Austin makes $10 an hour working as a cashier at a bookstore. His employer requires him to work at least 10 hours per week and his current school schedule limits him to a maximum of 25 hours per week.

1. Write an equation that represents Austin's gross pay where x represents the number of hours he works per week and f(x) (as in functions) represents his gross pay.

2. What is the domain and range in this situation?

Answer:

Option B

Step-by-step explanation:

→ Find the option with the smallest power

Option B

Natalie’s current available balance is $116.07.

To find current available balance, we need to subtract pending deposits/ credits with pending withdrawals/ debits.

Account Balance = Pending deposits / credits – Pending Withdrawals /debits

= $126.02- $97.68 = $28.34

Available Balance = Account Balance + Current Posted Balance

= $28.34 +$87.73 = $116.07

Current Available Balance = $116.07

The balance in checking or demand accounts that is available for use by the client or account holder is known as the available balance. The accessible balance of an account holder may not match the current balance. Any unfinished transactions are often included in the current balance.

Pending Deposit Credits: Pending check deposits that haven't been processed, haven't been credited to your account, or didn't have availability when we got them.

Pending Deposit Debits: Your account is put on hold for the transaction's amount until it is processed.

Hence Natalie’s current available balance is $116.07.

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The value of X in the equation that allows a solution with the values of "a" and "b" is x = 16

An equation is the equality that has mathematical expressions on both sides of it, they can be functions, polynomials or others, there are no limits for them.

  Equations can be graphed, just like a function.

   We write the given equation

b = 3x + 4a

 and we have the values of the coefficients a and b, and these are:

  We substitute these values in the equation:

b = 3x + 4a

(12) = 3x + 4(-9)     :::: We solve the equation

12 = 3x -36

3x = 12 + 36

3x = 48

x = 48/3

x = 16

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Answer:

5/6

Step-by-step explanation:

Get LCD of 30 and add

9/30 + 16/30

25/30

Reduce

5/6

Answer:

Step-by-step explanation:

simplify

6/7x + 7= 31

6/7x+7-7=31-7

6/7x=24

6/7x=24/6/7

28

6/7(28)+15-8=31

24+15-8=31

39-8=31

The dimensions of the decks increased by the 11 feet.

According to the statement

We have to find that the length by which we increase the dimensions.

So, For this purpose, we know that the

The Area is the amount of space occupied by a two-dimensional figure.

From the given information:

Ashley has a deck that measures 22 feet by 11 feet. She wants to increase each dimension by equal lengths so that its area is tripled.

Then

The shape of the deck is the rectangle then dimensions is 22 feet by 11 feet.

Then

Area of the deck with the given dimensions =  Length * Breadth

Area of the deck with the given dimensions =  22* 11

Area of the deck with the given dimensions =  242.

Then the dimensions increased by the x

Then

Area of the deck with the given dimensions =  Length * Breadth

Area of the deck with the given dimensions =  (22+x)* (11+x)

Area of the deck with the given dimensions =  242 + 22x+11x+x^2

Area of the deck with the given dimensions =  242 + 33x+x^2

Then according to given details:

x^2 + 33x + 242 = 3*242

x^2 + 33x + 242 = 726

x^2 + 33x = 726 - 242

x^2 + 33x = 484

x^2 + 33x - 484 = 0

After solving

The value of the x become

x = 11 and x = -44

Then second option be neglected.

Then the length increased by the 11 feet.

So, The dimensions of the decks increased by the 11 feet.

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Answer:

55 sq ft

Step-by-step explanation:

okay so the are of the lil square is 9 sq ft and the area of the big square is 64 sq ft so j subtract the small from the big

Answer: 55cm ^2

Step-by-step explanation:

Area of a square is A=a^2

Area of small square is 3cm^2 = 9cm^2

Large square has an area of 8cm^2 = 64cm^2

64 - 9 = 55 cm^2

Therefore the remaining area is 55 centimeters squared

Bounce 2 is 2

Bounce 4 is 1/2

Bounce 5 is 1/4

Bounce 6 is 1/8

all of your equivalent heights are correct.

The inequality that represents the number of nights he can stay in Dallas is 155n+ 99 ≤ 850 (option d).

Here are inequality signs and what they mean:

Since his budget is $850, he can spent a total of $850 or less than $850 on the trip. The sign that would be used to represent this is ≤.

(Total hotel stay cost) + cost of flight ≤. budget

(cost per night x number of hotel stays) + $99 ≤ $850

155n + $99 ≤ 850

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Answer:

Answer is D

Step-by-step explanation:

The product of  -2.1. (-3.5) is  7.35

The product of  (-2.1 ) and (-3.5) =  [tex]-2.1\times-3.5[/tex]

                                                    =  7.35

So, the product of (-2.1) and (-3.5) is 7.35.

