David and Josh are both practicing for an upcoming swim tournament. Every week, David swims for 3x hours at an average speed of x laps per hour. Josh swims 5 more hours per week than David, but at an average speed that is 4 laps per hour less than David's average speed.


Which of the following functions will give the total distance, in laps, that Josh swims each week?

Answers

Answer 1
Answer: 3x^2 - 7x - 20

Explanation:

This questions has 4 answer choices to select the right one.

These are the answer choices:

A) f(x) = 3x^2 - 17x + 20
B) f(x) = 3x^2 + 7x - 20
C) f(x) = 3x^2 - 7x - 20
D) f(x) = 3x^2 + 17x + 20

Solution:

Translate the given word statements into algebraic expressions:


1) Every week, David swims for 3x hours at an average speed of x laps per hour =>

time = 3x
speed = x

2) Josh swims 5 more hours per week than David =>

time = 5 + 3x

speed that is 4 laps per hour less than David's average speed =>

speed = x - 4

3) distance, in laps, that Josh swims each week, equal time * speed

=> distance = (3x + 5) (x - 4)

4) Expand the parenthesis:

a) distributive property: (3x)(x) + (3x)(-4) + 5(x) + 5(-4) = 3x^2 - 12x + 5x - 20 =

= 3x^2 - 7x - 20

Answer: 3x^2 - 7x - 20 (option C)


Related Questions

Keisha's boat has a top speed of 9 miles per hour in still water. While traveling on a river at top speed, she went 10 miles upstream in the same amount of time she went 20 miles downstream. Find the rate of the river current.

Answers

If she went 10 miles upstream in the same time as she went 20 miles downstream, that means the downstream speed is twice the upstream speed.

The speed is still water is 9 mph.
The speed of the current is c.
Going downstream, the current adds speed, so the sped downstream is 9 + c.
The speed upstream is 9 - c.
9 + c is twice 9 - c.

9 + c = 2(9 - c)

9 + c = 18 - 2c

3c = 9

c = 3

Answer: The speed of the current is 3 mph.

Check:
9 + c = 12
9 - c = 6
By taking into the account the speed of the current, the downstream speed, 12 mph, is indeed twice the upstream sped, 6 mph.

Jenna has 8 pairs of jeans. Three of them are blue. What percentage of her jeans is blue?
= 37.5%
But my question is this:
Jenna bought two more pairs of jeans.
If both of them are blue, what percentage of her jeans is blue now?

If both of them are not blue, what percentage of her jeans is blue now?

Answers

a) blue/total = (3+2)/(8+2) = 5/10 = 50%

b) blue/total = (3)/(8 +2) = 3/10 = 30%

A space shuttle orbits earth at a rate of about 4,375 miles in 15 minutes. At the rate, how far does the space shuttle travel around earth in 1 hour?

Answers

4,375*4=17500


Hope this helps
First you would divide 4,375 by 15 and will get 291.6

There min in and 1hour so
291.6 times 60= 17,596

The shuttle will go 17,596 miles in an hour.

Reciprocal of 1/10 = ?

Reciprocal of 16 = ?

Answers

The reciprocal of 1/10 is 10/1 or 10. The reciprocal of 16 is 1/16. Basically to make it easier think of flipping or switching the numerator and denominator. Hope this was helpful.
The reciprocal of 1/10 is 10/1. The reciprocal of 16 is 1/16. The reciprocal is just flipping the fraction around changing the numerator to the denominator and other way around. The reciprocal of 16 is 1/16 because 16 as a fraction is 16/1 so flipping it would be 1/16.

Identify the graph that displays the altitude of a skydiver as he is taken up in a plane and then jumps.

Answers

the graph would probably have an inclined line and then a declining line

Answer:

A is your answer

Graph Below

A computer program in Shannon’s computer carries out a single mathematical operation in 1.5 × 10-6 seconds. How much time would the program take to complete 2.5 × 103 mathematical operations?

Answers

1/1.5 * 10^-6 = 2500/x
x = 1.5 * 10^-6 * 2500
x = 0.00375 or 3.75 * 10^-3 second.
Good question. 

You forgot A, B, C, and D but the correct answer is option D, 3.75 x 10 ^ -3 seconds

an artist painted a 6 foot tall painting, then decide to also create a smaller version. if she uses a scale of 4 inches=1.5 feet, what will be the height of the smaller painting

Answers

let
x----------------- > the height of the smaller painting
y-----------------> the height of the tall painting-----------> 6 ft

the scale factor is-------------- > x/y
(x/y)=(4 in)/(1.5 ft)
x=y*[(4 in)/(1.5 ft)]-------> 6*(4 in)/(1.5 ft)=16 in

the answer is x=16 in

Final answer:

To determine the height of the smaller version of the painting using the scale of 4 inches = 1.5 feet, we first convert the original height to inches (6 feet = 72 inches) and then use a proportion to find that the height of the smaller painting is 16 inches.

