What are the solutions to the absolute value inequality |x − 70| ≤ 3?

Remember, the inequality can be written as −3 ≤ x − 70 ≤ 3

or as x − 70 ≤ 3 and x − 70 ≥ −3.

Answers

Answer 1

Answer:

67 ≤ x ≤ 73

Step-by-step explanation:

The absolute value of a real number x is the non negative value of x. Therefore the absolute value of x (|x|) = x for x ≥ 0 and -x for x < 0.

An expression |x - a| = b signifies that x - a = b or -(x - a) = b

Given that |x − 70| ≤ 3, hence:

|x − 70| ≤ 3

x - 70 ≤ 3 or -(x - 70) ≤ 3

x ≤ 3 + 70 or x - 70 ≥ -3

x ≤ 73 or x ≥ -3 + 70

x ≤ 73 or x ≥ 67

67 ≤ x ≤ 73

Hence the solution of |x − 70| ≤ 3 is 67 ≤ x ≤ 73


Related Questions

here is the screenshot for anyone who is willing to help me

Answers

Answer:

1. 6,000

2. 7,000-4,000=3,000

3. 0

4. 15

5, 6/8 7/8

6. greater than

7. equal to

8. 520,685

9. the 5

10a. 3210

10b. 2346

--------------------

1. 7,000

2. all of them

3. two

4. 3

5. 2

6. b

7a. 3 b. 2

8. 14/30

9. 3/8

10. N=175

Step-by-step explanation:

At soccer practice, Tracey's best kick traveled a distance of 1,200 inches. For how many yards did she kick the ball? Express your answer as a
fraction written in simplest form.

Answers

Answer:

100/3 yards

Step-by-step explanation:

36 inches=1 yard, so 1200/36 will equal how many yards 1200 inches is.

Simplify:

1200/36

divide numerator and denominator by 12 and you get 100/3

100/3 yards

Tracey kicks the ball for 100/3 yards.

Given that, at soccer practice, Tracey's best kick travelled a distance of 1,200 inches.

We need to find out for how many yards did she kick the ball.

How to convert inches to yards?

Inch-to-yard conversion explanation

So to convert from a value in inches to one in yards, we need to divide by 36. To convert a value in yards to inches, we need to multiply by 36.

Now, the number of yards =1200/36=100/3

Hence, Tracey kicks the ball for 100/3 yards.

To learn more about the yards visit:

https://brainly.com/question/28365360.

#SPJ2

Solve for the following equation
R-(-5)=-9

Answers

r=-14

hope this helps:)
The answer is R= -14

Please help me answer this with the correct answer :)

Explain your answer

I will give braisnlt :) c

Answers

Pretty sure is 63 degrees since the one next to it is exactly the same and its 63 degrees

2. The cost of a home entertainment center is $4700. We can finance this by paying $300 down and
$388.67 per month for 12 months.
a. Determine the amount financed.
b. Determine the total installment price.
c. Determine the finance charge.

Answers

Answer:

well. 372.

You don't have to buy a house. It doesn't really matter tho

You can live in an apartment or even hotel/motel. Enjoy

Step-by-step explanation:

PLZ HELP!!! I need help ASAP

Answers

You distribute the negative in the second equation

Answer:

The two problems/expressions are the same because of the negative and positive rule.

Step-by-step explanation:

+ - = -

- + = -

- - = +

+ + = +

Help ASAP! And explain!

Answers

Answer:

Option (2)

Step-by-step explanation:

Given:

AC is an angle bisector of ∠DAB and ∠DAB

m∠BCA ≅ m∠DCA

m∠BAC ≅ m∠DAC

To Prove:

ΔABC ≅ ΔADC

Solution:

               Statements                                  Reasons

1). m∠BCA ≅ m∠DCA                            1). Given

2). m∠BAC ≅ m∠DAC                           2). Given

3). AC ≅ AC                                            3). Reflexive property

4). ΔABC ≅ ΔADC                                 4). ASA property of congruence

Therefore, Option (2) will be the correct option.

what has a quotiont of 9 and a reminder of 5

Answers

Answer:

Division problems with quotient of 9 and remainder of 5 could include:-

23/2 = 9 + 5/2

32/3 = 9 + 5/3

41/4 = 9 + 5/4

50/4 = 9 + 5/5

But you could justifiably object that more natural forms for the answers would be 11 + 1/2, 10 + 1/3, 10 + 1/4 and 10 , and so you may well prefer such as

59/6 = 9 + 5/6

77/8 = 9 + 5/8  ….. and so on

As you can see the general pattern is (9n + 5)/n = 9 + 5/n

You can now make up your own examples, like 212/23 = 9 + 5/23

Step-by-step explanation:

Find x.
20 cm
12 cm
Х
X =
cm

Answers

use pythagorean therom, so A^2 would be 12 since it’s the same lengths the square sides, and C^2 is 20. X= 16

HELP I DONT UNDERSTAND OR MAYBE I DO BUT IM YK I JUST NEED HELP PLEASE

Answers

Answer:

9/16

Step-by-step explanation:

;)

Answer:

-0.5625

Step-by-step explanation:

-0.75 x 0.75 = -0.5625

Manny runs 15 3/4miles each week. Zander runs
5/6
olu
as many miles each week as Manny.
How many miles does Zander run each week?

