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## #1 2021-09-13 08:20:53

Member
Registered: 2021-02-20
Posts: 15

### Algebra

Hi,

I need help solving this exercise. Thank you!

6. The width, w, of a rectangular rug is 4 less than its length, L .  If the perimeter of the rug is 120 feet, which equation could be used to find the dimensions of the rug?

A. L(4-L) = 120
B. L(L-4) = 120
C. 2(L-4) + 2L = 120
D. 2(4-L) + 2L = 120

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## #2 2021-09-13 12:30:44

ganesh Registered: 2005-06-28
Posts: 34,492

### Re: Algebra

The correct answer is option C; 2(L-4) + 2L = 120

Step-by-step explanation: First of all we need to identify the variables and these are L, which is the length and W which is the width. The width is 4 less than the length of the rectangular rug. That means if the length is L, the width would be L - 4.

Also the perimeter has been given as 120. Note also that the perimeter is calculated as follows;

Perimeter = 2(L + W)

Substituting for the known values we now have;

120 = 2(L + L - 4)

120 = 2L + 2L - 8

Rearranging the right hand side now gives us

120 = 2L + (2L - 8)

120 = 2L + 2(L - 4).

It is no good to try to stop knowledge from going forward. Ignorance is never better than knowledge - Enrico Fermi.

Nothing is better than reading and gaining more and more knowledge - Stephen William Hawking.

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## #3 2021-09-19 04:22:42

Member
Registered: 2021-02-20
Posts: 15

### Re: Algebra

Hi,
Thank you for your help! I am also struggling with these exercises.

9. The Jamison family kept a log of the distance they traveled during a trip, as represented by the graph below.  The points on the graph indicate (total elapsed time, total distance traveled at the given point in time). So, (10, 390) means that after 10 hours, the family had traveled 390 miles total.

During which interval was their average speed the least?
A. The first hour to the second hour
B. The second hour to the fourth hour
C. The sixth hour to the eighth hour
D. The eighth hour to the tenth hour

10. Which linear equation BEST represents the line of best fit for the scatter plot?

A. y = (1/3)x – 1
B. y = 3x + 1
C. y = (-1/3)x + 1
D. y = 3x – 1

12. The value of the y-intercept for the graph of 4x – 5y = 40 is

A. 10
B. 4/5
C. -4/5
D. -8

13. Solve the system of equations using substitution or elimination:

x = 3y + 6
2x – 4y = 8

A. (21, 9)
B. (24, 10)
C. (15, 7)
D. (0, -2)

14. The scatterplot shows the relationship between the weekly total sales (\$) and the number of different rug designs a rug store has.  Based on this relationship, use the line of best fit to predict what the total sales will be when the store has 110 different rug designs.

A. \$31,000
B. \$0
C. \$38,000
D. \$35,000

17. If 3x - 4y = 9, then x equals

A. 3-4y
B. 9-4y
C. 9+4y/3
D. 9-4y/3

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## #4 2021-09-19 04:38:48

Bob Registered: 2010-06-20
Posts: 9,275

### Re: Algebra

Q9. For least speed you want the line segment with the lowest upward slope. (so the increase in distance is least for a fixed increase in time).

Q10. The line of best fit seems to have a positive gradient of about 3 and an intercept of -1.  That should make it easy to pick the right equestion.

Q12. The y intercept is when x=0.

Q13. As you have x = for one of the equations it is probably quickest to use substitution.  Put x = 3y + 6 into the other equation to give

2(3y+6) -4y = 8.

Simplify and solve for y.  Then work out x.

Q14. Find x = 110 on the x axis.  Go straight up until you reach the line.  Go horizontally back to the y axis. that's the answer.

Q17 3x - 4y = 9,

You can make x the subject of the equation in two steps. (i) Add 4y to both sides. (ii) Now divide by 3.

But ..... if that is exactly how the question was set then none of these answers is correct.  After step (i) everything has to be divided by 3 so there's a bracket needed.

Hope that helps,

Bob

Children are not defined by school ...........The Fonz
You cannot teach a man anything;  you can only help him find it within himself..........Galileo Galilei
Sometimes I deliberately make mistakes, just to test you!  …………….Bob Offline

## #5 2021-09-20 07:05:52

Member
Registered: 2021-02-20
Posts: 15

### Re: Algebra

Hi!

