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3 years ago

Explain how I would use Distributive Property (GCF) to factor the following expression: 4m + 16

Mathematics

1 answer:

taurus [48]3 years ago

6 0

Answer:

4(m+4)

Step-by-step explanation:

4m+16

Rewriting

4*m + 4*4

Factor out 4

4(m+4)

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Complete the identity.<br> 1) sec^4 x + sec^2 x tan^2 x - 2 tan^4 x = ?

Alecsey [184]

Answer:

See Explanation

Step-by-step explanation:

<em>Question like this are better answered if there are list of options; However, I'll simplify as far as the expression can be simplified</em>

Given

$sec^4 x + sec^2 x tan^2 x - 2 tan^4 x$

Required

Simplify

$(sec^2 x)^2 + sec^2 x tan^2 x - 2 (tan^2 x)^2$

Represent $sec^2x$ with a

Represent $tan^2x$ with b

The expression becomes

$a^2 + ab- 2 b^2$

Factorize

$a^2 + 2ab -ab- 2 b^2$

$a(a + 2b) -b(a+ 2 b)$

$(a -b) (a+ 2 b)$

Recall that

$a = sec^2x$

$b = tan^2x$

The expression $(a -b) (a+ 2 b)$ becomes

$(sec^2x -tan^2x) (sec^2x+ 2 tan^2x)$

..............................................................................................................................

In trigonometry

$sec^2x =1 +tan^2x$

Subtract $tan^2x$ from both sides

$sec^2x - tan^2x =1 +tan^2x - tan^2x$

$sec^2x - tan^2x =1$

..............................................................................................................................

Substitute 1 for $sec^2x - tan^2x$ in $(sec^2x -tan^2x) (sec^2x+ 2 tan^2x)$

$(1) (sec^2x+ 2 tan^2x)$

Open Bracket

$sec^2x+ 2 tan^2x$ ------------------This is an equivalence

$(secx)^2+ 2 (tanx)^2$

Solving further;

................................................................................................................................

In trigonometry

$secx = \frac{1}{cosx}$

$tanx = \frac{sinx}{cosx}$

Substitute the expressions for secx and tanx

................................................................................................................................

$(secx)^2+ 2 (tanx)^2$ becomes

$(\frac{1}{cosx})^2+ 2 (\frac{sinx}{cosx})^2$

Open bracket

$\frac{1}{cos^2x}+ 2 (\frac{sin^2x}{cos^2x})$

$\frac{1}{cos^2x}+ \frac{2sin^2x}{cos^2x}$

Add Fraction

$\frac{1 + 2sin^2x}{cos^2x}$ ------------------------ This is another equivalence

................................................................................................................................

In trigonometry

$sin^2x + cos^2x= 1$

Make $sin^2x$ the subject of formula

$sin^2x= 1 - cos^2x$

................................................................................................................................

Substitute the expressions for $1 - cos^2x$ for $sin^2x$

$\frac{1 + 2(1 - cos^2x)}{cos^2x}$

Open bracket

$\frac{1 + 2 - 2cos^2x}{cos^2x}$

$\frac{3 - 2cos^2x}{cos^2x}$ ---------------------- This is another equivalence

8 0

3 years ago

Will mark brainiest! !!50 Points!! The first question since it got cut off is : (A) is the sequence arithmetic, geometric, or ne

blagie [28]

Answer:

Geometric

Step-by-step explanation:

8 0

2 years ago

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Write an equation in slope-intercept form for the following line:<br> (-14.1) and (13,-2)

vesna_86 [32]

Answer:

$y=-\frac{1}{9}x-\frac{5}{9}$

Step-by-step explanation:

$(-14,1)(13,-2)$

Use the slope-intercept formula:

$y=mx+b$

m is the slope and b is the y-intercept. Use the slope formula first:

$\frac{y_{2}-y_{1}}{x_{2}-x_{1}} =\frac{rise}{run}$

Rise over run is the change in the y-axis over the change in the x-axis. Plug in the coordinates:

$(-14(x_{1}),1(y_{1}))\\(13(x_{2}),-2(y_{2}))$

$\frac{-2-1}{13-(-14)}$

Simplify parentheses (two negatives makes a positive):

$\frac{-2-1}{13+14}$

Simplify:

$\frac{-3}{27} =-\frac{3}{27}=-\frac{1}{9}$

The slope is $-\frac{1}{9}$ . Insert into the equation:

$y=-\frac{1}{9}x +b$

Now, to find the y-intercept, take one of the points and substitute for the x and y values of the equation:

$(13,-2)\\-2=-\frac{1}{9} (13)+b$

Solve for b, the y-intercept. Simplify parentheses:

$-\frac{1}{9}*\frac{13}{1}=-\frac{13}{9}$

$-2=-\frac{13}{9} +b$

Add $-\frac{13}{9}$ to both sides:

$-2+\frac{13}{9}=-\frac{13}{9} +\frac{13}{9} +b\\\\-2+\frac{13}{9} =b$

Simplify:

$-\frac{2}{1} +\frac{13}{9}\\\\-\frac{18}{9}+\frac{13}{9}\\ \\b=-\frac{5}{9}$

The y-intercept is $-\frac{5}{9}$ . Insert this into the equation:

$y=-\frac{1}{9} x-\frac{5}{9}$

Finito.

8 0

3 years ago

Help pls I give brainlest

dedylja [7]

Answer:

y = 1/2x - 3

Step-by-step explanation:

The line intercepts with the y-axis at -3 and its pattern is going right two and up one.

6 0

3 years ago

Simplify this expression 3p+2p-p

madam [21]

Answer:

Step-by-step explanation:

3p + 2p - p

= 3p + p

= 4p

(add the co-efficients)

3 0

3 years ago

Read 2 more answers