Given: 6|x/3| < 18
Part A: Show the step(s) to get the absolute value expression by itself.

Part B: Write the two equations used to solve the absolute value equation.

Part C: Solve the equations and check your equations.

Answers

Answer 1

Answer:

see below

Step-by-step explanation:

6|x/3| < 18

Divide by 6

6/6|x/3| < 18/6

|x/3| < 3

Now we get two equations, one positive and one negative, remembering to flip the inequality

x/3 < 3   x/3 > -3

Multiply by 3 to isolate x

x/3 *3 < 3*3  and  x/3*3 > -3*3

x < 9          and      x > -9

Rewriting

-9 < x<9

Check -12

6|-12/3| < 18

6|-4| <18

24<18  False  good

Check 0

0<18  true

Check 12

6|12/3| < 18

6|4| <18

24<18  False  good


Related Questions

A university lecturer has an annual salary of $60000. If this increases by 2% of the previous year each year, what will her salary be after 10 years.

Answers

Answer:

73,139.67

Step-by-step explanation:

What would be the volume of this solid if the height were halved and the other dimensions were reduced proportionally? Round to the nearest whole number.
The image?is of a?parallelogram prism standing on its face and making an angle of 60 degrees with horizontal. The dimension of prism is 3 cm by 4cm by 10 cm.

Answers

Please give you books and lemme study for you, so I can take do your homework and take all your tests, and at the end you will graduate without put anything in you brain cells. I hope this is helpful hopefully you learn something. And please give 5 stars rating and if you want to brake it down step by step please don’t hesitate to ask me.

June and the total of 4/6 hour on her math and reading homework which pair of models could show the amount of time in hours she spends on each subject

Answers

Answer:

2/3

Step-by-step explanation:

The base of a rectangular prism has an area of 12 square centimeters. The height of the rectangular prism is 3
centimeters.
What is the volume, in cubic centimeters, of this rectangular prism?

Answers

Answer:

36

Step-by-step explanation:

12x3=36

Lxwxh

Axh

Answer:

18,6,108

Step-by-step explanation:

edge2020

If you spend $448.37 on a car each month, what is your new subtotal of take-home pay after expenses?

Answers

Answer:

$629.75

Step-by-step explanation:

2,939.12 (Monthly net pay) - 1379 (Mortgage) - 302 (Food) - 448.37 (Car) - 230 (Gas) = 629.75 (Subtotal)

The solutions of a quadratic equation are 5 and -1. What is the factored form of a related quadratic function?

Answers

Answer:

f(x)=(x+1)(x-5)

Step-by-step explanation:

The solutions to a quadratic equation are going to be your x-intercepts, or when y is equal to zero. For y to be zero, all you have to do is have one value equal to zero. When x is 5, (x-5) is equal to zero. When x is -1, (x+1) is equal to zero. This is one example of what your quadratic equation could be.

The work of a student to solve 2(5y-2)=12+6y is shown below

Answers

Answer:y=4

Step-by-step explanation:

2(5y-2)=12+6y

10y-4=12+6y

4y-4=12

4y=16

y=4

I'm a bit stuck, well uhhh you'll see. Please help!! is she 25 or 26 ? ? ?

Answers

Answer:

25 years old

Step-by-step explanation:

19+3=22

19+6=25

19+25+22=66

she is 25 years old

In a survey of students, 1162 stated they cheated and 2468 stated they did not. If one student is randomly selected what is the probability that they cheated

Answers

Answer:

[tex] n = 1162 +2468 =3630[/tex]

And the probability that they cheated and we can use the classical definition of probability given by:

[tex] p =\frac{successes}{Total}[/tex]

And replacing we got:

[tex] p=\frac{1162}{3630}= 0.320[/tex]

So then the probability of people cheated is 0.320 or 32% approximately

Step-by-step explanation:

For this problem we know that in a survey of students, 1162 stated they cheated and 2468 stated they did not.

The total of people is given by:

[tex] n = 1162 +2468 =3630[/tex]

And the probability that they cheated and we can use the classical definition of probability given by:

[tex] p =\frac{successes}{Total}[/tex]

And replacing we got:

[tex] p=\frac{1162}{3630}= 0.320[/tex]

So then the probability of people cheated is 0.320 or 32% approximately

A robot’s height is 1 meter 20 centimeters. How tall is the robot in millimeters?

Answers

Answer:

1200 millimeters

Step-by-step explanation:

Which binomial is a factor of 9x2 – 64?

