Mathematics High School

A publisher claims that the average salary paid at its company is $37,500 but it could differ as much as $4,500. Write and solve an absolute value inequality to determine the range of salaries at this company.

|x − 37500| ≤ 4500; The salaries range from $33,000 to $42,000
|x − 37,500| ≤ 4500; The salaries are less than $33,000 or greater than $42,000.
|x − 37500| ≥ 4500; The salaries range from $33,000 to $42,000
|x − 37,500| ≥ 4500; The salaries are less than $33,000 or greater than $42,000.

Answers

Answer 1
|x − 37500| ≤ 4500; The salaries range from $33,000 to $42,000

Related Questions

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

Julie yard is rectangular.One side of the yard is 100 feet wide. The total area of the yard is 3,000 square feet. What is the length of the other side of the yard?

Answers

Area= length x width
Divide area by width to find missing side
3000➗100= 30
The other side is 3O feet .

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

The function f(x) = x2 – 4x + 4 is shifted 3 units to the right to create g(x).

A. g(x) = (x – 3)2 – 4(x – 3) + 4
B. g(x) = (x2 – 4x + 4) – 3
C. g(x) = (x2 – 4x + 4) + 3
D. g(x) = (x + 3)2 – 4(x + 3) + 4

Answers

Answer:

answer is A for APEX..

Step-by-step explanation:

The function f(x) = [tex]x^{2} -4x+4[/tex] is shifted 3 units to the right to create

g(x) = [tex](x-3)^{2}-4(x-3)+4[/tex] .

What is shifting of a function?

A shift is a rigid translation in that it does not change the shape or size of the graph of the function. All that a shift will do is change the location of the graph. A vertical shift adds/subtracts a constant to/from every y-coordinate while leaving the x-coordinate unchanged.

Given

f(x) = [tex]x^{2} -4x+4[/tex]

The function f(x) = x2 – 4x + 4 is shifted 3 units to the right to create g(x).

If the function is shifted to the left it is going to plus(+).

If the function is shifted to the right it is going to minus(-).

So, x = x - 3

g(x) = [tex](x-3)^{2}-4(x-3)+4[/tex]

The function f(x) = [tex]x^{2} -4x+4[/tex] is shifted 3 units to the right to create

g(x) = [tex](x-3)^{2}-4(x-3)+4[/tex] .

Option A is correct.

Find out more information about shift here

https://brainly.com/question/11943912

#SPJ2

A triangle has sides of lengths 6, 2, 7. Is it right triangle?

Answers

By the pythagoreans' theorem,

All right-angle triangle with the opposite squared + adjacent squared = hypotenuse squared.

6² + 2² ≠ 7²
Therefore the triangle is not a right angle triangle

Answer is B.

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

Graph each equation by using the x- and y-intercepts

Answers

You have the correct graph. Plug in y = 0 and solve for x to get x = -3. Do the same for x = 0 and solve to get y = -3. 

x intercept = -3 which is the point (-3,0)
y intercept = -3 which is the point (0,-3)

Nice job on getting the correct graph with the correct points.

Find the y-intercept of the line whose equation is 2x - 3y = -6.

Answers

to find y intercept, make x = 0 then solve equation:

2x-3y=-6

2(0) - 3y=-6

-3y =-6

y = -6 / -3

y=2

 so y intercept is (0,2)

the answer to your problem is (2x-3y=12) good luck ;)

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.

Solve the following system of equations.

x − 2y = 5
−3x + 2y = 7

A. x = 3, y = −1
B. x = 11, y = 11/2
C. x = 3, y = 1
D. x = −6, y = -11/2

Answers

Hey Kayla!

Let me help you out real quick.

x - 2y = 5
-3x + 2y = 7

We need to solve x - 2y =5 for x
x - 2y = 5
x = 5 + 2y
Now substitute 2y + 5 for x in -3x + 2y = 7
-3x + 2y = 7
-3(2y + 5) + 2y = 7
-6y - 15 + 2y = 7
-4y - 15 = 7
-4y = 7 + 15
-4y = 22
y = 22/-4
y = -11/2

Now we need to substitute -11/2 for y in x= 2y + 5
x = 2y + 5
x = 2(-11/2) + 5
x = -22/2 + 5
x = -6

Thus,

The answer is x = -6 and y = -11/2

The correct answer is option D

Good luck with your studies :)

You got it! 

