Mathematics High School

Which conjunction or disjunction is equivalent to the following inequality?
|a - 9| ≤ 4

a - 9 ≤ 4 AND a - 9 ≤ - 4

a - 9 ≤ 4 AND a - 9 ≥ - 4

a - 9 ≤ 4 OR a - 9 ≤ - 4

a - 9 ≤ 4 OR a - 9 ≥ - 4

Answers

Answer 1
Use the general definition:

|x - a| ≤ k => - k ≤ x - a ≤ k

So, |a - 9| ≤ 4 => - 4 ≤ a - 9 ≤ 4

Which is a - 9 ≥ - 4 and a - 9 ≤ 4.

That is the second option.

Answer: a - 9 ≤ 4 and a - 9 ≥ - 4
Answer 2

Answer:

a - 9 ≤ 4 and a - 9 ≥ - 4

Step-by-step explanation:

Related Questions

n Monday, Elsbeth’s bank account balance was -$16.75. On Tuesday, she deposited a check for $5.72. On Thursday, she deposited $16.75. What is her new balance? -16.75 + (5.72 + 16.75) Use the commutative property to get: -16.75 + (16.75 + 5.72) Use the associative property to get: (-16.75 + 16.75) + 5.72 On Friday, Elsbeth deposited her pay check for $872.56. What was the account’s final total? -$866.84 $878.28 $895.03 $903.10

Answers

Start by writing out the costs; 

-$16.75+($5.72+16.75) 
=5.72 

$5.72 + $872.56= 878.28

Hope I helped :) 

Answer:

Option B. $878.28

Step-by-step explanation:

On Monday, Elsbeth's bank account balance was =  $-16.75

She deposited a check = $5.72

On Thursday, she deposited = $16.75

Her new balance = -16.75+( 5.72 + 16.75)

                            = $5.72

On Friday Elsbeth deposited her pay check for = $872.56

The account's final total = 872.56 + 5.72 = $878.28

Elsbeth's account's final total was $878.28.

Option B. $878.28.

Graph ƒ(x) = -x + 2. Click on the graph until the graph of ƒ(x) = -x + 2 appears.

Answers

f(x) = -x + 2 is a reflection across the x-axis and a phase shift two units up.

The last graph is correct, with the points at (0,2) and (2,0)

Answer with Step-by-step explanation:

We have to graph f(x) =  -x + 2

When x=0 , f(x) = 2

When f(x)=0 , x=2

Hence, the graph passes through the points:

(0,2) and (2,0)

So, the correct graph of f(x) = - x + 2 is the last one which is shown below

What is the function

Answers

The graph shows us that the slope of f(x) is -2. Now we gotta find the slope of g(x) to compare it to that of f(x). The equation of g(x) is in slope-intercept form (y = mx + b, where m is the slope and b is the y-intercept), so the slope is given to us for that one as well: it's -6. A line with a slope of -6 will be steeper than a line with a slope of -3, therefore the answer is B - the slope of f(x) is less than the slope of g(x).
Hope this helps.

Calvin cleans 3/5 of his bathroom with 1/3 of a bottle of cleaning solution how much solution would he use if he cleaned the whole bathroom

Answers

The answer is:  "5/9 of a bottle" .
_________________________________
Explanation:
______________________________________________
(1/3) / (3/5) = x / (5/5) ;  solve for "x" ;  in which "x" is the number of bottles used to clean the whole bottle;

Rewrite as:

(1/3) / (3/5) = x / (1) ;

Rewrite as:  (1/3) / (3/5) = x ;

 {since "x / 1 = x" ;  since any value, divided by "1", results in that same value}.
_________________________________________
 (1/3) / (3/5) = x

 (1/3) / (3/5) = (1/3) * (5/3) = (5*1) / (3*3) = x = 5/9 .
_________________________________
The answer is:  "5/9 of a bottle" .
_________________________________
The whole bathroom means 1.
Next, what we have to do is compare the statements. That will be;
3/5 of bathroom=1/3 solution
1=Y
I represented the unknown with Y
Next, you need to cross and multiply. That means 1 will multiply 1/3 to give 1/3 and Y will multiply 3/5 to give 3Y/5. So you will have;
3Y/5=1/3
Cross and multiply again. 5 will multiply 1 to give 5 and 3Y will multiply 3 to give 9Y. That will be;
9Y=5
Divide both sides by 9. That will be;
Y=5/9
The answer is 5/9 of the bottle.
Hope that helped. Have a nice day


Megan has a bag of beads. She uses 28 beads to make each necklace. She makes 12 necklaces. Megan has 135 beads left over.

