Need help! Pythagorean Theorem!

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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ANSWER ASAP PLEASE!! OTHER ANSWER CHOICES ARE 5/12 and 7/12.BRAKE DOWN!!

Yuri [45]

Answer:

A=1/12

Step-by-step explanation:

3/4-2/3=3*3/4*3-2*4/3*4=9/12-8/12=1/12

6 0

4 years ago

There are 200 employees in your company. Fifty of them do not have company insurance what percentage of the employees do not hav

const2013 [10]

25% of the workers don't have company health insurance

6 0

3 years ago

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A rectangular piece of plywood has a diagonal that measures three times the width. The length of the plywood is three feet more

Karolina [17]

Answer:

The length of diagonal is 4.922 feet.

Step-by-step explanation:

Let the width be = w

Let the diagonal be = d

Let the length be = l

Given is that the diagonal measures three times the width, this gives: $d=3w$

Also given is the length of the plywood is three feet more than the width. This is : $l=x+3$

Now, in terms of x we get:

Width = x

Length = (x+3)

Length of Diagonal = 3x

Now applying Pythagorean Theorem

$a^{2}+b^{2}=c^{2}$

$x^{2}+(x+3)^{2}=(3x)^{2}$

$x^{2}+x^{2}+6x+9=9x^{2}$

Solving this we get,

$-7x^{2}+6x+9=0$

We will use quadratic formula to solve this and get the answer,

x = 3/7 +/- (12√2) / -14

x = 1.64075 or x = -0.783612(neglect this negative value)

So, x = 1.64075 feet

Now length of diagonal is 3x = 3*1.64075 = 4.922 feet

So, length of diagonal is 4.922 feet.

3 0

3 years ago

Complete the statements.

miss Akunina [59]

Is there supposed to be a picture I’m sorry I don’t see it

5 0

3 years ago

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