What is f(-4) if f(x)=|7x-3|

Answers

Substitute the given into the function

f(-4) = |7(-4) - 3|
now solve
f(-4) = |-28 - 3|
f(-4) = | -31| 
the absolute value of |-31| is 31
so, 
f(-4) = 31

Hope this helps :)
f(-4) means subsitute -4 for every x you see in the function

f(-4)=|(7(-4)-3|
f(-4)=|-28-3|
f(-4)=|-31|

|-31| means absolute value of -31 which just takes the distance the number is from 0 (or makes it positive if it is negative and leaves it alone if it is positive)

|-31|=31
f(-4)=31

Please help!!!

System of Equations Applications


Bill and Cody are selling cookie dough for a school fundraiser. Customers can buy packages of white chocolate chip cookie dough and packages of double chocolate chip cookie dough. Bill sold 9 packages of white chocolate chip cookie dough and 2 packages of double chocolate cookie dough for a total of $200. Cody sold 2 packages of white chocolate chip cookie dough and 13 packages of double chocolate chip cookie dough for a total of $283. find the cost each of one package of white chocolate chip cookie dough and one package of double chocolate chip cookie dough.

Answers

We will use w for white choco cookies and b for choco cookies.
Bill sold 9 for w and 2 for b for a total of 200. So 9w + 2b = 200
Cody sold 2 for w and 13 for b for a total of 283. So 2w + 13b = 283

Lets solve by elimination.

[tex]\begin{bmatrix}9w+2b=200\\ 2w+13b=283\end{bmatrix}[/tex]

[tex]\mathrm{Multiply\:}9w+2b=200\mathrm{\:by\:}2:\quad 18w+4b=400[/tex]
[tex]\mathrm{Multiply\:}2w+13b=283\mathrm{\:by\:}9:\quad 18w+117b=2547[/tex]

[tex]\begin{bmatrix}18w+4b=400\\ 18w+117b=2547\end{bmatrix}[/tex]

18w + 117b = 2547
-
18w + 4b = 400
/
113b = 2147

[tex]\begin{bmatrix}18w+4b=400\\ 113b=2147\end{bmatrix}[/tex]

[tex]113b=2147 \ \textgreater \ \mathrm{Divide\:both\:sides\:by\:}113 \ \textgreater \ \frac{113b}{113}=\frac{2147}{113} \ \textgreater \ b=19[/tex]

[tex]\mathrm{For\:}18w+4b=400\mathrm{\:plug\:in\:}\ \:b=19[/tex]

[tex]18w+4\cdot \:19=400 \ \textgreater \ \mathrm{Multiply\:the\:numbers:}\:4\cdot \:19=76 [/tex]

[tex]18w+76=400 \ \textgreater \ \mathrm{Subtract\:}76\mathrm{\:from\:both\:sides} [/tex]

[tex]18w+76-76=400-76 \ \textgreater \ 18w=324 \ \textgreater \ \mathrm{Divide\:both\:sides\:by\:}18[/tex]

[tex]\frac{18w}{18}=\frac{324}{18} \ \textgreater \ w=18[/tex]

Therefore the cost of the white chocolate chip cookies is $18 and the double choco is $19
Bill: 9w+2d=$200
Cody:. 2w+13d= $283

2(9w+2d=$200)
-9(2w+13d=$283)

18w+4d=$400
-18w-117d=-$2547

-113d= -2147

d= $19

9w+2(19)=200

9w+38=200

9w= 162

w= $18

double chocolate chip cookie dough:$19
white chocolate chip cookie dough: $18

Rational Exponent
Explain why the square root of a number is defined to be equal to that number to the 1/2 power.

Answers

The concept of radicals and radical exponents is tricky at first, but makes sense when we look into the logic behind it. 