Answers

If you are asking for how many beads she used in total for the 12 necklaces it is 
336. If you are asking how many beads she had before making the necklaces it is 471. If you are asking how many necklaces can she make with the leftover beads it is about 4. Hope this helps plz mark a crown. 

If y = 2x - 3, then which of the following ordered pairs lies on the graph?

Answers

2,3 would be one of the odered pairs that you could use, unless the answers are different than that. Hope I was a help to you!

Lester has sold $51 worth of sports drinks at his concession stand today. Each drink sells for $3. He hopes to sell at least $300 worth of drinks over the course of the entire day. Let x be the number of drinks he will sell over the rest of the day. Which inequality precisely represents the condition of Lester meeting his goal?
A.51 + 3x ≥ 300
B.51 + 3x > 300
C.3x ≥ 300+ 51
D. 3x > 300 + 51

Answers

First you should evaluate the givens. We know that so far Lester has sold $51 of drinks. Every drink costs $3 and he wants to sell at least $300 worth of drinks at the end of the day. x represents the number of drinks he wants to sell, which must be at least $300. Now we can put this into an inequality.

Since Lester wants a minimum of $300, he needs the amount to be equal to or greater than 300, because if it were any less he would not meet his goal.

> 300

Every drink costs $3, and x represents the number of drinks he needs to sell to get at least $300. Multiplying 3 and x together will give us the rest of the $300 answer.

3x > 300

We cannot forget that Lester already has $51, however, so we will add this to the amount of money from the rest of the drinks he needs to sell.

51 + 3x > 300

This makes A. our final answer. I hope my explanation made sense!

What is the equation in point slope form of the line that passes through the point (−1, −3) and has a slope of 4?

y−1=4(x−3)
y+3=4(x+1)

Answers

I agree with the second answer. Was this correct?



If inflation is 4% a year compounded annually, what will it cost in 20 years to buy a house currently valued at $75,000.00?

Answers

1.04^20=2.2
75000*2.2=$164334 as the value of the house in 20 years
☺☺☺☺

Compound interest is the interest that is made from the principal and the interest as well in consecutive years.

The cost of the house in 20 years valued currently at $75,000 is $1,64,250.

What is compound interest?

Compound interest is the interest that is made from the principal and the interest as well in consecutive years.

The formula for amount compounded anually:

A = P [tex](1 + \frac{R}{100})^{n}[/tex]

We have,

Principal = $75,000

Rate = 4%

Time = n = 20 years

The amount after 20 years:

A = P [tex](1 + \frac{R}{100})^{n}[/tex]

A = 75,000 [tex](1 + 0.04)^{20}[/tex]

A = 75,000 x [tex]1.04^{20}[/tex]

A = 75,000 x 2.19

A = $1,64,250

Thus,

The cost of the house in 20 years valued currently at $75,000 is $1,64,250.

Learn more about compound interest here:

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Which of the following are the factors of t4 – 81? A. (t – 3)(t + 3)(t2 + 9) B. (t – 3)2(t + 3)2 C. (t – 3)(t + 3)2 D. (t2 – 9)(t2 – 9)

Answers

The answer is letter D
I am pretty sure the factors of t4 - 81 is D

Math Help??


What is the value of X?

Answers

Heres an example i dont have the anwser to your question tho Hope i helped(1) x + 2y = 4 

(2) 5x + y + 15 = 3x - 3y + 23

What is the x-intercept of a line that passes through the point (3, 4) and has a slope of 2?

Answers

Y-int = -2
work attached 

When multiplying numbers in scientific notation you blank the coefficients and substract the exponents?

