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3 years ago

The product of (a + b)(a − b) is a2 − b2. (1 point)

Mathematics

1 answer:

notka56 [123]3 years ago

6 0

Answer:

Always

Step-by-step explanation:

the product of

${a}^{2} - {b}^{2} = (a +b)(a -b )$

is always same

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1. if csc β = 7/3 and cot β = - 2√10 / 3, Find sec β

slava [35]

Step-by-step explanation:

$\tan \beta = \frac{1}{ \cot \beta } = - \frac{3}{2 \sqrt{10} } = - \frac{3 \sqrt{10} }{20}$

$\csc \beta \tan \beta = \frac{1}{ \cos \beta } = \sec \beta$

Therefore,

$\sec \beta = ( \frac{7}{3} )( - \frac{3 \sqrt{10} }{20} ) = - \frac{7 \sqrt{10} }{20}$

$\csc y = \frac{1}{ \sin y} = - \frac{ \sqrt{6} }{2}$

$= > \sin y = - \frac{ \sqrt{6} }{3}$

Use the identity

$\cos y = \sqrt{1 - \sin ^{2} y} \: \: \: \: \: \: \: \: \: \: \: \\ = \sqrt{1 - {( - \frac{ \sqrt{6} }{3}) }^{2} } = - \frac{ \sqrt{3} }{3}$

We chose the negative value of the cosine because of the condition where cot y > 0. Otherwise, choosing the positive root will yield a negative cotangent value. Now that we know the sine and cosine of y, we can now solve for the tangent:

$\tan \beta = \frac{ \sin y}{ \cos y} =( - \frac{ \sqrt{6} }{3} )( - \frac{3}{ \sqrt{3} } ) = \sqrt{2}$

3. Recall that sec x = 1/cos x, therefore cos x = 5/6. Solving for sin x,

$\sin x = \sqrt{1 - \cos ^{2} x} = \sqrt{ \frac{11}{6} }$

Solving for tan x:

$\tan x = \frac{ \sin x}{ \cos x} = (\frac{ \sqrt{11} }{ \sqrt{6} } )( \frac{6}{5} ) = \frac{ \sqrt{66} }{5}$

5 0

3 years ago

What is the first step to 7(x – 4) = 84.

ss7ja [257]

Parenthesis according to the PEMDAS rule

So
7(x - 4) = 84

Would be

7x -28 = 84

Hope this helped :)

5 0

3 years ago

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Ten students share 8 pieces of poster board equally. what fraction of a piece of poster board does each friend get?

padilas [110]

8:10= 0,8

0,8 or 4/5
hope this help

7 0

4 years ago

0.7 (3s + 4)-1.1s = 7.9

vichka [17]

Answer:

s = 5.1

Step-by-step explanation:

$0.7 (3s + 4)-1.1s = 7.9\\$

Multiply both sides of the equation by 10

$0.7\left(3s+4\right)\cdot \:10-1.1s\cdot \:10=7.9\cdot \:10\\\\= 7\left(3s+4\right)-11s=79\\$

Expand

$\mathrm{Expand\:}7\left(3s+4\right)-11s:\\\quad 10s+28$

Subtract 28 from both sides

$10s+28-28=79-28$

Simplify

$10s=51$

Divide both sides of the equation by 10

$\frac{10s}{10}=\frac{51}{10}$

Simplify

$s=\frac{51}{10}\\\\Decimal = 5.1$

3 0

3 years ago

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What is the factored for of the polynomial x2 - 16x + 48

mel-nik [20]

What two factors of 48 add up to -16? -4 and -12

So the factored form would be (x-4)(x-12)

5 0

3 years ago

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