Math Is Fun Forum

  Discussion about math, puzzles, games and fun.   Useful symbols: ÷ × ½ √ ∞ ≠ ≤ ≥ ≈ ⇒ ± ∈ Δ θ ∴ ∑ ∫ • π ƒ -¹ ² ³ °

You are not logged in.

#26 Help Me ! » Factoring Polynomials » 2021-11-08 09:16:36

jadewest
Replies: 5

Hi,
I need help with checking if these are correct.
Thank you!

A.  Factor the following polynomials completely.

1. 125x^3 + 64

(5x)^3 + 43

125x^3 + 64 = (5x + 4) ( (5x)^2 - (5x) (4) + 42 )

(5x + 4) ( 25x^2 - 20x + 16 )

2. x^9 + 1

(x^3)^3 + 1^3
x^9 + 1 = (x + 1) (x^2 - (x) (1) + 1^2)

(x + 1) (x^2 - x + 1)

3. 2m^4 - 2mn^3

2m^3

2m^3 (m) - 2m^3 (n)

2m^3 (m - n)

4. 3a^4 + 81a

3a

3a (a^3) + 3a (27)

3a (a^3 + 27)

B.   Can these be factored using the methods (GCF, squares, cubes) discussed in this lesson? Yes or No?  Explain why or why not in a complete sentence.

5. 7x^5 - 64y

This can't be factored, because 7 and 64 don't share a GCF.

6. a^4 + 1

This can't be factored, because sum of squares cannot be factored using real numbers.

7. a^4 – 64

This can be factored with the difference of squares which leads to the answer: (a^2 + 8) (a^2 - 8)

C.    Factor completely using Grouping

8.  xy – 5y – 2x + 10

y (x - 5) - 2 (x - 5)

(x - 5) (y - 2)

9.  x^3 + x^2 - x – 1

x^2 (x +1) - 1 (x + 1)

(x + 1) (x^2 - 1)

#27 Re: Help Me ! » Factoring Polynomials » 2021-11-03 09:41:02

Hi,
I apologize for the confusion! I put ^ to indicate power.

A.  Factor the following polynomials completely.

1. 125x^3 + 64

(5x)^3 + 43

125x^3 + 64 = (5x + 4) ( (5x)^2 - (5x) (4) + 42 )

(5x + 4) ( 25x^2 - 20x + 16 )

2. x^9 + 1

(x^3)^3 + 1^3
x^9 + 1 = (x + 1) (x^2 - (x) (1) + 1^2)

(x + 1) (x^2 - x + 1)

3. 2m^4 - 2mn^3

2m^3

2m^3 (m) - 2m^3 (n)

2m^3 (m - n)

4. 3a^4 + 81a

3a

3a (a^3) + 3a (27)

3a (a^3 + 27)

B.   Can these be factored using the methods (GCF, squares, cubes) discussed in this lesson? Yes or No?  Explain why or why not in a complete sentence.

5. 7x^5 - 64y

This can't be factored, because 7 and 64 don't share a GCF.

6. a^4 + 1

This can't be factored, because sum of squares cannot be factored using real numbers.

7. a^4 – 64

This can be factored with the difference of squares which leads to the answer: (a^2 + 8) (a^2 - 8)

C.    Factor completely using Grouping

8.  xy – 5y – 2x + 10

y (x - 5) - 2 (x - 5)

(x - 5) (y - 2)

9.  x^3 + x^2 - x – 1

x^2 (x +1) - 1 (x + 1)

(x + 1) (x^2 - 1)

#28 Re: Help Me ! » Factoring Polynomials » 2021-11-02 05:10:40

Hi,

Thank you for your help! I have solved the other exercises, I just need to see if they are correct.

