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3 years ago

Trevor is swimming laps to raise money for the local food bank. He earns $1.85 per lap and has already swum 23 laps.

1 answer:

5 0

Thank you for posting your question here at brainly. I hope the answer will help you. Feel free to ask more questions here.

The inequality is 1.85x - 42.55 > 100. 42.55 is the amount already raised, 1.85x is number of laps times the money raised by them.

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A fence must be built to enclose a rectangular area of 45 comma 000 ftsquared. Fencing material costs $ 3 per foot for the two s

Tatiana [17]

Answer:

150 feet by 300 feet.

Step-by-step explanation:

The fence is to enclose a rectangular area of 45,000 ft squared.

If the dimensions of the rectangle are x and y

Area of a rectangle = xy

xy=45000
$x=\frac{45000}{y}$

Perimeter of the Rectangle =2x+2y

Fencing material costs $ 3 per foot for the two sides facing north and south and $6 per foot for the other two sides.

Cost of Fencing, C=$(6*2x+3*2y)=$(12x+6y)

Substitute $x=\frac{45000}{y}$ into the Cost to get C(y)

C=12x+6y

$C(y)=12(\frac{45000}{y})+6y\\C(y)=\frac{540000+6y^2}{y}$

The value at which the cost is least expensive is at the minimum point of C(y), when the derivative is zero.

$C^{'}(y)=\dfrac{6y^2-540000}{y^2}$

$\dfrac{6y^2-540000}{y^2}=0\\6y^2-540000=0\\6y^2=540000\\y^2=\frac{540000}{6} =90000\\y=\sqrt{90000}=300$

Recall,

$x=\frac{45000}{y}=\frac{45000}{300}=150$

Since x=150, y=300

The dimensions that will be least expensive to build is 150 feet by 300 feet.

6 0

3 years ago

A lawyer charges a $75 consultation fee and then $120 per hour thereafter.

Ainat [17]

Answer:

(a) The dependant veriable is the $120 per hour and the independant veriable is the $75 consultaion fee.
(b) The table of vaules for this would look like this, $\frac{C}{T} \frac{75}{0} \frac{195}{1} \frac{315}{2} \frac{435}{3} \frac{555}{4}$ , where C = cost and T = time.
(c) The relationship between C and T is linear, beacause with the more hours you take the cost increases.
(d) Yes, it is sensible because the points would be in line due to the steady increase of the hourly rate.

(e) For every hour spent the cost increases 120 dollars.
(f) The fixed cost is 75 dollars for consultation and the veriable cost is 120 per hour.

3 0

2 years ago

2000 tickets sold for $20000 student tickets are $10 regular tickets $20 how many of each ticket sold

schepotkina [342]

They sold 2000 student tickets and 0 regular tickets

6 0

3 years ago

It's alright if you don't know all the answers to the questions! This is due today!!

Degger [83]

Answer:

this is really confusing but i will see if i can find anything

Step-by-step explanation:

7 0

3 years ago

Read 2 more answers

A rectangle is drawn so that the width is 1 feet shorter than the length. The area of the rectangle is 20 square feet. Find the

klemol [59]

Answer:

Length = 5 feet

Step-by-step explanation:

The formula for finding the area of a rectangle is:

Area = Length x Width

The problem said that the width is 1 foot shorter than the length. This can be shown like this:

Width = (Length - 1)

Going back to our formula for finding area, we can replace Width with (Length - 1). We can also put 20 as the area since the problem already told us that the area of the rectangle is 20 square feet. By now, your equation should look similar to this:

Area = Length x Width

Area = Length x (Length - 1)

20 = Length x (Length - 1)

Now, we can go on to figuring out what the length is. For now, the length is going to be referred to as ' x '.

20 = Length x (Length - 1)

20 = (x)(x - 1)

*Distribute x to (x - 1)*

20 = x² - x

*This is beginning to look like a quadratic equation. Let's move all of the terms over to one side.*

20 = x² - x

0 = x² - x - 20

*It would appear that we need to factor this equation to get our answer.*

x² - x - 20

This would be the factored version of our equation because the factors -4 and 5 give us a product of -1 but also give us a sum of -1.

(x - 5) (x + 4)

From here, our options are narrowed down to 5 and -4. As we know, lengths cannot be real which means...

Length = 5 feet

~Hope this helps!)

5 0

3 years ago