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Helen [10]
3 years ago
7

Explain why there are either two, one, or no solutions for absolute value equatins. Demonstrate an example for each

Mathematics
2 answers:
AleksAgata [21]3 years ago
4 0

<u>No solution</u>: because the absolute value is positive and can't equal a negative

|x| = -1          

<u>One solution: </u>because zero only has one sign

|x| = 0      ⇒ x = 0      

<u>Two solutions:</u> absolute value is positive whether x is positive or negative.

|x| = 2     ⇒ x = 2 or x = -2      

AVprozaik [17]3 years ago
4 0
Absolute value equations |a|=b have two solutions only if b>0, because it means that a=b or a=-b. Example:
|x + 1| = 1 \\ x = 0 \: or \: x = - 2
Absolute value equations |a|=b have one solution only if b=0, because 0=-0. Example:
|x + 1| = 0 \\ x = - 1
Absolute value equations |a|=b have no solution only if b<0, because absolute value can't have a negative value. Example:
|x + 1| = - 1 \\ x \in \varnothing
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Intel estimates that about 12 quintillion transistors are shipped around the globe each year. If that represents 10,000 times th
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Answer:

Number on ants on Earth = 1.2 × 10¹⁵

Step-by-step explanation:

1 quintillion = 10¹⁸ or (1000000000000000000)

∴ 12 quintillion = 12 × 10¹⁸

12 quintillion = 10,000 × Number of ants on Earth

Let the number of ants on Earth = n

12 quintillion = 10,000 × n

dividing both sides by 10,000

12 quintillion ÷ 10,000 = n

n = \frac{12\ \times\ 10^{18} }{10,000} \\n =  \frac{12\ \times\ 10^{18} }{10^{4}}\\n = 12\ \times\ \frac{10^{18}}{10^{4}} \\applying\ the\ second\ law\ of\ indices\ (\frac{x^m}{x^n} = x ^{m-n})\\ n = 12\ \times\ 10^{(18 - 4)\\n = 12\ \times 10^{14}\\in\ standard\ form\\n = 1.2\ \times 10\ \times\ 10^{14}\\\therefore n = 1.2\ \times\ 10^{15}

Number on ants on Earth = 1.2 × 10¹⁵

6 0
3 years ago
If 40 is decreased by 60%, what is the new amount?
Kay [80]

Answer:

16

Step-by-step explanation:

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3 years ago
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12 touchdowns in 6 games unit rate
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If Angle L=105 degrees, What is the measurement of angle N???
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7x + 2y = -1<br> 3x – 4y = 19
jeka94

Answer:  Y = - 4 & x = 1

Step-by-step explanation:

Systems of linear equations: We will solve this using substitution but you can use 2 more ways.

7x + 2y = -1

2x - 4y = 19

Leave X  alone first: -------------------

10x - 2y = 18

10x/10 = 18 + 2y/10

x = 9/5 + y/5

Solve for y:

7(9/5 + y/5) + 2y = -1

63/5 + 7y/5 + 2y - 1

63/5 + 7y/5 = 10y/5 = -1

63/5 + 17y/5 = -1 (-5/5)

17y/5 = -68/5 (cancel the 5)

y = -68/17

y = - 4 (Your Answer)

7x + 2(- 4) = -1

7x + (-8) = -1

7x = 7

x =   1

CHECK=

7(1) + 2(-4) = -1

7+ (-8) = -1.

-1=-1

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3 years ago
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