The quotient is the number which is produced when we perform division operations on two numbers. Fundamentally, it is the result of the division method. There are four primary wordings utilized within the arithmetic division such as divisor, dividend, quotient and remainder.

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The maximum and the minimum weight for the bags of sand are 36 and 35 pounds respectively

Here, we have

Weight = 35 pounds

Labeled weight = within 8 ounces

Convert ounce to pounds

So, we have:

Labeled weight = within 0.5 pound

The equation is then represented as

|x - 35| = 0.5

Where x represents the labeled weight

In (a), we have

|x - 35| = 0.5

Expand

x - 35 = 0.5 and x - 35 = -0.5

Add 35 to both sides

x = 36 and x = 35

Hence, the maximum and the minimum weight for the bags of sand are 36 and 35 pounds respectively

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In the given triangle the statement that holds true is [tex]b^2+c^2 < a^2[/tex]. Therefore, the option (c) is the correct option.

In the cosine formulas, the cosine (cos) function is discussed. Consider a right-angled triangle with one acute angle, x. The cosine formula is cosx = (adjacent side) / (hypotenuse), where "adjacent side" refers to the side adjacent to angle x and "hypotenuse" refers to the longest side of the triangle.

As per cosine rule fore given [tex]$\triangle$[/tex]ABC:

[tex]$\cos \theta=\frac{b^2+c^2-a^2}{2 b c}$$$[/tex]

According to the question;

For a given [tex]$\triangle$[/tex]ABC;

cos e < 0.

Therefore, [tex]\quad \frac{b^2+c^2-a^2}{2 b c} < 0 \\[/tex]

[tex]b^2+c^2 < a^2[/tex]

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The volume of pyramid is 9.16×10⁷ feet³.

We are given the measure of each side of Great Pyramid, which will be it's length and width. Also, we are given height. The formula for calculation of volume of pyramid is -

Volume = (length×width×height)÷3

Keep the values in formula to find the volume of Great Pyramid

Volume = (756×756×481)÷3

Performing multiplication on Right Hand Side of the equation to find the volume of Great Pyramid-

Volume = 274908816÷3

Solving the Right Hand Side of the equation, by performing division, we get the volume of Great Pyramid -

Volume = 9.16×10⁷ feet³

The volume of Great Pyramid is 9.16×10⁷ feet³.

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  955°C is  temperature (in celsius) is the rate constant equal to 0.08857 sec-1.

What is the short definition of activation energy?

The least amount of energy necessary to bring atoms or molecules into a state where they can undergo chemical transformation or physical transport is known as the activation energy .

K = [tex]A . e^{\frac{-Eq}{RT} }[/tex]

logk = logA = Eq/RT

log0.02629 = log5.57 × [tex]10^{10}[/tex] sec-1  -  [tex]\frac{125.6 * 10^{3} }{8.314 * T}[/tex]

                   = log5.57  + [tex]log 10^{10}[/tex]  - [tex]\frac{12.56 * 10^{3 J} }{8.314 * T}[/tex]

                   = log5.57  + 10log10 - 15.10 * 10³ J/T

   -1.5483 = 0.7458 + 10 - 15.10 * 10³/ T

  -1.5483 = 10.7458 - 15.10 * 10²/T

 - 15.10 * 10³/ T   = -1.5483 - 10.7458

   15.10 * 10³ /T = 12.2941

 T = 15.10 * 10³/ 12.2941

       = 1228K

       = 955°C

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Answer:

Step-by-step explanation:

cos(30) x tan (60) + sin (30) = (√3)/2 x √3 + 1/2 = 3/2 + 1/2 = 4/2 = 2

Answer:

5 50bw syfnauw dux fyq euw eywvr6b

Step-by-step explanation:

[tex](x+4)(2x+5)\\\\2x^2+5x+8x+20\\\large\boxed{2x^2+13x+20}[/tex]

The value of the inequality is x > 6

Inequalities are defined as mathematical relations that makes a non-equal comparison between two numbers , elements or expressions.

They are also used to compare two numbers on the number line by their size.

It is an order relationship showing —greater than, greater than or equal to, less than, or less than or equal to

Given the expression;

|1.3x + 7.8| > 0

collect like terms

1. 3x > 0 + 7. 8

1.3x > 7. 8

Make 'x' the subject

Divide both sides by 1. 3

1. x/ 1. 3 > 7. 8/ 1. 3

x > 6

Thus, the value of the inequality is x > 6

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The constant of variation in  y = (3/2)x is (3/2)

y = kx                           (Where k is the constant)

Here, y = (3/2)x

so k = (3/2)

To solve linear equations, utilize the steps that are provided below.