When we write a radical in exponential form, like writing √x as x^(1/2), we are simply putting the power of the radical in the denominator (bottom number) of the exponent, and the numerator is the power we raise the exponent to, or the power that would be inside the radical. 
In our example, √x is really ²√(x¹), or the square root of x to the first power. For this reason, we write it as x^(1/2).

Let's say we wanted to write the cubed root of x squared, in exponential form. 
In radical form, it would look like this:
³√(x²) . This means we square x, and then take the cubed root.
In exponential form, remember that we take the power of the radical (3), and make that the denominator of the exponent, and keep the numerator as the power that x is raised to (2). 
Therefore, it would be x^(2/3), or x to the 2 thirds power. 

Just like when multiplying by a fraction, you multiply by the numerator and divide by the denominator, in exponential form, you raise your base number to the power of the numerator, and take the root of the denominator. 

Answer:

Sample Response:

Squaring and square root are inverses, so one should "undo" the other. That is, squaring the square root of a number results in the number. Using the power of a power rule, you multiply the exponents. Since a number to the first power is itself, the product of the exponents must equal 1. This means that the power of the square root must be the reciprocal of 2, or one half.

Step-by-step explanation:


Un número entero de tres dígitos es igual a 25 veces la suma de sus dígitos. Si los tres dígitos se invierten, el número que resulta excede al número dado por 198.
El dígito de las decenas en uno menos que la suma de los dígitos de las centenas y de las unidades. Encuentra el número.

Answers

La repuesta es 375，porque 3+7+5 es 15，y 15x25 es 375. Tambien el digito de las decenas es uno menos que la suma de los digitos de las centenas y de las unidades.

If you shift the linear parent function, f(x) = x, down 6 units, what is the equation of the new function?

A. g(x) = x + 6
B. g(x) = x
C. g(x) = 6x
D. g(x) = x – 6

Answers

Answer:

Option D is correct

[tex]g(x) = x-6[/tex]

Step-by-step explanation:

Vertically down :

If y =f(x) is a parent function, then the new function g(x) b units  vertically down is, g(x) = f(x) -b.

As per the statement:

Given the parent function:

[tex]f(x) = x[/tex]

To shift linear parent function vertically down 6 units.

By definition we have;

g(x) = f(x) -6

⇒[tex]g(x) = x-6[/tex]

Therefore, the equation of new function g(x) is, [tex]g(x) = x-6[/tex]

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.

The sides of a triangle are in the ratio 5:12:13. Describe the length of the shortest side is the perimeter is not more than 120 inches

Answers

5,12,13 is a triple, i.e. integer values of a right triangle.  It's Perimeter is 30.
Then <= 120 yields 4 times this triple, yielding another triple of 20,48,52

which of these ordered pairs is a solution to the inequality 4x+y>-6

Answers

The ordered pair is (1, -1) a solution to the inequality 4x+y>-6. which is the correct answer would be option (C).

What is inequality?

Inequality is defined as mathematical statements that have a minimum of two terms containing variables or numbers that are not equal.

We must determine if the inequality holds for a certain set of ordered pairs in order to determine which ordered pairs constitute the answer to the inequality.

We have been given inequality is:

⇒ 4x + y > -6

Option (A) (1, -12)

⇒ 4x + y > -6

Substitute x = 1 and y = -12 in the inequality, we get

⇒ 4(1) + (-12) > -6

⇒ -8  > -6

This is false.

Option (B) (0, -9)

⇒ 4x + y > -6

Substitute x = 0 and y = -9 in the inequality, we get

⇒ 4(0) + (-9) > -6

⇒ -9  > -6

This is false.

Option (C) (1, -1)

⇒ 4x + y > -6

Substitute x = 1 and y = -12 in the inequality, we get

⇒ 4(1) + (-1) > -6

⇒ 3  > -6

This is true.

Hence, the correct answer would be an option (C).

Learn more about the inequalities here:

brainly.com/question/20383699

#SPJ2

We start with triangle ABC and see that angle ZAB is an exterior angle created by the extension of side AC. Angles ZAB and CAB are a linear pair by definition. We know that m∠ZAB + m∠CAB = 180° by the . We also know m∠CAB + m∠ACB + m∠CBA = 180° because . Using substitution, we have m∠ZAB + m∠CAB = m∠CAB + m∠ACB + m∠CBA. Therefore, we conclude m∠ZAB = m∠ACB + m∠CBA using the .

