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3 years ago

3. Simplify the expression (x3 - 5x2 + 7x - 12) = (x – 4) using long division. Show your work.

Mathematics

1 answer:

ankoles [38]3 years ago

3 0

Answer:

x^2-x+3

Step-by-step explanation:

(x^3-5x^2+7x-12)÷(x-4)

x^3−5x^2+7x−12

Factors of 12,

1,2,3,4,6,12

Substitute 4 into x. Since the result is 0, x-4 is a factor..

4^3−5×4^2+7×4−12=0

x-4

x^2 -x 3

x-4 | x^3 -5x^2 7x -12

x^3 -4x

-x^2 7x -12

-x^2 4x

3x -12

3x -12

x^2−x+3

(x^2−x+3)(x−4)

x−4

(x^2−x+3)

Answer = x^2-x+3

Hopes this helps

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The total cost for dinner last night was 43.57. Tax is 9% and I want to leave a 20% tip. What will my final total be including t

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Answer: $56.20

Step-by-step explanation:

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3 years ago

If the equation is an identity or if it has no solution, write identity or no solution.

Ksenya-84 [330]

Answer:

7n + 5 − 9n = 8 − 2n − 3 = true

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Step-by-step explanation:

Left-hand side:

Simplify the following:

7 n - 9 n + 5

Grouping like terms, 7 n - 9 n + 5 = 5 + (7 n - 9 n):

5 + (7 n - 9 n)

7 n - 9 n = -2 n:

Answer: -2 n + 5

____________________________

Right-hand side:

Simplify the following:

-2 n - 3 + 8

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(8 - 3) - 2 n

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4 years ago

Write each ratio statement as a fraction and reduce to lowest terms if possible:

qwelly [4]

The answers are:

18 to 24 = $\frac{18}{24} = \frac{3}{4}$

5 to 15 = $\frac{5}{15} = \frac{1}{3}$

14:42 = $\frac{14}{42} = \frac{1}{3}$

15 cents to 18 cents = $\frac{15}{18} = \frac{5}{6}$

Explanation:

To write a fraction using a ratio, simply use the first number as the numerator (top number), in this case, the numbers 18, 5, 14, and 15, and the second or biggest number as a denominator (bottom number), in this case, the numbers 24, 15, 42 and 18. This means the fractions are $\frac{18}{24}$ , $\frac{5}{15}$ , $\frac{14}{42}$ , and $\frac{15}{18}$ .

The second step is to reduce or simplify the fractions, which means the numbers in a fraction are divided by the same factor (a number that divides another without a remainder). Additionally, to do this, it is important to reduce the fraction to its minimum.

$\frac{18}{24}$ divide this by 6, which is equivalent to $\frac{3}{4}$

$\frac{5}{15}$ divide this by 5, which is equivalent to $\frac{1}{3}$

$\frac{14}{42}$ divide this by 14. which is equivalent to $\frac{1}{3}$

$\frac{15}{18}$ divide this by 3, which is equivalent to $\frac{5}{6}$

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