Cassandra is trying to think of a good way to keep her financial records. She makes a lot of purchases, using cash, debit cards, and credit cards about equally. When she gets home every day, she tends to be very tired and doesn’t like to do a lot of organized thinking. She tends to lose individual pieces of paper if she doesn’t file them immediately. What might be a good method for Cassandra to use?

Answer:

Let x represents the number of hours of labor and y represents the total charges.

Since, in the given situation,

The total charges = A fixed charge for house call + Extra charge per hours,

Fixed charge for house call = $ 45,

Extra charges for every hour = $ 25,

⇒ Extra charge for x hours = 25 x,

Thus, the total charges for x hours,

y = 45 + 25 x

Which is the required equation that will use to determine the amount to charge each customer.

By comparing this equation with y = mx + c,

m = 25

Answer:

Option C is the correct answer : [tex]y=\frac{(x-1)}{3}[/tex]

Step-by-step explanation:

[tex]y=3x+1[/tex]

For finding the inverse of this function, we will interchange x and y, then solve for y.

[tex]3y=x-1[/tex]

[tex]y=\frac{x-1}{3}[/tex]

Hence, option C is the correct answer : [tex]y=\frac{(x-1)}{3}[/tex]

Answer:

D

Step-by-step explanation:

i just did the quiz

The marginal revenue for 100 units sold is 180 dollars per unit. We cannot precisely estimate the total revenue for 100 or 101 units sold without further information.

In this problem, we're dealing with the concept of marginal revenue. The marginal revenue function gives us the change in total revenue for each additional unit sold. That is given in this case as R'(q)=240-18√q.

To find the marginal revenue at 100 units, we simply substitute q = 100 into our function: R'(100)=240-18√100 = 240 - 18*10 = 180 dollars per unit.

The total revenue given a specific quantity is typically found by integrating the marginal revenue function. However, without the constants of integration or the original revenue function, we cannot accurately compute the total revenue for 100 or 101 units sold in this case.

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Answer:-24.87 is the correct answer, i checked it!

Step-by-step explanation:

To write a percent as a fraction in lowest terms,  first remember that a percent is a ratio that compares a number to 100. In this case, 40% can be written as the ratio 40 to 100 or [tex]\frac{40}{100}[/tex]. Notice however that [tex]\frac{40}{100}[/tex] is not in lowest terms so we need to divide the numerator and the denominator by 20 which gives us [tex]\frac{2}{5}[/tex].

Answer:

less than $896.00

Step-by-step explanation:

A common rule is that housing expenses should not be more than 28% of your monthly income.

your monthly income = $3,200

so your housing expense should not be more than 28% of $3,200

= [tex]\frac{28}{100}[/tex] × 3,200

= 0.28 × 3,200 = $896.00

So you can spend less than $896.00 on housing expenses.

Answer: The answer is [tex]\dfrac{5}{8},~\dfrac{3}{2}[/tex] and no extraneous solution.

Step-by-step explanation: The given equation is

[tex]2|7-7x|=2x+4.[/tex]

We are given to solve this equation and also find its extraneous solution.

The solution is as follows:

[tex]2|7-7x|=2x+4\\\\\Rightarrow |7-7x|=x+2\\\\\Rightarrow 7-7x=x+2,~~~~~-7+7x=x+2\\\\\Rightarrow 8x=5,~~~~~~~~~~~~~~~~\Rightarrow 6x=9\\\\\\\Rightarrow x=\dfrac{5}{8},~~~~~~~~~~~~~~~~~\Rightarrow x=\dfrac{3}{2}.[/tex]

now, for [tex]x=\dfrac{5}{8}[/tex], we have

[tex]L.H.S.=2|7-7\times \dfrac{5}{8}|=\dfrac{21}{4},\\\\R.H.S.=2\times\dfrac{5}{8}+4=\dfrac{21}{4}.[/tex]

So, this solution is not extraneous.

For [tex]x=\dfrac{3}{2}[/tex], we have

[tex]L.H.S.=2|7-7\times \dfrac{3}{2}|=7,\\\\R.H.S.=2\times\dfrac{3}{2}+4=7.[/tex]

So, this solution is also not extraneous.

Hence, the solution is [tex]\dfrac{5}{8},~\dfrac{3}{2}[tex] and there is no extraneous solution.

To create a log expression that simplifies to 7^x = 64, we need to use the logarithmic and exponential laws.

To create a log expression that simplifies to 7^x = 64, we need to use the logarithmic and exponential laws.

Therefore, the log expression that simplifies to 7^x = 64 is x = 6 * log7(2).

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Answer:

-3/2 ≤ x < 5  

Step-by-step explanation:

2x - 3 < x + 2 ≤ 3x+5

Solve the inequality separately

2x-3 <x+2  and x+2≤ 3x+5

LEts solve one by one

2x-3 <x+2

Subtract x from both sides

x -3 < 2

add 3 on both sides

x< 5

x+2≤ 3x+5

Subtract 3x from both sides

-2x + 2 ≤ 5

Subtract 2 from both sides

-2x ≤  3

Divide both sides by -2

x ≥ -3/2

we got x>= -3/2 and x<5

so x lies between -3/2  and 5

-3/2 ≤ x < 5

The solution to the given inequality is -3/2 ≤ x < 5.

To solve the given inequality: 2x - 3 < x + 2 ≤ 3x + 5, we can break it down into two separate inequalities and solve them individually.

2x - 3 < x + 2:

Subtracting x from both sides:

2x - x - 3 < x - x + 2

x - 3 < 2

Adding 3 to both sides:

x - 3 + 3 < 2 + 3

x < 5

Now x + 2 ≤ 3x + 5:

Subtracting x from both sides:

x - x + 2 ≤ 3x - x + 5

2 ≤ 2x + 5

Subtracting 5 from both sides:

2 - 5 ≤ 2x + 5 - 5

-3 ≤ 2x

Dividing both sides by 2:

-3/2 ≤ x

Combining the results from both inequalities:

-3/2 ≤ x < 5

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Answer:

The below attached graph shows the given inequality.

Step-by-step explanation:

Here, the given inequality,

x - 2y > -12

Since, related equation of the inequality,

x - 2y = -12

Which is a line passes through (-12, 0) and (0, 6)

Also, '>' represents dotted line,

So, join these two points by dotted line in the coordinate plan,

Now,

0 - 2(0) > -12 (True)

i.e. shade the region of the line that contains origin.

By the above explanation we will get the graph of given inequality ( shown below )