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3 years ago

Factor the following expression using the GCF: 42pr – 3p. Please help!

Mathematics

1 answer:

REY [17]3 years ago

3 0

Answer:

3p(14r-1)

Step-by-step explanation:

Factor out by 3 since 42 and 3 are both divisible by 3: 3(14pr-p)

Since "p" can be factored out, we then have: 3p(14r-1)

So what we found out was that the GCF of 42pr-3p is 3p

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Find the GCF of 14a3b5c, 35a4c4, and 7a2bc2 The GCF is

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I think the answer is 70a^4b^5c^4.

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3 years ago

Find the? inverse, if it? exists, for the given matrix.<br><br> [4 3]<br><br> [3 6]

True [87]

Answer:

Therefore, the inverse of given matrix is

$=\begin{pmatrix}\frac{2}{5}&-\frac{1}{5}\\ -\frac{1}{5}&\frac{4}{15}\end{pmatrix}$

Step-by-step explanation:

The inverse of a square matrix $A$ is $A^{-1}$ such that

$A A^{-1}=I$ where I is the identity matrix.

Consider, $A = \left[\begin{array}{ccc}4&3\\3&6\end{array}\right]$

$\mathrm{Matrix\:can\:only\:be\:inverted\:if\:it\:is\:non-singular,\:that\:is:}$

$\det \begin{pmatrix}4&3 \\3&6\end{pmatrix}\ne 0$

$\mathrm{Find\:2x2\:matrix\:inverse\:according\:to\:the\:formula}:\quad \begin{pmatrix}a\:&\:b\:\\ c\:&\:d\:\end{pmatrix}^{-1}=\frac{1}{\det \begin{pmatrix}a\:&\:b\:\\ c\:&\:d\:\end{pmatrix}}\begin{pmatrix}d\:&\:-b\:\\ -c\:&\:a\:\end{pmatrix}$

$=\frac{1}{\det \begin{pmatrix}4&3\\ 3&6\end{pmatrix}}\begin{pmatrix}6&-3\\ -3&4\end{pmatrix}$

$\mathrm{Find\:the\:matrix\:determinant\:according\:to\:formula}:\quad \det \begin{pmatrix}a\:&\:b\:\\ c\:&\:d\:\end{pmatrix}\:=\:ad-bc$

$4\cdot \:6-3\cdot \:3=15$

$=\frac{1}{15}\begin{pmatrix}6&-3\\ -3&4\end{pmatrix}$

$=\begin{pmatrix}\frac{2}{5}&-\frac{1}{5}\\ -\frac{1}{5}&\frac{4}{15}\end{pmatrix}$

Therefore, the inverse of given matrix is

$=\begin{pmatrix}\frac{2}{5}&-\frac{1}{5}\\ -\frac{1}{5}&\frac{4}{15}\end{pmatrix}$

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3 years ago

What does the mean, median, mode mean?

Keith_Richards [23]

Mean: average of the numbers median: middle of the numbers mode: which number appears the most

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3 years ago

Read 2 more answers

Find the slope of a line perpendicular to 2x-y-16

Alekssandra [29.7K]

put the equation 2x - y = 16 in the form of y = mx + c

2x - y = 16

2x = 16 + y

y = 2x - 16

the slope of this line is 2. the slope of a line perpendicular to it would be the negative reciprocal of 2. in other words, it would multiply with 2 to give -1.

you can form this equation with that info

2x = -1

x = -1/2

you can flip and change the sign (numerator) of 2/1

2/1

= -1/2

6 0

3 years ago

1. If the length of a rectangle is 6 more than its width, and its perimeter is 48

Salsk061 [2.6K]

For this case we have that by definition, the perimeter of the rectangle is given by:

$P = 2w + 2L$

Where:

W: Is the width of the rectangle

L: is the length of the rectangle

According to the data we have:

$L = 6 + w\\P = 48$

Substituting:

$48 = 2w + 2 (6 + w)\\48 = 2w + 12 + 2w\\48 = 4w + 12\\48-12 = 4w\\36 = 4w\\w = \frac {36} {4}\\w = 9$

So, the width of the rectangle is 9 inches

$L = 6 + 9 = 15$

So, the length of the rectangle is 15 inches

Answer:

the width of the rectangle is 9 inches

the length of the rectangle is 15 inches

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3 years ago