Answers

Answer: Zander Runs, 13.125 miles. You take the mixed number and change it into an improper fraction. So you get 63/4 then multiply that by 5/6 and get 13.125 miles there is your answer. I hope this helps you

Step-by-step explanation:

The point (-6, 5) was translated right 4 and down 6. What are the coordinates of the new
point?
O (10,11)
O (-2,1)
O (-2,-1)
O
(-10, 11)

Answers

(-2, -1) is the answer

(-6, 5)
(-6 +4, 5 -6)
=
(-2, -1)
B. (-2,-1) Is the answer I’m pretty sure e

An experiment was conducted as a one-way factorial design with K sample means, each based on n scores. What is the number of degrees of freedom for the between mean squares

Answers

Answer:

The mean squares has d.f (n-1)

Step-by-step explanation:

The total number of degrees of freedom is n-1 as there is only one restriction of computing the grand mean. The d.f for k samples is k-1 beacuase the mean of the sample means must equal the grand mean. Similarly , the d.f for within SS is n-k , due to the k restrictions of computing the k sample means. Hence we find that

Total df= Within df + Between df

n-1=  (n-k)+(k-1)

Between SS has (k-1) d.f

Within SS has (n-k) d.f

These two quantities are known as mean squares and has d.f (n-1)

Olivia is cutting a 1 1/2 m by 3/4 m piece of rectangular paper into two pieces along its diagonal.

Find the area of each of the pieces.

Answers

Answer:

[tex]area = length \: \times \: width \\ = \frac{11}{2} \times \frac{3}{4} \\ = \frac{(11 \times 3)}{(2 \times 4)} \\ = \frac{33}{8} \\ area = 4.125 \: {m}^{2} \\ or \\ area = 4 \frac{1}{8} \: {m}^{2} [/tex]

Answer the question above ​

Answers

Answer:

[tex]tan\:\left(\frac{5\pi }{6}\right)=tan\left(-\frac{\pi }{6}\right)[/tex]

Option A is correct.

Step-by-step explanation:

We need to find equivalent of [tex]tan\:\left(\frac{5\pi }{6}\right)[/tex]

First we solve [tex]tan\:\left(\frac{5\pi }{6}\right)[/tex]

We get [tex]-\frac{1}{\sqrt{3} }[/tex]

Now checking all the options.

Option A: [tex]tan\:(-\frac{\pi}{6} )[/tex]

Solving [tex]tan\left(-\frac{\pi }{6}\right)\: we\: get\: \mathbf{ -\frac{1}{\sqrt{3} }}[/tex]

Option B: [tex]tan\left(\frac{7\pi }{6}\right)[/tex]

Solving [tex]tan\left(\frac{7\pi }{6}\right)\: we\: get\: \mathbf{\frac{1}{\sqrt{3} }}[/tex]

Option C: [tex]cot\left(\frac{5\pi }{6}\right)[/tex]

Solving [tex]cot\left(\frac{5\pi }{6}\right)\:we\:get\:\mathbf{-\sqrt{3} }[/tex]

Option D : [tex]tan\left(-\frac{5\pi }{6}\right)[/tex]

Solving [tex]tan\left(-\frac{5\pi }{6}\right) \:we\:get:\mathbf{\frac{1}{\sqrt{3} } }[/tex]

So, looking at the options, only Option A has the same result as given question

So, [tex]tan\:\left(\frac{5\pi }{6}\right)=tan\left(-\frac{\pi }{6}\right)[/tex]

Option A is correct.

Devante has a lunch account in the school cafeteria His starting balance at the beginning of the month is $35.50. The first wook, Davante bought 3 lunches and his account balance was $28.00. The second week. Devante

bought 5 lunches and his account balance was 515 50

In a model that relates the balance of his lunch account as a function of the number of lunches he buys, what does the rate of change represent?


