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3 years ago

How do you solve and graph |x+y|>1

1 answer:

6 0

Set up two inequalities for the absolute value inequality.
First inequality and second inequality: x + y > 1 or x + y < -1
Notice I used or between the inequalities. If your absolute value expression is greater than the constant, it is a disjunction.

Graph the individual inequalities on the same plane and that is your solution.

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Simplify the following expression as much as you can use exponential properties. (6^-2)(3^-3)(3*6)^4

gtnhenbr [62]

Answer:

Simplifying the expression $(6^{-2})(3^{-3})(3*6)^4$ we get $\mathbf{108}$

Step-by-step explanation:

We need to simplify the expression $(6^{-2})(3^{-3})(3*6)^4$

Solving:

$(6^{-2})(3^{-3})(3*6)^4$

Applying exponent rule: $a^{-m}=\frac{1}{a^m}$

$=\frac{1}{(6^{2})}\frac{1}{(3^{3})}(18)^4\\=\frac{(18)^4}{6^{2}\:.\:3^{3}} \\$

Factors of $18=2\times 3\times 3=2\times3^2$

Factors of $6=2\times 3$

Replacing terms with factors

$=\frac{(2\times3^2)^4}{(2\times 3)^{2}\:.\:3^{3}} \\=\frac{(2)^4\times(3^2)^4}{(2)^2\times (3)^{2}\:.\:3^{3}} \\$

Using exponent rule: $(a^m)^n=a^{m\times n}$

$=\frac{(2)^4\times(3)^8}{(2)^2\times (3)^{2}\:.\:3^{3}} \\=\frac{2^4\times 3^8}{2^2\times 3^{2}\:.\:3^{3}}$

Using exponent rule: $a^m.a^n=a^{m+n}$

$=\frac{2^4\times 3^8}{2^2\times 3^{2+3}}\\=\frac{2^4\times 3^8}{2^2\times 3^{5}}$

Now using exponent rule: $\frac{a^m}{a^n}=a^{m-n}$

$=2^{4-2}\times 3^{8-5}\\=2^{2}\times 3^{3}\\=4\times 27\\=108$

So, simplifying the expression $(6^{-2})(3^{-3})(3*6)^4$ we get $\mathbf{108}$

7 0

3 years ago

Which of the following angles are supplementary to _1?<br><br> Plsss Help

dolphi86 [110]

Angle 8 because supplementary is two angles whose sum is 180°.

6 0

3 years ago

Read 2 more answers

Oscar was not safeguarding his personal identification and chose a two-digit PIN for his debit card using the numbers 0 - 9. Wit

ryzh [129]

There are 90 different identification numbers possible.

<h3>What are the permutation and combination?</h3>

In terms of mathematical concepts, “permutation” and “combination” are related to each other.

The combination is the counting of selections that we make from n objects.

Oscar was not safeguarding his personal identification and chose a two-digit PIN for his debit card using the numbers 0 - 9.

There are 10 possible values for each digit of the PIN (namely: 0, 1, 2, 3, 4, 5, 6, 7, 8, 9), so there are;

10 × 10 = 100 total possible PINs.

Now, because you can't use the same number twice, we subtract 10 from 100 because there are 10 numbers that can match themselves.

100 -10 =90

Hence, there are 90 different identification numbers possible.

Learn more about combination here;

brainly.com/question/24138361

#SPJ2

5 0

2 years ago

Read 2 more answers

What i 12% of 32? is 32the part or the whole???

Valentin [98]

32 is the whole 12.16 is 12 percent of 32

7 0

3 years ago

Ms.Lawrence had 550 in her bank account. The next day she withdrew 120 to buy groceries. She deposited 200 two days later. Fout

hjlf

Answer:

541

Step-by-step explanation:

550-120+200-89=541

7 0

3 years ago