Answers

For the sake of example, let's multiply the two numbers [tex]2.3 \times 10^5 [/tex] and [tex]3.5 \times 10^7[/tex] together. Altogether, we have:

[tex]2.3\times10^5\times3.5\times10^7[/tex]

Rearranging the expression, we can group the exponents and coefficients together:

[tex]2.3\times3.5\times10^5\times10^7[/tex]

Multiplying each out, we notice that since [tex]10^5[/tex] and [tex]10^7[/tex] have the same base (10), multiplying them has the effect of adding their exponents, which leaves us with:

[tex]2.3\times3.5\times10^{5+7}=8.05\times10^{12}[/tex]

The takeaway here is that multiplying two numbers in scientific notation together has the effect of multiplying its coefficients and adding its exponents.

solve this inequality 2(4x-3)≥-3(3x)+5x?

Answers

the first option, x is greater than and equals to 0.5

Answer:

x ≥0.5

Step-by-step explanation:

Given : 2(4x-3)≥-3(3x)+5x.

To find : solve this inequality.

Solution : We have given that

2(4x-3)≥-3(3x)+5x.

Distributes 2 over (4x-3) and -3 over 3x.

8x - 6 ≥ -9x + 5x .

8x - 6 ≥ -4x .

On adding both side by 4x

8x + 4x - 6 ≥ 0 .

12 x - 6 ≥ 0

On adding both sides by 6.

12 x ≥ 6.

On dividing both sides by 12.

x ≥ [tex]\frac{6}{12}[/tex] .

x ≥ [tex]\frac{1}{2}[/tex] .

x ≥0.5.

Therefore, x ≥0.5

PLZ HELPP ME WITH THIS MATH PROBLEM

Answers

(fog)(x) = f(g(x))

= (1 - 5x^2)^3, all real numbers

answer is B.

Do the dimensions of 9 cm, 40 cm, and 41 cm form a right triangle? explain.

Answers

yea because 9^2 +40^2=41^2 this is the law

Please help me i really need help

Answers

f(5) = 12230.590464
f(10) = 9972.48954
9972.49/12230.59 = .815
1 - .815 = .185
every 5 years it loses 18.5% of it's value.

When applying for a loan, you should _____.

Answers

you should also have a little money saved aside so that you can pay them the money you saved and then work for the rest of the money you need to pay off

sorry if im incorrect



Given: -7x < -21.

Choose the solution set.
A. {x | x < -3}
B. {x | x > -3}
C. {x | x < 3}
D. {x | x > 3}

Answers


[tex] - 7x < - 21[/tex]
Divide both sides by - 7. Switch the direction of the inequality when dividing by a negative number.
[tex]x > 3[/tex]
The answer is D.

PLEASE HELP

simplify the expression

2. 10r^(-7)t^3

Answers

10r^(-7)t^3
= 10t^3 / r^7

hope it helps

x(x+8) = 256 square yards
solve for x


im having a lot of trouble please help

Answers

We want to solve
x(x + 8) = 256

Expand the left side.
x² + 8x = 256
Collect all terms on the left side.
x² + 8x - 256 = 0

Solve with the quadratic formula.
x = (1/2)*[-8 +/- √(8² -4*1*(-256)) ]
   = -4 +/- (1/2)*√(1088)
   = -4 +/- 16.4924
x = 12.4924, or x = -20.4924

Answer: x = 12.4924 or x = -20.4924

The table below represents the distance a person runs as a function of time:
Time distance meters
x f(x)
10 60
13 78
16 96
19 114

he average rate of change of the function between x = 10 to x = 16 is m/s and represents the person's speed. (3 points)

Answers

The given data is

  x   f(x)
---- ------
10   60
13   78
16   96
19   114

f(x) =  distance, m
x = time, s

Between x = 10 to x = 16,
f(x) varies by 96 - 60 = 36 m,
x vaires by 16 - 10 = 6 s.

The average speed is
v = (36 m)/(6 s) = 6 m/s.

Answer: 6 m/s

Jackson can lay 6000 ft² of tile in 3 h. What is Jackson’s tile-laying rate?