Thank you so much for your help! I have a few final questions I need help with.

22. Graph the line with the slope ½ and y-intercept 3.

23. Simplify  (a3b)2

A. a^3b^2
B. a^6b
C. a^6b^2
D. a^9b^2

25.

Which of the following is the equation of the line that has x-intercept -2 and y-intercept -6?

A.
y = -3x - 6

B.
y = -2x - 6

C.
y = -6x - 2

D.
y = 3x - 2

26. Sue has 5 gallons of paint.  After painting 800 square feet of walls in her house, she has 3 gallons left.  The graph below shows Sue’s situation.

What is the equation of this linear function?  What is the slope and what does it represent?

A. y = -(1/400)x + 5 ; slope = - 1/400 ; this means that for every gallon of paint used, 400 sq. ft. of area is painted.
B. y = -(1/40)x + 5 ; slope = - 1/40 ; this means that for every gallon of paint used, 40 sq. ft. of area is painted.
C. y = -(1/800)x + 5 ; slope = - 1/800 ; this means that for every gallon of paint used, 800 sq. ft. of area is painted.
D. y = -(1/4)x + 5 ; slope = - 1/400 ; this means that for every gallon of paint used, 4 sq. ft. of area is painted.

29. If you graph y = x2 – 6x +9, the y-intercept of the graph of the equation is _____ .

A. -3
B. 9
C. 2
D. 0

30. Reserved tickets for the football game cost \$20 each and general admission tickets cost \$12 each.  The total ticket sales brought in \$900.  The equation below can be used to find out how many of each type of ticket was sold, where x is the number of reserved tickets and y is the number of general admission tickets.

20x + 12y = 900

Which of the following graphs shows the graph of this equation?

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## #6 2021-09-21 19:38:32

Bob Registered: 2010-06-20
Posts: 9,275

### Re: Algebra

hi

Several of these involve straight line graphs.  There are several helpful pages on the main MIF site.

Have a look at these:

https://www.mathsisfun.com/equation_of_line.html

https://www.mathsisfun.com/data/straight_line_graph.html

And for Q29 (which isn't a straight line):

https://www.mathsisfun.com/data/function-grapher.php

So what else have we got?

Q23. The rules for algebra are just the rules for arithmetic. So change 'a' to 3 and b to 5 and work out the value of the expression.  Then substitute these same values into each possible answer to see which one is correct.

Q30 is another straight line graph but not given in y = mx + c format.  But you can change it so it is:

20x + 12y = 900

subtract 20 x

12y = -20x + 900

divide by 12

y = -20/12 times x + 900/12

Hope that helps,

Bob

Children are not defined by school ...........The Fonz
You cannot teach a man anything;  you can only help him find it within himself..........Galileo Galilei
Sometimes I deliberately make mistakes, just to test you!  …………….Bob Offline

## #7 2021-09-26 01:41:01

Member
Registered: 2021-02-20
Posts: 15

### Re: Algebra

Hi,

I just wanted to ask to make sure that my answer was right, for Q29 the answer is 2 or 9?

Thank you so much!!

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## #8 2021-09-26 04:33:58

Bob Registered: 2010-06-20
Posts: 9,275

### Re: Algebra

hi

On the y axis the x coordinate is always zero.  The graph cuts the y axis at a point called the intercept.  So just put x=0

You get y=9 I hope.

Bob

Children are not defined by school ...........The Fonz
You cannot teach a man anything;  you can only help him find it within himself..........Galileo Galilei
Sometimes I deliberately make mistakes, just to test you!  …………….Bob Offline

## #9 2021-09-29 10:16:15

Member
Registered: 2021-02-20
Posts: 15

### Re: Algebra

Hi,

Thank you so much!
I also wanted to make sure that I got the correct answer for Q30. I got alternative A. Is that correct?

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## #10 2021-09-29 19:00:13

Bob Registered: 2010-06-20
Posts: 9,275

### Re: Algebra

Answer A looks good to me. Bob

Children are not defined by school ...........The Fonz
You cannot teach a man anything;  you can only help him find it within himself..........Galileo Galilei
Sometimes I deliberately make mistakes, just to test you!  …………….Bob Offline