Answers

Answer:

Factor:

9x2 – 64

=(3x+8)(3x−8)

3x – 8

how to find the mean median and mode for 6 5 6 7 6 6 7 4 6 7 7 6 7 7 7 4 7​

Answers

Answer:

the answer is 7 fiyfooutdt7odtudoutdup tiff 7tduptftucoutctuco7tc

Answer:

the medium is 7

Step-by-step explanation:

The sum of an 84-number series is –7,980. What is the sum of the first and last numbers?

Answers

Answer:

- 190

Step-by-step explanation:

Since the sum of 84 number series is -7980. We have to find the sum of first and last numbers. Since sum of an arithmetic sequence is represented as. S =. (First + last) =. So the total of first and last term is (-190). Option B. -190 is the correct option.

Answer:

B) -190

Step-by-step explanation:

Trust

what times 8 equals 2
2=x8

x=?
Please help! :0

Answers

Answer:

1/4 or .25

Step-by-step explanation:

8x =2

Divide by 8 on both sides

8x=2

__. ___

8.     8

x = 2/8=1/4 or .25

Answer: x equals 1/4 or 25% or 0.25

-25z+1+35z=10z+1 how mu

Answers

The question is unfinished but if it’s supposed to be evaluated the answer is 0.

About 450 manta rays are seen near lady Elliot island each year if you were to spot one manta ray at random what is the probability that it would be clouseau

Answers

Answer:

Probability that if a manta ray is spotted at random, it would be clouseau = Total number of Clouseau spotted each year) ÷(Total number of manta rays seen each year)

Step-by-step explanation:

The information given is not enough to determine the probability.

We need to know, how many Clouseau are seen each year, then we can find the desired probability.

The Parameters:

Total number of manta rays seen each year = 450

Probability that if a manta ray is spotted at random, it would be clouseau,

P = Total number of Clouseau spotted each year, C) ÷(Total number of manta rays seen each year, T)

P = C/T

P = C/450

Directions: Solve each volume problem using the information given. Use 3.14 for pi and label your answer with the appropriate units.

1.) The school cheer leading team uses megaphones in their routines. Each megaphone is a cone. The radius of the megaphone is 5.1 inches and the height of the megaphone is 19.3 inches. What is the volume of the megaphone?





2.) You and your friends buy ice cream cones at the local ice cream shop. The radius of the ice cream cone is 44 millimeters and the volume of the ice cream cone is 356,456.2136 cubic millimeters. What is the height of the ice cream cone?

Answers

Answer:

A. 525.42 inches^3

B. 175.91 mm

Step-by-step explanation:

a. Here we are asked to calculate the volume of the cone given the radius and the height of the cone.

Mathematically, the volume of the cone can be calculated using the formula below;

V = 1/3 * π * r^2 * h

where r is the radius which is 5.1 inches and h is the height of the megaphone = 19.3 inches

Plugging these values, we have;

V = 1/3 * 3.14 * 5.1^2 * 19.3 = 525.42 inches^3

b. Here we are tasked with calculating the height given the value of the volume and the radius.

mathematically, the formula to use is

V = 1/3 * π * r^2 * h

where V = 356,456.2136 cubic millimeter and r is 44mm

plugging these values we have

356,456.2136 = 1/3 * 3.14 * 44^2 * h

h =( 1,069,368.6408)/6,079.04

h = 175.91 mm

Suppose that in 8 minutes,40 gallons of water came out of a pipe. What was the rate in gallons per minute?

Answers

Answer:

5 galon  por min uto

Step-by-step explanation:

AEFG - ALMN. Find LM.

Answers

Answer:

The solution is 2.5. The problem can be solved using the proportion:  

2

4

=

x

5

Step-by-step explanation:

I hope it makes since =)

It’s delta math for it

Answers

Answer:

[tex]\sqrt{x^{2}-7[/tex]

Step-by-step explanation:

Negative exponents flip the fraction, fraction exponents imply a radical to the denominator's degree, so flip the fraction and take the square root of what is in parentheses

We know that :

[tex]\bigstar \ \ \boxed{\mathsf{a^{-1} = \dfrac{1}{a}}}[/tex]

[tex]\mathsf{Given \ question \ is : \dfrac{1}{(x^2 - 7)^{\frac{-1}{2}}}}[/tex]

Using the above formula, we can write it as :

[tex]\implies \mathsf{\dfrac{1}{\dfrac{1}{(x^2 - 7)^{\frac{1}{2}}}}}[/tex]

[tex]\implies \mathsf{(x^2 - 7)^{\frac{1}{2}}}[/tex]

[tex]\implies \mathsf{\sqrt{x^2 - 7}}[/tex]

what is 3.39 as a fraction

Answers

Answer:

339/100

Step-by-step explanation:

the answer is 339/100

PLEASE HELP!! WILL GIVE BRAINLIEST IF RIGHT

An account earns annual simple interest, Find the interest earned, principal, interest rate, or time.
Interest earned: ?
Principal: $1250
Interest rate: 3%
Time: 4 years

Answers

Answer:

:

I think I know how to solve this. You are trying to find the interest earned.