Answers

Final answer:

To prove that m∠ZAB = m∠ACB + m∠CBA, we start with triangle ABC and use the fact that angles in a triangle add up to 180°. Angle ZAB and CAB are a linear pair, so they add up to 180°. By substitution, we can conclude that m∠ZAB = m∠ACB + m∠CBA.

Explanation:

To prove that m∠ZAB = m∠ACB + m∠CBA, we start with triangle ABC. Angle ZAB is an exterior angle created by the extension of side AC. Angle ZAB and CAB are a linear pair, which means they add up to 180°. We also know that angle CAB + angle ACB + angle CBA = 180° because the angles in a triangle add up to 180°. Using substitution, we have m∠ZAB + m∠CAB = m∠CAB + m∠ACB + m∠CBA. Therefore, we can conclude that m∠ZAB = m∠ACB + m∠CBA using the fact that the angles in a triangle add up to 180°.

Learn more about Triangles here:

https://brainly.com/question/37610445

#SPJ3

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!

|3x-2|+2y if x=-4,y=7,and z=-9

Answers

The answer would be 26 because you would replace all the variables making the equation be |3*-4-2|+2*7. Then you would solve the absolute value making it 12+2*7. Next solve the multiplication making the equation 12+14 making your answer 26.

Randy is twice as old as his sister jane. together the sum of their ages is 15. how old is randy?

Answers

Final answer:

Randy is 10 years old.

Explanation:

The question is about solving a simple algebraic equation involving ages.

We are told Randy is twice as old as his sister Jane, and the sum of their ages is 15 years.

If we let Jane's age be represented by 'j', then Randy's age would be '2j' as he is twice as old as Jane.

The equation to represent the sum of their ages is:

j + 2j = 15

To find Jane's age, we combine the like terms:

3j = 15

Now, we divide both sides of the equation by 3 to isolate 'j':

j = 15 / 3

j = 5

Therefore, Jane is 5 years old. To find Randy's age, we multiply Jane's age by 2:

Randy's age = 2 * Jane's age

Randy's age = 2 * 5

Randy's age = 10

So, Randy is 10 years old.

For the following geometric sequence, find the recursive formula.
{-80, 20, -5, ...}

Answers

Divides by -4 throughout
common ratio/r=-1/4
ar^(n-1), where a is the first term
substitute all the numbers in it
-80(-1/4)^(n-1)

Answer:

[tex]a_n =-\frac{1}{4} \cdot a_{n-1}[/tex]

Step-by-step explanation:

{-80, 20, -5, ...}

General recusive formula for geometric sequence is

[tex]a_n = r \cdot a_{n-1}[/tex]

Where 'r' is the common ratio

To find common ratio 'r' we divide second term by first term

[tex]r=\frac{20}{-80} =-\frac{1}{4}[/tex]

Replace 'r' with -1/4

First term is -80

Recursive formula becomes

[tex]a_n =-\frac{1}{4} \cdot a_{n-1}[/tex]

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:

https://brainly.com/question/30105263

#SPJ2

50 POINTS! + BRAINLIEST! PLEASE HELP

Answers

slope = rise over run = y/x

A (-1,3) slope = 3/-1 = -3

B (1,2) slope = 2/1 = 2

C (-3,-1) slope = -1/-3 = 1/3

2 lines need to be negative reciprocals in order to be a right triangle

negative reciprocal of -3 is 1/3

 so this is a right triangle

Answer: yes it is

Step-by-step explanation: put into a graph and it will become clear

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?



The number 1.258201... can be classified as which of the following? Select all that apply. Real, rational, irrational, whole, integer ,natural
Its a multiple choice question

Answers

It is real and irrational.

The decimal does not terminate and the decimal pattern does not repeat, so the number can not be rationalized.

The number can be classified as both real and irrational

The given number:

= 1.258201

A real number is any  number that can represent a distance along a line

A rational number is a real number that can be expressed in form a ratio, it usually have terminating decimals.