Lets take an example of solve z for 7z – (3z – 4) = 12

Here is no multiplication or division, so this will be easy to solve

⇒ 7z – (3z – 4) = 12

⇒ 7z – 3z + 4 = 12

⇒ 4z = 12 – 4

⇒ 4z = 8

⇒ z = 8/4

⇒ z = 2

See, that was so simple, using the mentioned methods, every linear equation can be solved easily.

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The fraction for 0.1515... is 5/33

It is possible to convert non terminating decimals to fraction. Because decimals are originally obtained from fractions itself.

If we have a terminating decimal number, by multiplying and dividing with powers of 10 gives a fraction.

For example, for the decimal 0.25, multiply and divide it with 100 which gives, 25/100 = 1/4.

Now we need to find the fraction corresponding to the decimal 0.1515..

Let x = 0.1515...

First we take 100x = 15.1515...

Now we can subtract the decimal part completely from 15.1515... since it is non terminating.

Now, 100x - x = 15.1515..- 0.1515.. = 15

Therefore, 99x = 15

and x = 15/99 = 5/33

So 5/33 is the fraction for the decimal 0.1515...

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Step-by-step explanation:

we must want to find C

The slope of the line containing (-3,-5) and (-3,-1) is Infinity.

The slope of a straight line can be written as follows,

m =  [tex](y_{2} - y_{1} )/(x_{2} - x_{1} )[/tex]                 equation1

The line is containing the points (-3,3) and (4,3). So, we can write

[tex]y_{2}[/tex] = -1 , [tex]y_{1}[/tex] = -5 , [tex]x_{2}[/tex] = -3 , and [tex]x_{1}[/tex] = -3 .

On substituting the values of variables in equation1, we will get

m = ( (-1)-(-5) ) / ( (-3)-(3) ) = (4/0) = Infinity.

As the slope of a line is Infinity, so we can conclude that the given line is a straight line.

Here:

m = the slope of the line

( [tex]x_{1}[/tex] , [tex]y_{1}[/tex] ) are the first coordinates.

( [tex]x_{2}[/tex] , [tex]y_{2}[/tex] )are the second coordinates.

The slope of the line containing (-3,-5) and (-3,-1) is Infinity.

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Answer:

slope = -4

Step-by-step explanation:

slope = [tex]\frac{y2-y1}{x2-x1}[/tex] = [tex]\frac{-10 - (-2)}{-2 - (-4)}[/tex] = [tex]\frac{-10 + 2}{-2 + 4}[/tex] = [tex]\frac{-8}{2}[/tex] = -4

The system of equations, -x + y = -2 and 2x - 2y = 0, has no solution.

A system of linear equations is a set of two or more equations which includes common variables. To solve system of equations, we must find the value of the unknown variables used in the equations that must satisfy both equations.

Given two equations in x and y,

-x + y = -2     (equation 1)

2x - 2y = 0     (equation 2)

Rewrite equation 1 as an equation of y and substitute to equation 2.

(equation 1) -x + y = -2     ⇒     y = x - 2

2x - 2y = 0     (equation 2)

2x - 2(x - 2) = 0

2x - 2x + 4 = 0

4 = 0

Since we do not have a definite value for x, and neither will be for y, the system of equation has no solution.

Checking the slope,

(equation 1) -x + y = -2     ⇒     y = x - 2

m = 1

(equation 2) 2x - 2y = 0     ⇒     y = x

m = 1

Since the two equations has the same slopes but different y-intercepts, then these two equations must be parallel with each other.

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The sum of finite arithmetic series 1+4+7+ . . . . . .+31 is S(11) = 176

The given  arithmetic series is:

      1+4+7+ . . . . . .+31

From the above series, we know that:

The first term, a(1) = 1

The last term, a(n) = 31

The common difference, d = 4 - 1 = 3

Recall the formula to find the nth term of an arithmetic sequence:

a(n) = a(1) + (n-1) . d

Substitute a(1) = 1, a(n) = 31, and d = 3:

31 = 1 + (n-1) . 3

31 = 3n - 2

3n = 33

n = 11

In an arithmetic series, the sum of the first n terms is given by:

S(n) = n/2 [ a(1) + a(n) ]

Substitute n = 11, a(1) = 1, and a(n) = 31:

S(n) = 11/2 (1 + 31)

S(11) = 11. 16 = 176

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