A: the number of lunches he purchases


B: the starting balance of his lunch account


C: the amount of money in his lunch account


D: the amount of money he pays for each lunch

Answers

Answer:

D the amount of money he pays for each lunch

Step-by-step explanation:

In each lunch Devante has, he pays 2,50 $ according to:

Money in t = t₀     he has  35,50 $      paid 3 lunches and spent

35,50 - 28  =  7,5

Then the cost of each lunch is    7,5 / 3   =  2,5 $

After that

bought    5 lunches and spent   28  - 15,5  = 12,50

Again    12,5 / 5   =  2,5 $

Now the model for the situation is a straight line with a slope 2,5

In an  x , y cartesian system in which  y is money in the account  and x is the number of lunches, such a straight line will be

y  =  b  -  m*x      ( b the intercept on y  and  m the negative slope)

y  =  35,50 - 2,5*x

So  answering the question is lyrics  D  the amount of money he pays for each lunch

Can you help me with these 5 questions please?!​

Answers

Answer:

1. A 2. 9$ 3. C 4. C 5. Because you can see the prices and the difference between prices

Rate pls

The student council needs posters for the Winter Carnival. The print shop charges $15 for each print job. Each poster will cost an additional
$1.35.
Which equation shows the relationship between the number of posters, n, and the total cost, c, in dollars?

O A. c = 1.35n + 15
O B. n = 1.35n + 15
O C. c = 16.35n
O D. n = 16.35c

Answers

Answer: A. c = 1.35n + 15

Step-by-step explanation:

Given: Charge for each job = $15

Additional cost per poster = $ 1.35

Total cost = Charge for each job + (Additional cost per poster) (Number of posters)     ...(i)

Varaibles:

c= Tota; cost for n posters.

Substitute all values in (i), we get

[tex]c=15+1.35n[/tex]

Hence, the required equation : c = 1.35n + 15

Hence, the correct option is A. c = 1.35n + 15.

The U-Pick-It Farm wants to find out which type of berries their customers
prefer to pick.
Determine which of the following would result in an unbiased sample set.
Customers who are picking blueberries
Customers who have not started picking berries
Customers who are picking raspberries
Customers who are picking strawberries

Answers

Answer:

Customers who have not started picking berries

Step-by-step explanation:

this is becuase the costomers have not started so there is not an assumption yet. If they are picking blueberries, raspberries, or strawberries you already know what they prefer to pick.

Suppose you have a population in which 60% of the people approve of gambling. Is the value 0.60 a parameter or a statistic

Answers

Answer:0.60 is a parameter .

Step-by-step explanation:

In statistics, a parameter is a number that summarize the data for a whole population.

On the other hand , statistic gives a measure for sample of population.

Given: We have a population in which 60% of the people approve of gambling.

60% = 0.60

Since it is a measure for the population , it is denoted as population parameter.

Hence, 0.60 is a parameter not statistic.

which expression is equivalent to (5^-2) (5^-1)​

Answers

Answer:

C) [tex]\frac{1}{125}[/tex]

Step-by-step explanation:

on edg

what is 100 × 100
A: 1000
B: 700
C: 200
D: None of the Above​

Answers

Answer:

The answer is 10,000

Step-by-step explanation:

So the answer is not there so it is none of the above

100 x 100 is 10,000 so the answer would be none of the above

HURRY PLEASE!!! IM BEING TIMED. I WILL GIVE YOU BRAINLIEST!

Answers

Answer:

Josh charges $5 more than Lindsay

Step-by-step explanation:

Answer:

b

Step-by-step explanation:

lindsay's equation is y=6x+15.

you compare the first row and second row to find the cost per dog and then subtract from the total to find the initial cost.

Find the value of each expression
-22-(-5)

Answers

Answer:

-17

Step-by-step explanation:

-22-(-5) = -22+5 = -17

Answer:

the answer is -17

Step-by-step explanation:

-22-(5)-22+5=-17

Given that z is a standard normal random variable, find the value of z for each situation. a. The area to the right of z is 0.01.

Answers

Answer: =1.34

Step-by-step explanation:

In standard density curve

P(Z<z) = Area left of z, P(Z>z) = area right of z.

P(Z<z) +P(Z>z) =1

Given:  z is a standard normal random variable.

To find : value of z if rea to the right of z is 0.01.

i.e. P(Z>z) =0.01

P(Z<z) =1-0.01 = 0.09

from z-score table, z value for this is 1.34.

Hence, z= 1.34

Help me please?? ????

Answers

Answer:

40 days

Step-by-step explanation:

8 × 5 = 40

[character limit pass]

What is happening to the pieces (units) when the numerator and denominator are getting larger?
I NEED HELP!!!!!!

Answers

Answer:

the number itself, (units) are getting bigger

Step-by-step explanation:

Write an equation to show " buying 2 boxes of crayons and $4.00 each."

Answers

Answer:

4+4is the answer hope ot helps

Which simplified ratio correctly compares 30 inches to 2 feet?
01:15
O 15:1
O 5:4
04:5

Answers

Answer:

15:1

Step-by-step explanation:

30/2=15

2/2 = 1

15:1

Please help I’m stuck on this...30 points for the best answer pls hurry and help

Answers

Answer:

it is A, the first one

Step-by-step explanation:

bc +6 and then -10 it ends up on -4

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