An irrational number is any real number that cannot be expressed in form of ratio, it doesn't have terminating or repeating decimals.

A whole number does not contain fractions, it is usually positive integers.

Integers are whole numbers that includes negative and positive numbers.

The given number is a real number but it doesn't contain terminating or repeating decimals. Hence it is irrational number.

Learn more here: https://brainly.com/question/21957255

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)

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

Zack is purchasing a bag of apples. The cost of apples is proportional to the weight of the apples in pounds as shown on the graph. Which statements are true about the cost of the apples?

Which statements are true about the cost of the apples?

Select each correct answer

1 lb of apples will cost Zack $2.50.

10 lb of apples will cost Zack t $4.

4 lb of apples will cost Zack $10.

2.5 lb of apples will cost Zack $1.

Answers

Answer:

1 lb of apples will cost Zack $2.504 lb of apples will cost Zack $10

Step-by-step explanation:

The graph axesand common sense tell you that each ordered pair represents ...

  (weight, cost)

So the ordered pairs (1, 2.50) and (4, 10) mean ...

  1 lb of apples will cost Zack $2.50

  4 lb of apples will cost Zack $10

A and C should be the correct answers if I'm not mistaken

Other Questions
Colton has trouble remembering information for his tests because he crams the night before. Which would be the best study habit for Colton to commit to? Explain why thanatology is a subfield of psychology. What proportion of the colonial population lived in cities? which of the following is an example of a want,versus a need? Which is the most likely reason that Chaucer begins The Canterbury Tales' prologue with a description of spring? A.) To surprise the reader by connecting spring to the idea of a long journey B.) To indicate the short period of time available to make pilgrimage C.) to establish a mood of gentle anticipation before introducing the characters D.) The foreshadow the harshness of the journey the characters are about to make. The energy of the Sun is converted into energy by the plants. Identify each sentence as simple, compound, complex, or compound-complex. "In spite of the harmful effects of kudzu, it still has several benefits." I have read all about simple, compound, complex, and compound-complex. However, I cannot figure out how it works in an actual sentence. What am I looking for? In spite of the harmful effect of kudzuIs this a dependent clause? I think so because it needs more to complete it. It still has several benefits. This to me also sounds like a dependent clause. And a fragment is not an option. What am I missing? Please help me with this. It will be so appreciated. Bonjour! j' (1) cours de littrature le jeudi. nous (2) un professeur sympa. mais ma copine caroline n' (3) pas de chance. elle (4) un professeur d'histoire dsagrable. elle et ses camarades de classe (5) un examen difficile vendredi. tu (6) envie de rencontrer mon professeur de littrature? please please please help me :( A movie rental website charges $5.00 per month for membership and $1.25 per movie.How many movies did Andrew rent this month if this month's bill was $16.25? What involves extensive in depth studies of an individual? Climate and environment affected what choice for hunter-gatherers?leaderslanguageenemieshousing DNA replication is the process by which DNA is copied during the cell cycle. True or False. Is it possible to construct a triangle with side lengths of 11 cm, 15 cm, and 21 cm? Why or why not? name three quaderlateral that only sometimes have right angle The volume of this rectangular prism is 6x3. What does the coefficient 6 mean in terms of the problem? A.The total volume of the prism is 6 cubic units. B.The length is 6 times the width. C.The width is 6 times the height and the length. D.The length of the prism is 6 units. FREE POINTS!!!!!!!!!! 10 POINTS Len's recipe for blueberry muffins calls for 110.25 grams of brown sugar for the muffin batter and an additional 55.45 grams of brown sugar for the topping. Len wants to make 4.5 batches of muffins. Enter the total amount of brown sugar that Len will need 15. Who did John Adams nominate to be the Commander-in-Chief of the Continental Army? The discovery of rich deposits of oil has changed the lives of the Arabs.True or False Abbey gets paid a flat rate of $10.00 to mow her neighbor's lawn plus an additional $5 per hour to rake the leaves. The money she earns is represented by the equation m = 5h + 10, where m represents the amount of money she earns, in dollars, and h is the number of hours she rakes leaves for. Which of the following equations can be used to find h, the number of hours she rakes leaves for? Steam Workshop Downloader