3.008x10-8: This number is not correctly written in scientific notation. To rewrite it correctly, we move the decimal point to the left so that there is only one non-zero digit to the left of the decimal point. This gives us 3.008x10-9.

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Answer:

1. B. (8 x 20) - (8 x 1)

2. D. (2 x 9) + (2 x 3)

3. A. (7 x 50) - (7 x 2) = 350 - 14 = 336

4. C. (9 x 80) + (9 x 1) = 729