Explanation:

The student's question involves using a scale to determine the height of a smaller version of a painting. The scale given is 4 inches = 1.5 feet. To begin, we convert the original height of the painting from feet to inches since the scale is in inches. The original height of 6 feet is equivalent to 72 inches (because 1 foot is equal to 12 inches).



Next, we set up a proportion using the scale:



4 inches / 1.5 feet = x inches / 6 feet



Now we solve for x, which represents the height of the smaller painting in inches:



4 / 1.5 = x / 6

4 / 1.5 * 6 = x

x = 4 * 6 / 1.5

x = 24 / 1.5

x = 16 inches



Thus, the height of the smaller version of the painting will be 16 inches.

movie mania charges a subscription fee of $30 and an additional fee of 5 per movie

Answers

Movie mania is earning:
[tex]M_m: y=\frac{30+5x}{x} [/tex],
per movie.
Movie time is earning 
[tex]M_t: y=\frac{25+6x}{x}[/tex], 
per movie.
Anna wants her customers to pay more than they would at Movie Time but less than Movie Mania. 
The answer would be D :
[tex]y\ \textgreater \ \frac{6x+25}{x}\\ y\ \textless \ \frac{5x+30}{x}[/tex]

Membership in the Volunteers Club increased by 15% from last year. If the number of members last year was m, complete a simplified expression to represent the number of members this year. Enter your answer in the box.

Answers

For this case what you can do is the following rule of three:
 m ---> 100%
 x ----> 115%
 Clearing the value of x we have:
 x = (115/100) * (m)
 x = 1.15 * (m)
 Answer:
 a simplified expression to represent the number of members this year is:
 x = 1.15 * (m)

Joe’s current age is five times Mary’s age ten years ago. If Mary is currently m years old, what is Joe’s current age in terms of m?

Answers

Answer:

5m + 10

That should be it, you may need to simplify.

Sorry if its wrong, but i think this is it.

Step-by-step explanation:

Container A can hold 9 cups of liquid. container B can hold 5 pints of liquid. Container c can hold 2 quarts of liquid. Whice container has the greatest capacity? Explain

Answers

Hello!

1 cup = 0.5 pints

1 cup = 0.25 quarts

That means that 9 cups are equivalent to 4.5 pints and 2.25 quarts of liquid.

1 pint = 2 cups

1 pint = 0.5 quarts

That means that 5 pints are equivalent to 10 cups and 2.5 quarts of liquid.

1 quart = 4 cups

1 quart = 2 pints

That means that 2 quarts are equivalent to 8 cups and 4 pints of liquid.

FINAL ANSWER:

Judging by our calculations, Container B has the greatest capacity.

solve the following system using substitution x+4y=21 4x-y=16

Answers

x+4y=21
4x-y=16

Isolate one of the variables
x + 4y = 21
subtract 4y from both sides
x = -4y + 21

Plug that into the other equation
4x - y = 16
4(-4y + 21) - y = 16
-16y + 84 - y = 16
combine like terms
-17y + 84 = 16
subtract 84 from both sides
-17y = -68
divide both sides by -17
y = 4

Plug that into the equation
x+4y=21
x + 4(4) = 21
x + 16 = 21
subtract 16 from both sides
x = 5

Hope this helps!

Scientist determine that Antarctica average winter temperature was 34.44 Celsius the difference between the temperature and Antartica highest record temperature was 49.44 degrees what was the highest record temperature

Answers

If the average temperature in Antacrctica were 34.44 °C, the ice sheet would have melted long ago. We expect you intend -34.44 °C.

Then the highest recorded temperature is
  -34.44 °C +49.44 °C = 15 °C . . . . . . . . . . about 59 °F

Gracie can purchase 5 oranges for $4 but she only wants one what is the cost of one orange

Answers

the cost of one orange is $1.25
what you do is you divide 5 by 4 so 5 divided by 4= 1.25
hope this helps!

In a basic sine curve, where can the zeros NOT be found?

a. middle
b. beginning
c. maximum point
d. end

Answers

the most brainliest answer A) middle

Answer: Option 'C' is correct.

Step-by-step explanation:

Since we know that

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

It is an odd function.

