Combine place values to subtract

Tamara and Clyde got different answers when dividing 2x4 + 7x3 – 18x2 + 11x – 2 by 2x2 – 3x + 1. Analyze their individual work.

Umnica [9.8K]

The statements and their individual answers are not provided in the question. However, please check the explanation given below for the equation.

Step-by-step explanation:

The equation given is $\frac{2x^{4} + 7x^{3} + 18x^{2} + 11x -2}{2x^{2} - 3x + 1 }$

Divide the leading term of the dividend by the leading term of the divisor: $\frac{2x^{4} }{2x^{2} } = x^{2}$

Multiply it by the divisor: $x^{2} ({2x^{2} -3x +1) = 2x^{4} - 3x^{3} + x^{2}$

Subtract the dividend from the obtained result: $(2x^{4} + 7x^{3} + 18x^{2} + 11x - 2) - (2x^{4} - 3x^{3} + x^{2} ) = (10x^{3} + 17x^{2} + 11x -2)$

Divide the leading term of the obtained remainder by the leading term of the divisor: $\frac{10x^{3}}{2x^{2} } = 5x$

Multiply it by the divisor: $5x (2x^{2} - 3x + 1) = 10x^{3} - 15x^{2} + 5x$

Subtract the remainder from the obtained result: $(10x^{3} + 17x^{2} + 11x -2) - (10x^{3} - 15x^{2} + 5x) = (32x^{2} + 6x - 2)$

Divide the leading term of the obtained remainder by the leading term of the divisor: $\frac{32x^{2} }{2x^{2} } = 16$

Multiply it by the divisor: $16 (2x^{2} - 3x +1) = 32x^{2} - 48x +16$

Subtract the remainder from the obtained result: $(32x^{2} + 6x - 2) - (32x^{2} - 48x +16) = 54x - 18$

Since the degree of the remainder is less than the degree of the divisor, then we are done.

Therefore, $\frac{2x^{4} + 7x^{3} + 18x^{2} + 11x -2}{2x^{2} - 3x + 1 } = (x^{2} + 5x +16 + \frac{54x - 18}{2x^{2} - 3x +1})$

7 0

3 years ago

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I need help which letter is it?

aniked [119]

Answer:

D. -2n - 6 = 9

Step-by-step explanation:

The first step you have to do is the distributive property in the given equation. So, you multiply n and 3 by -2. The resulting equation is -2n - 6 = 9.

7 0

3 years ago

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Carl has 3 1/2 cups of blueberries. He is storing them in containers that each hold 2/3 cup. How many containers can he fill? Fi

aivan3 [116]

Answer:

The total number of containers than can be filled = $5\frac{11}{50}$

Step-by-step explanation:

The amount of blueberries Carl has = 3 1/2 cups

Now, $3\frac{1}{2} = 3 + \frac{1}{2} = 3 + 0.5 = 3.5$

⇒The amount of blueberries Carl has = 3. 5 cups

Also,the amount of blueberries each container can store = 2/3 cups

Now, $\frac{2}{3} = 0.67$

⇒The amount of blueberries each container can store = 0.67 cups

So, \textrm{Total cpus that can be filled by blueberries} = \frac{\textrm{Toaal amount of blueberries to be stored}}{\textrm{Bluebeeries stored in 1 cup}}

= $\frac{3.5 cup}{0.67 cup} = 5.22$

Now, $5.22 = 5 + 0.22 = 5 + \frac{22}{100} = 5 + \frac{11}{50} = 5 \frac{11}{50}$

Hence, the total number of cups than cen be filled with the blue berries = 5 11/50

⇒ Blueberries can fill 5 full cups and 11/50th of the 6th cup.

3 0

4 years ago

A jar contains 100 gum balls. There are 12 blue gum balls, 15 green gum balls, 37 red gum balls, and 36 yellow gum balls. What i

MissTica

Yellow gumballs = 36
Total = 100
$\frac{36}{100} = \frac{9}{25}$
The probability of randomly selecting a yellow gumball is
$\frac{9}{25}$
Hope this helps.

7 0

4 years ago

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A grocery cart contains eggs for 89¢, bread for 95¢, fruit for $1.79, meat for $2.89, and vegetables for $1.29. What is the tota

NemiM [27]

Answer:

$7.81

Step-by-step explanation:

89¢ + 95¢ + $1.79 + $1.29 + $2.89

So numerically to add it the equation is...

0.89 + 0.95 + 1.79 + 2.89 + 1.29 = $7.81

3 0

4 years ago