A.  Factor the following polynomials completely. 

1. 125x3 + 64

(5x)3 + 43

125x3 + 64 = (5x + 4) ( (5x)2 - (5x) (4) + 42 )

(5x + 4) ( 25x2 - 20x + 16 )

2. x9 + 1

(x3)3 + 13
x9 + 1 = (x + 1) (x2 - (x) (1) + 12)

(x + 1) (x2 - x + 1)

3. 2m4 - 2mn3

2m3

2m3 (m) - 2m3 (n)

2m3 (m - n)

4. 3a4 + 81a

3a

3a (a3) + 3a (27)

3a (a3 + 27)

B.   Can these be factored using the methods (GCF, squares, cubes) discussed in this lesson? Yes or No?  Explain why or why not in a complete sentence.

5. 7x5 - 64y

This can't be factored, because 7 and 64 don't share a GCF.

6. a4 + 1

This can't be factored, because sum of squares cannot be factored using real numbers.

7. a4 – 64

This can be factored with the difference of squares which leads to the answer: (a2 + 8) (a2 - 8)

 C.    Factor completely using Grouping

8.  xy – 5y – 2x + 10

y (x - 5) - 2 (x - 5)

(x - 5) (y - 2)

9.  x3 + x2 - x – 1

x2 (x +1) - 1 (x + 1)

(x + 1) (x2 - 1)

#29 Help Me ! » Factoring Polynomials » 2021-11-01 10:21:29

jadewest
Replies: 6

Hi,

I need help solving this problem.

10. Suppose a football is kicked from the ground and its height, h, in feet above the ground is given by h = -3.9t2 + 15.6t.

The time, t, represents the number of seconds after the ball is kicked. At what time does the football hit the ground?

#30 Re: Help Me ! » Algebra » 2021-09-29 10:16:15

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?

Jade

#31 Re: Help Me ! » Algebra » 2021-09-26 01:41:01

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!!

#32 Re: Help Me ! » Algebra » 2021-09-20 07:05:52

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.

A. Image link: https://www.compuhigh.net/testeditor/upload/pics/algebra2/Graph38a.PNG
B. Image link: https://www.compuhigh.net/testeditor/upload/pics/algebra2/Graph38b.PNG
C. Image link: https://www.compuhigh.net/testeditor/upload/pics/algebra2/Graph38c.PNG
D. Image link: https://www.compuhigh.net/testeditor/upload/pics/algebra2/Graph38d.PNG

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.

Image link: https://www.compuhigh.net/testeditor/upload/pics/algebra2/algebra2_pretest_4_paint.png

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?

A. Image link: https://www.compuhigh.net/testeditor/upload/pics/algebra2/Graph60a.PNG
B. Image link: https://www.compuhigh.net/testeditor/upload/pics/algebra2/Graph60b.PNG
C. Image link: https://www.compuhigh.net/testeditor/upload/pics/algebra2/Graph60c.PNG
D. Image link: https://www.compuhigh.net/testeditor/upload/pics/algebra2/Graph60d.PNG

#33 Re: Help Me ! » Algebra » 2021-09-19 04:22:42

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.

Image link: https://www.compuhigh.net/testeditor/upload/pics/algebra2/algebra2_pretest_1_jamisondistancelog.png

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?

Image link: https://www.compuhigh.net/testeditor/upload/pics/algebra2/algebra2_pretest_2_lineofbestfit.png

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.

Image link: https://www.compuhigh.net/testeditor/upload/pics/algebra2/algebra2_pretest_3_rugsales.png

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

#34 Help Me ! » Algebra » 2021-09-13 08:20:53

jadewest
Replies: 9

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

#35 Re: Help Me ! » Proofs » 2021-03-01 11:38:43

Hi Bob,

What is confusing me right now is that from the formula in D it turns out to be 2 diagonals.
(4-3)* 4/2=
= 1*2
=2 diagonals

   The statement says that it has 2 diagonals. Given is when the statement is given, it means that it is provided to me in the problem. That is why I was going for given in this exercise.

#36 Help Me ! » Proofs » 2021-02-28 07:40:20

jadewest
Replies: 3

Hello!!

I have completed a lesson about proofs. I am unsure about two questions I've answered.

