Factor completely 16a^3b^7 + 2a^6b^4 − 22a^4b^5.

It's a horizontal line y = -9.

Look at the picture.

Answer: B.

The equation representing the total number of books, including those on three shelves and in a stack, is 84 + x = 85. By solving this equation, we find that there is 1 book in the stack.

The question involves formulating an equation to represent the total number of books given the number of books on shelves and in a stack. Since there are three shelves each with 28 books, we first calculate the total number of books on the shelves. Then, we let x represent the number of books in the stack. The equation that represents the total number of books is:

3 shelves × 28 books per shelf + x books in the stack = 85 books total

This simplifies to:

84 + x = 85

To solve for x, we subtract 84 from both sides:

x = 85 - 84

Thus, x = 1, meaning there is 1 book in the stack.

In the 2008 election, the fractions of 'blue' and 'red' states when expressed in lowest terms were 14/25 and 11/25 respectively. In decimal form, these values are 0.56 and 0.44.

When solving fractions in mathematics, there are straightforward steps to follow. In the context of the 2008 election with the “red” and “blue” states, this means calculating the fraction of each in relation to the total number of states which is 50 in the US. The total number of red states was 22 and the total number of blue states was 28.

To express this as fractions we utilize the simple fraction formula of Part/Whole. For the blue states, the fraction becomes 28/50. To bring this to its lowest terms divide both the numerator and the denominator by their greatest common divisor which in this case is 2, so the fraction becomes 14/25.

Similarly, for the red states, we use the fraction formula where the red states are the part (22) and the whole is all the states (50). This gives a fraction of 22/50 which simplifies to 11/25 when reduced to lowest terms.

When these fractions are expressed as decimals, 14/25 equals to 0.56 while 11/25 equals to 0.44.

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Nora should choose Option 1 because it will take her 4 nights to finish instead of 25 nights with Option 2.

Let's break down Nora's situation step by step:

1. Calculate the total number of pages in the book:

  Since Nora has already read thirty percent of the book, we can find the total number of pages by dividing the portion she read by 30% (or 0.30). Let's denote the total number of pages as ( P ).

[tex]\[ P = \frac{{\text{portion Nora read}}}{{\text{percentage read}}} = \frac{{\text{portion Nora read}}}{{0.30}} \][/tex]

2. Calculate the portion of the book Nora has already read:

  If Nora has already read thirty percent of the book, then she has already read [tex]\( 0.30 \times P \)[/tex] pages.

3. Calculate the number of pages Nora has remaining:

  Subtract the pages Nora has already read from the total number of pages in the book.

[tex]\[ \text{Pages remaining} = P - (0.30 \times P) = P(1 - 0.30) = 0.70P \][/tex]

4. Option 1: Read 25% of the remaining pages each night:

  Nora's plan is to read 25% of the remaining pages each night. Since she has (0.70P) pages remaining, she will read [tex]\( 0.25 \times 0.70P \)[/tex] pages each night.

5. Option 2: Read 28 pages each night:

  Nora's other option is to read 28 pages each night.

6. Compare the two options:

  To determine which option Nora should choose, we compare the number of nights it will take her to finish each option.

  - With Option 1, the number of nights Nora will need to finish the book is [tex]\( \frac{{0.70P}}{{0.25 \times 0.70P}} \).[/tex]

  - With Option 2, the number of nights Nora will need to finish the book is [tex]\( \frac{{0.70P}}{{28}} \).[/tex]

7. Choose the more efficient option:

  Nora should choose the option that requires fewer nights to finish the book.

Let's summarize the steps:

1. Calculate the total number of pages in the book.

2. Determine the portion of the book Nora has already read.

3. Calculate the number of pages Nora has remaining.

4. Calculate the number of pages Nora will read each night for Option 1.

5. Compare the number of nights needed for each option.

6. Choose the option that requires fewer nights to finish the book.

This process will help Nora decide which option is more efficient for her to finish reading the book.

Let's denote:

- Total number of pages in the book as ( P ).

- Number of pages Nora has already read as ( 0.30P ).

- Number of pages Nora has remaining as ( 0.70P ).

With Option 1, Nora will read [tex]\( 0.25 \times 0.70P = 0.175P \)[/tex] pages each night.

To find the number of nights needed to finish with Option 1:

[tex]\[ \text{Number of nights with Option 1} = \frac{{0.70P}}{{0.175P}} = 4 \][/tex]

With Option 2, Nora will read 28 pages each night.

To find the number of nights needed to finish with Option 2:

[tex]\[ \text{Number of nights with Option 2} = \frac{{0.70P}}{{28}} = 25 \][/tex]

Nora should choose Option 1 because it will take her 4 nights to finish instead of 25 nights with Option 2.

Answer: 49, 64, and 81

Step-by-step explanation: To find the next three terms in this pattern, begin by studying the pattern.

Notice that the difference between 1 and 4 is positive 3, the difference between 4 and 9 is positive 5, the difference between 9 and 16 is positive 7, the difference between 16 and 25 is positive 9, and the difference between 25 and 36 is positive 11.

Since the differences are increasing by 2 each time, we can find the next term in the pattern by adding 36 + 13 to get 49. Next, we will add 49 + 15 to get 64. Then, we will add 64 + 17 to get 81.

Thus, the next three terms in the pattern are 49, 64, and 81.

she will need to earn $1300

( subtract what she already has from 1300)