It has a period of 2π because the sine wave repeats after every 2π units.

It value lies between -1 and 1.

And we know that

[tex]\sin 0^\circ=0^\circ[/tex]

And 0 occurs exactly middle of -1 and 1.

So, the zeroes can be found in the middle, beginning and at the end.

But at maximum point, there will be no zero.

As when it attains its maximum point, it won't touch x-axis.

Hence, Option 'C' is correct.

Karina read a total of 20 2/4 pages in her science and social studies books combined she read 12 3/4 pages in her science book how many pages did she read in her social studies book?

Answers

7 3/4 pages in her social studies book

Final answer:

To find out how many pages Karina read in her social studies book, you subtract the number of pages read in the science book from the total pages read. After doing the math, Karina read 8 1/4 pages in her social studies book.

Explanation:

Karina read a total of 20 2/4 pages in both her science and social studies books combined. It is mentioned that she read 12 3/4 pages in her science book. To find out how many pages she read in her social studies book, one must subtract the pages read in the science book from the total pages read.

The subtraction of mixed numbers involves the following steps:

First, make sure the fractions have the same denominator.

Then, subtract the fractions.

If necessary, borrow from the whole number and reduce the fractions further.

Finally, subtract the whole numbers.

In this case:

Total pages - Science book pages = Social Studies book pages

20 2/4 - 12 3/4 = 7 5/4 or 8 1/4 pages (since 5/4 is equal to 1 and 1/4).

Therefore, Karina read 8 1/4 pages in her social studies book.

what is the difference of the rational expressions below? 13x/5 - 4x/5
a. 9x/5
b. 17x/5
c. 52x/5
d. 52x/25

Answers

The answer is:
a. 9x/5
13x/5 - 4x/5
 What you must do in this case is a sum of fractions.
 Step 1:
 Common factor 5 in the denominator
 Step 2:
 Perform subtraction of numerator
 Step 3:
 Rewrite the expression.
 See attached image.
 Answer:
 a. 9x/5

The boys' basketball team at Washington High School has been doing really well so far this year. In the past six games, they've scored the following points.

84, 67, 74, 87, 67, 73

What is the mean of their scores, rounded to the nearest tenth?

Answers

The mean of their scores is their sum divided by the number of scores.
.. (84 +67 +74 +87 +67 +73)/6 = 452/6 ≈ 75.3

Answer:

(84 +67 +74 +87 +67 +73)/6 = 452/6 = 75.3

Step-by-step explanation:

Exactly what you see :]

if the area of a rectangle is 42 feet. what could be possible lengths and widths of the rectangle? 42=__×___

Answers

6×7
because 6×7=42
I hope this helps!
Hello!

We know that it is a rectangle, so its length will be longer than its width, unlike a square.

Here are some possible widths:

42 = 7 × 6

42 = 14 × 3

42 = 21 × 2

42 = 42 × 1

These are the factors of 42.

Keshawn is constructing the inscribed circle for △PQR . He has already used his compass and straightedge to complete the part of the construction shown in the figure. Which construction could be his next step? Construct the angle bisector of ∠XQR . Construct the line through points P and X. Construct the perpendicular bisector of PQ¯¯¯¯¯ . Construct the perpendicular to QR¯¯¯¯¯ that passes through point X.

Answers

Answer:

Construct the perpendicular to QR¯¯¯¯¯ that passes through point X.

Step-by-step explanation:

the second of two numbers is 4 more than the first the sum of the numbers is 56 find the numbers

Answers

Answer:

  26, 30

Step-by-step explanation:

If you subtract from the sum the excess of the second over the first, you have a sum that is twice the first.

  first number = (56 -4)/2 = 26

The second number is 4 more, so is ...

  second number = 26 +4 = 30

_____

Check

Their total is 26 +30 = 56, as required.

An airplane is flying at an altitude of 10,000 feet when it receives clearance to land at the airport. The angle of depression from the airplane to the airport is 4o. What is the horizontal (ground distance) from the airport to the airplane's position?

Answers

Since we know that The angle of depression from the airplane to the airport is 40°, and its altitude is 10000 feet, we can create a right triangle using the horizontal of the plane, the angle of depression, and the altitude as one of the legs of our right triangle. the horizontal (ground distance) from the airport to the airplane's will be the same as the adjacent leg of our depression angle. To find the adjacent leg we'll need a trig function that relates our leg with the depression angle and the opposite leg. That trig function is tangent. So lets set up an equation and solve it to find our distance:
[tex]tan(40)= \frac{10000}{leg} [/tex]
[tex]leg= \frac{10000}{tan(40)} [/tex]
[tex]leg=11917.54[/tex]

We can conclude that the horizontal (ground distance) from the airport to the airplane's position is 11,917.54 feet.