Answers

divide 6000 by 3

6000 / 3 = 2000

 so he can do 2000 sq ft per hour

The answer by musiclover10045 is correct - 2000 is the answer. I got it right on my quiz.


1. Daniel served Dinner for table 14. The check came to $100. The customers tipped him 25%. How much was his tip?

2. Sammy served lunch for table 7. The total came to $55. The customers gave a 15% tip to Sammy. How much was his tip?

3. Cat served dessert for table 3 The total cost was $20. The customers give a tip of 12% to cat. How much was your tip?

At the Yum Yum Cafe , the waiters come binder tips and divide the total by the number of waiters. Today’s tip total is $132, and three waiters are working. How much money in tips does each waiter get?

Answers

Daniel, Sammy, and Cat receive $25, $8.25, and $2.40 respectively in tips. The total tip amount for the day is $132, and with three waiters working, each waiter gets an equal share of $44 in tips.

Calculating Tips for Waiters

To calculate the tip for each waiter, we will multiply the total bill amount by the percentage of the tip and then convert that percentage into a decimal. Here are the step-by-step solutions for each waiter:

Daniel's Tip: For Table 14, the bill was $100. A 25% tip is calculated as $100 x 0.25 = $25.

Sammy's Tip: For Table 7, the bill was $55. A 15% tip is calculated as $55 x 0.15 = $8.25.

Cat's Tip: For Table 3, the bill was $20. A 12% tip is calculated as $20 x 0.12 = $2.40.

To find out how much each waiter gets from the total tips, we add up all the tips: $25 + $8.25 + $2.40 = $35.65. Since the total tip amount for the day is $132, we divide this by the number of waiters working, which is three: $132 / 3 = $44. Therefore, each waiter gets $44 in tips.

The sum of 6 consecutive odd numbers is 204. What is the fourth number in this sequence?

Answers

204 /6 = 34

29 +31 +33 + 35 +37 +39 = 207

4th number = 35

The fourth number is 35

Estimate the decimal factors, then multiply to estimate the product.

1. 5.3 rounded to the nearest whole number is ____ .

2. 7.9 rounded to the nearest whole number is ____ .
3. (5.3)(7.9) ≈ ____ .

Answers

1) 5
2) 8
3) you can easily look that up i wouldn’t know it off the top of my head

Answer:

1. 5

2. 8

3. 40

Step-by-step explanation: So rounding the factors is an easy way to estimate the product of 5.3 and 7.9.

The real answer is 41.87 and 40 is a reasonable approximation, Your welcome.

What number is 30% of 150?.

Answers

Here is your answer:

30% of 50=45

Your answer is 45 because...

150/x=100/30
(150/x)*x=(100/30)*x
150=3.33333333333*x
(3.33333333333) to get x
150/3.33333333333=x
45=x
x=45

Your answer is...
x=45

which blood type was donates by the largest percent of people?

Answers

The answer is o+ Hope this helped.

Let f(x)=8^x.

Which function represents a transformation of f(x) by a vertical stretch with factor 2??

A- g(x)=1/2*8^x

B- g(x)=8^2x

C- g(x)=2*8^x

D- g(x)=8 1/2^x

Please help and give reasoning with your answer. I’m very unsure.

Answers

Final answer:

The function that represents a vertical stretch of factor 2 of f(x) = 8^x is g(x) = 2 * 8^x.

Explanation:

The function that represents a vertical stretch of factor 2 of the function f(x) = 8^x is g(x) = 2 * 8^x.

To understand why, consider that a vertical stretch by a factor of 2 means that every y-coordinate in the graph is multiplied by 2. So, if we want to stretch the function f(x) = 8^x vertically by a factor of 2, we multiply the function by 2 to get g(x) = 2 * 8^x.

Learn more about Vertical stretch of function here:

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The following triangle FOX is transformed using a rotation: Triangle FOX is shown. F is at negative 1, 1, O is at negative 2, 3, X is at negative 3, 0. Which could be coordinates of F'O'X' after the rotation? (4 points)

Answers

I think it is 1,1,O but I don’t think you should believe me because I don’t know this very well

The answer is F=(1,1), O=(3,2), X=(0,3)

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