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2 years ago

Completely factor the polynomial. 16x 2 - 25

Mathematics

1 answer:

Sunny_sXe [5.5K]2 years ago

5 0

Answer:

(4x-5)(4x+5)

Step-by-step explanation:

16x^2 - 25

Rewriting

(4x)^2 - 5^2

We recognize that this is the difference of squares

a^2 - b^2 = (a-b) (a+b)

(4x)^2 - 5^2 = (4x-5)(4x+5)

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Use the augmented matrix method to solve the following system of equations. Your answers may be given as decimals or fractions.

Alexandra [31]

Answer:

$x\ =\ \dfrac{21}{5}$

$y\ =\ \dfrac{3}{5}$

z = 2

Step-by-step explanation:

Given equations are

x - 2y - z = 2

x + 3y - 2z = 4

-x + 2y + 3z = 2

from the given equations the augmented matrix can be written as

$\left[\begin{array}{ccc}1&-2&-1:2\\1&3&-2:4\\-1&2&3:2\end{array}\right]$

$R_2=>R_2-R_1\ and\ R_3=>R_3+R_1$

$=\ \left[\begin{array}{ccc}1&-2&-1:2\\0&5&-1:2\\0&0&2:4\end{array}\right]$

$R_2=>\dfrac{R_2}{5}$

$=\ \left[\begin{array}{ccc}1&-2&-1:2\\0&1&\dfrac{-1}{5}:\dfrac{2}{5}\\0&0&2:4\end{array}\right]$

$R_1=>R_1+2.R_2$

$=\ \left[\begin{array}{ccc}1&0&-1-\dfrac{2}{5}:2+\dfrac{4}{5}\\\\0&1&\dfrac{-1}{5}:\dfrac{2}{5}\\\\0&0&2:4\end{array}\right]$

$=\ \left[\begin{array}{ccc}1&0&\dfrac{-7}{5}:\dfrac{14}{5}\\\\0&1&\dfrac{-1}{5}:\dfrac{2}{5}\\\\0&0&2:4\end{array}\right]$

$R_3=>\dfrac{R_3}{2}$

$=\ \left[\begin{array}{ccc}1&0&\dfrac{-7}{5}:\dfrac{14}{5}\\\\0&1&\dfrac{-1}{5}:\dfrac{2}{5}\\\\0&0&1:2\end{array}\right]$

$R_1=>R_1+\dfrac{7}{5}R_3\ and\ R_2+\dfrac{1}{5}R_3$

$=\ \left[\begin{array}{ccc}1&0&0:\dfrac{14}{5}+\dfrac{7}{5}\\\\0&1&0:\dfrac{2}{5}+\dfrac{1}{5}\\\\0&0&1:2\end{array}\right]$

So, from the above augmented matrix, we can write

$x\ =\ \dfrac{21}{5}$

$y\ =\ \dfrac{3}{5}$

z = 2

7 0

3 years ago

Which terms are like terms in the following expression?

Reil [10]

Answer:

9x and -4x

This is the answer

8 0

2 years ago

What is 3/5 of 7 kg ?

MAVERICK [17]

What is 3/5 of 7 kg ?

of = multiplication

3/5 × 7 = ?
0.6 × 7 =
4.2

3/5 of 7 kg is 4.2 kg.

3 0

3 years ago

Read 2 more answers

During summer vacation, Erin read, on average, 4 pages per night. Once she returned to school, she averaged 3 pages per night. W

alexandr1967 [171]

Answer:

25% decrease.

Step-by-step explanation:

3/4=75%

100%-75%=25% decrease.

6 0

2 years ago

Which symbol makes a true statement? –2.75 ? –3 A. = B. > C.

Iteru [2.4K]

<span>–2.75 > –3

answer is </span><span>B. ></span>

7 0

3 years ago