Find the product of (4x − 3)(2x2 − 7x + 1).

Answers

Multiply each term in the left parentheses by each term in the right parentheses.

=(4x − 3)(2x2 − 7x + 1)

=(4x*2x2) + (4x*-7x) + (4x*1) + (-3*2x2) + (-3*-7x) + (-3*1)
multiply each set of parentheses

=8x3 - 28x2 + 4x - 6x2 + 21x-3
combine like terms

ANSWER:
=8x3 - 34x2 + 25x - 3

Hope this helps! :)

during the new year celebration there are orange, green purple, and blue fireworks. In how many different orders can the different colors of fireworks appear?

Answers

There are 256 possible combinations of fireworks, if they can be repeated in each 4 firework combinations.
If they cannot be repeated, there are 24 possible combinations.

There are 24 different orders in which the different colors of fireworks can appear.

What is an expression?

An expression contains one or more terms with addition, subtraction, multiplication, and division.

We always combine the like terms in an expression when we simplify.

We also keep all the like terms on one side of the expression if we are dealing with two sides of an expression.

Example:

1 + 3x + 4y = 7 is an expression.

3 + 4 is an expression.

2 x 4 + 6 x 7 – 9 is an expression.

33 + 77 – 88 is an expression.

We have,

If there are four colors of fireworks (orange, green, purple, and blue), then the number of different orders in which they can appear can be found by calculating the number of permutations of four objects, which is:

4! = 4 x 3 x 2 x 1 = 24

Therefore,

There are 24 different orders in which the different colors of fireworks can appear.

Learn more about expressions here:

https://brainly.com/question/3118662

#SPJ2

what is the proportion 5.2/8=y/6

Answers

It's another way to say
.. y/6 = 0.65

Multiply by 6 to find the value of y that makes it true as
.. y = 3.9

HELP!!

4. What are the values of x and y?
A) x=9/4, y=3/4
B) x=9/4, y=15/4
C) x=15/4, y=5/4
D) x=3/4, y=15/4

THANK YOU

Answers

All of the triangles are similar.

Ratio of short to long sides:
.. x/3 = 3/4
.. x = 9/4

Ratio of hypotenuse to long sides:
.. y/3 = 5/4
.. y = 15/4

The 2nd selection is appropriate.

An observer in a lighthouse 350 feet above sea level observes two ships directly offshore. The angles of depression to the ships are β = 7° and θ = 10.5° (see figure). How far apart are the ships? (Round your answer to one decimal place.) ft

Answers

The ships are 21.5 feet apart.

We have,

Let's denote the distance between the observer and Ship 1 as x and the distance between the observer and Ship 2 as y.

Using the angles of depression, we can establish the following relationships:

tan(β) = x / 350

tan(θ) = y / 350

We need to find the distance between the ships, which is the difference between x and y.

To find x and y, we can rearrange the equations as follows:

x = 350 * tan(β)

y = 350 * tan(θ)

Now, we can calculate the distances x and y using the given angles of depression:

x = 350 * tan(7°)

x ≈ 42.9 feet

y = 350 * tan(10.5°)

y ≈ 64.4 feet

The distance between the ships is the difference between x and y:

Distance = y - x

Distance ≈ 64.4 - 42.9

Distance ≈ 21.5 feet

Therefore,

The ships are 21.5 feet apart.

Learn more about trigonometric identities here:

https://brainly.com/question/14746686

#SPJ4

A grocer had 40 crates of tomatoes. Each crate contained 124 tomatoes. She threw away 24 rotten tomatoes and repack the rest into bag of 8 tomatoes each. How many bags of tomatoes were there?

Answers

40 * 124 = 4,960

4,960 - 24 = 4,936

4,936 / 8 = 617

There are 617 bags of tomatoes.
the grocer has 40 crates of tomatoes with 124 tomatoes in each crater
124*40=4960 tomatoes
24 are rotten
4960-24=4936
4936/8=617 bags

12km is equal to how many meters? (show all work)

Answers

One kilometer is equal to 1,000 meters, so to find 12 kilometers, you would do 12x1,000. 12x1,000=12,000

12 kilometers is equal to 12,000 meters.

This week laptops are 25 percent off if a laptop cost $340 what is it's sale price

Answers

The sale price is $255 ok got it? Hopefully u do
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