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Goryan [66]
3 years ago
13

Solve equation, check for extraneous solutions

Mathematics
1 answer:
fiasKO [112]3 years ago
8 0

Start with

1=\dfrac{1}{n^2}+\dfrac{n^2-4n-5}{3n^2}

We observe that both fractions are not defined if n=0. So, we will assume n \neq 0.

We multiply both numerator and denominator of the first fraction by 3 and we sum the two fractions:

1=\dfrac{3}{3n^2}+\dfrac{n^2-4n-5}{3n^2} = \dfrac{n^2-4n-2}{3n^2}

We multiply both sides by 3n^2:

n^2-4n-2=3n^2

We move everything to one side and solve the quadratic equation:

2n^2+4n+2=0 \iff 2(n^2+2n+1)=0 \iff 2(n+1)^2=0 \iff n+1=0 \iff n=-1

We check the solution:

1=\dfrac{1}{1}+\dfrac{1+4-5}{3} \iff 1 = 1+0

which is true

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Kara works at a fine jewelry store and earns commission on her total sales for the week. Her weekly paycheck was in the week tot
GrogVix [38]

Answer:

12.2%

Step-by-step explanation:

Her total paycheck minus her salary = the commission amount

So

6500 - 1000 = 5500

So....her commission as a percentage of sales  = 5500/ 45000 = about 12.2%

3 0
3 years ago
-12 + 8a = -a + 6(2a - 2)
pogonyaev

Answer:

41/6

Step-by-step explanation:

-12+81=-1+6(2a-2)

first distribute:

-12+81=-1+12a-12

combine like terms:

<u>-12+81</u>= <u>-1</u>+12a<u>-12</u>

69=-13+12a

add -13 with 69:

82=12a

divide 82 and 12:

82/12= 41/6

3 0
3 years ago
Read 2 more answers
How would I get a answer?
tresset_1 [31]

Answer:

0.07kg

Step-by-step explanation:

1kg = 1000g

so grams/1000 =kg

70/1000 = 0.07kg

3 0
3 years ago
What is the simplified form of this expression 7(^3sqrt2x)-3(^3sqrt16x)-3(^3sqrt8x)
trasher [3.6K]

Answer:

<h2>7 \sqrt[3]{2x}  - 6 \sqrt[3]{2x}  - 6x</h2>

Solution,

7( \sqrt[3]{2x} ) - 3( \sqrt[3]{16x} ) - 3( \sqrt[3]{8x} ) \\  = 7 \sqrt[3]{2x}  - 3 \times ( \sqrt[3]{2 \times 2 \times 2 \times 2x}  - 3 \times  \sqrt[3]{2 \times 2 \times 2x}  \\  = 7 \sqrt[3]{2x}  - 3 \times (2 \sqrt[3]{2} x) - 3 \times 2x \\  = 7 \sqrt[3]{2x}  - 3 \times 2 \times  \sqrt[3]{2x}  - 3 \times 2x \\  = 7 \sqrt[3]{2x}  - 6 \sqrt[3]{2x}  - 6x

Hope this helps...

Good luck on your assignment...

7 0
3 years ago
Solve this inequality: 3b – 7 &lt; 32
butalik [34]
It's a lot like solving equations.

3b-7 < 32
Add 7 to each side.
3b < 39
Divide by 3 on each side.
b < 13

Hope this helps :)
6 0
3 years ago
Read 2 more answers
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