Step-by-step explanation:

you take the interest rate and convert into a percentage. 3%=0.03You divide that decimal by 100. 0.03/100=0.003Take this number and multiply by the time. 0.0003x4=0.0012You then finally multiply that number by the principle and you have your answer. 0.0012x1250=1.5 percent

Answer:

t says or, so you can answer any however the answer to time would be 4 years or so

Step-by-step explanation:

10x5 = 50

50x50 = 2500

2500x.4= 1000

1000/250=4

4

Step-by-step explanation:

A teacup has a radius of 5 centimeters. What is the teacup's diameter? Help please.

Answers

Answer:10

Step-by-step explanation:

Radius is half the diameter

Answer:

10 cm

Step-by-step explanation:

the radius is half the diameter so 5x2=10cm

How would I write out,10 times a number increased by four is no more than 25 as an inequality?

Answers

Answer:

10x + 4 [tex]\geq[/tex] 25

Would this be -4? Just wanna confirm!

Answers

Answer:

Yes

Step-by-step explanation:

Answer:

True

Step-by-step explanation:

Help me please !!!!!

Answers

Answer:

C =119.32

A =1133.54

Step-by-step explanation:

UR is the radius = 19

Let pi = 3.14

The circumference is

C = 2*pi*r

C = 2 * 3.14 * 19

C =119.32

The area is given by

A = pi r^2

A = 3.14 * (19)^2

A =1133.54

easy geometric shapes questions help please! they go together

Answers

7.solution

v=4/3πr^3

=4/3π×6^3

=4/3×216cm^3π

=288cm^3π

8.solution

SA=4πr^2

=4×6^2π

=4×36cm^2π

=144cm^2π

Which number line shows the solutions to n<-3

Answers

Answer:

[In Picture]

Step-by-step explanation:

There are no given options.

However, I am able to recreate the best answer for the question given.

There would be arrow going to the left from -3. The arrow will include all numbers less than -3.

Since there is a less than sign, the circle at the beginning of the arrow is open.

Choose the option that closely matches the line shown.

The number line is the representation of numbers in real order.

The difference between the consecutive numbers in a number line is always positive.

The number line of n < - 3 is n less than -3.

The graph of the number line is given below.

What is a number line?

It is the representation of numbers in real order.

The difference between the consecutive numbers in a number line is always positive.

We have,

n < - 3

This is read as,

n is less than -3.

The graph of the number line is given below.

Thus,

The number line of n < - 3 is n less than -3.

The graph of the number line is given below.

Learn more about number line here:

https://brainly.com/question/13425491

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Simplify the given expression, using only positive
exponents. Then complete the statements that
follow
(x²y3)-1 72
(x-2y+z)2
x60, y#0, 2*0.
?
The exponent on x is
The exponent on y is
The exponent on z is

Answers

Answer: x=4 y=14 z=4

Step-by-step explanation:

On edge it is that

The required exponent on x is 4, the exponent on y is 14, and the exponent on z is 4.

What is simplification?

Using math and algebraic principles, simplification entails removing pointless variables, factors, or operations from an expression. Getting an expression that is simpler to use, manipulate, or solve is the aim. For example, simplifying an algebraic expression might involve combining like terms, factoring, or using the distributive property.

Here,
To simplify the given expression, we need to use the rules of exponents:

= [(x²y³)⁻¹ / (x⁻²y²z)²]²

= [(1 / x²y³) / (x⁻⁴y⁴z²)]²

= [(1 / x²y³) * (x⁴ / y⁴z²]²

= x⁴ / y¹⁴z⁴

Therefore, the exponent on x is 4, the exponent on y is 14, and the exponent on z is 4.

Learn more about simplification here:

https://brainly.com/question/12501526

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Bruno is sewing a large rectangular tablecloth for a restaurant. He has 30 square feet of fabric and the length of the table cloth needs to be 7.5 feet. What is the width of the tablecloth if he uses all of the fabric?

Answers

Answer:

Step-by-step explanation:

4 ft

Answer:

Step-by-step explanation:

4 ft

brainliest pls i need it :,)

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