3. I have drawn a polygon with eight sides, so it must be an octagon.

A. Definition of supplementary angles
B. unfounded
C. Definition of radius
D. 1267200 inches
E. Definition of an octagon
F. Given

    For this one I have selected alternative E, definition of an octagon, because it defines what an octagon is.


4. A square has two diagonals.

A. Given
B. unfounded
C. Definition of an octagon
D. The number of diagonals is (n-3)n/2, where n is the number of sides, which is 4 for a square.
E. 1267200 inches
F. Definition of supplementary angles

     For this one I have chosen alternative A, given, because a square has 2 diagonals and that is the exact thing that the statement is saying.

Am I correct in these two?

#38 Re: Help Me ! » The Cartesian Coordinate System and the Distance Formula » 2021-02-25 06:35:58

I think I finally got Q4!!! In the exercise it says this: (Draw from one to the next in the order given,
and then draw from the last back to the first). When I connect the points in the given order I notice that I create two right triangles that meet at the right angles. So, the right alternative is D.

#39 Re: Help Me ! » The Cartesian Coordinate System and the Distance Formula » 2021-02-25 05:19:20

Hi Bob,
So the right answer for Q14 would be the 4 * sqrt 13, or alternative D.

I'm sorry, but I'm still confused in Q4. Even if I put them in the order given in the exercise, the figure that comes out is a rhombus. I'm not sure what exactly I'm doing wrong.

#40 Help Me ! » The Cartesian Coordinate System and the Distance Formula » 2021-02-24 12:27:24

jadewest
Replies: 6

Hello,
I am having trouble with two exercises related to this subject.

The first one states:

4.

What shape do these four points make? (Draw from one to the next in the order given,
and then draw from the last back to the first).

(0,-1), (0,3), (1,1), (-1,1)

A. A square
B. Two acute angles that meet at the acute angles
C. A triangle
D. Two right triangles that meet at the right angles
E. A rhombus
F. Two obtuse triangles that meet at the hypotenuse

My problem is that the figure that comes out is a rhombus, which is the same figure for exercise 3. I am getting confused in whether I'm right or not.





The second exercise is:

Find the distance between the two points:
14. (9, 0) and (-3, -8)

A. 4
B. √(61)
C. √(290)
D. 4[√(13)]
E. 5[√(17)]
F. 3[√(180)]

This is what I've done:
distance = sqrt (-3-9)^2 + (-8-0)^2
d = sqrt (-12)^2 + (-8)^2
d = sqrt 144+64
d = sqrt 208

The problem is that my result is not an alternative.

Thank you in advance!!!

#41 Re: Help Me ! » Geometry » 2021-02-23 11:49:13

Hello,
Thank you for your help! I figured it out and waiting to see what my teacher will say.

#42 Re: Help Me ! » Geometry » 2021-02-22 08:58:52

Hello Bob,
So, here is what I have figured out:

central angle = 360°/5=72°
2 * side angle + central angle = 180°
2SA + 72° = 180°
SA = 54°

sin = opposite/adjacent
sin 54° = h/4
h is approximately 3.2cm

cos = adjacent/hypotenuse
cos 54° = x/4
x is approximately 2.4cm

A = 1/2bh
A = 1/2 * 4.8 * 3.2
A = 7.68cm^2

Is that correct?

#43 Re: Help Me ! » Geometry » 2021-02-21 01:21:45

Hello,
Thank you for the explanation! I have written the solution on my notebook, is it okay if I post it here so that I can check it's correct?

#44 Help Me ! » Geometry » 2021-02-20 11:40:40

jadewest
Replies: 7

Hello,

I'm having trouble solving this problem:

A pentagon’s radius (measure from center to vertex) measures 4 cm, what is the pentagon’s area?

I'm guessing that I'll have to solve this problem by using triangles. What is getting me confused is that I only have one measurement and can't think of how I can solve it? Would appreciate if someone could mentor me in solving it.

Board footer

Powered by FluxBB