All Answers 358512 Answers

One ordered pair (a,b) satisfies the two equations ab^4 = 48 and ab = 72. What is the value of b in this ordered pair?  

To find b, consider                                                  ab⁴  =  48  

We will divide both sides by ab.  

Since ab=72, we will divide the left side  

by "ab" and the right side by its equal 72.  

                                                                              ab⁴         48  

                                                                             ——   =   ——  

                                                                              ab           72  

Note that ab⁴ = (ab) * (b³)  

Cancel ab out of the left side.  

Reduce 48/72 on the right side.  

                                                                               b³           2  

                                                                             ——   =   ——  

                                                                                1            3  

                                                                                 b   =   cube root of (2 / 3)  

_.

[n + 1] / n * [n + 2] / [n + 1] * [n + 3] / [n + 2] *..............* [n + 20] / [n + 19] ==3

All cancel out except: [n + 20] / n ==3

[n + 20] ==3n

20 =3n - n

20 =2n

n ==10  and the first fraction is: [10 + 1] / 10 ==11 / 10 - this is the first fraction.

Check: 11/10 * 12/11 * 13/12 * 14/13 *............* 30 /29 ==3

Let a and b be the numerator and denominator of the first fraction. We know that a=b+1. The product of the fractions is: \begin{align*} \frac{a}{b}\cdot\frac{a+1}{b+1}\cdot\frac{a+2}{b+2}\cdots\frac{a+19}{b+19}&=\frac{a^{20}}{b^{20}}\ &=\frac{(b+1)^{20}}{b^{20}} \end{align*}We are given that this product equals 3, so [(b+1)^{20}=3b^{20}.]We can factor out a b20 from both sides to get [b^{20}(b+1)=3b^{20}.]This simplifies to b+1=3, so b=2. Then a=b+1=3, so the first fraction is 2/3​​.

Well, now there are two.  The OP can decide which one is more useful. 

Levans writes a positive fraction in which the numerator and denominator are integers, and the numerator is $1$ greater than the denominator. He then writes several more fractions. To make each new fraction, he increases both the numerator and the denominator of the previous fraction by $1$. He then multiplies all his fractions together. He has $20$ fractions, and their product equals $3$. What is the value of the first fraction he wrote?

This question has been solved. Search for it by putting your question in the "Search Box" in the top right-hand corner.

This question has been solved. Search for it by putting your question in the "Search Box" in the top right-hand corner.

This question has been solved. Search for it by putting your question in the "Search Box" in the top right-hand corner.

This question has been solved. Search for it by putting your question in the "Search Box" in the top right-hand corner.

I have to paint one side of a wall.  The wall is 12 meters tall and 120 meters long.  Each gallon of paint covers 150 square feet. If a foot is approximately 0.3048 meters, then what is the smallest whole number of gallons I can buy and have enough paint to cover the whole wall?  

You're going to have to convert those meters to square feet,  

so I think it's better to do it from the start.  Even though we'll  

have fractions to contend with, a calculator makes that easy.  

                                                                       12 m  

1 foot is 0.3048 meter, so the height is       –––––––––  =  39.3701 ft   

                                                                   0.3048 m/ft  

                                                                       120 m  

1 foot is 0.3048 meter, so the length is       –––––––––  =  393.7007 ft   

                                                                   0.3048 m/ft  

Area is height times length     (39.3701 ft)(393.7007 ft)  =  15,500.0359 sq ft  

1 gallon will cover 150 sq ft  

so divide that into the area               15,500.0359 sq ft  

                                                        –––––––––––––––  =  103.3335 gallons  

                                                           150 sq ft/gallon  

You can't buy just part of a gallon of paint,  

so we have to round that up to whole gallons                       104 gallons  

_.

I think there is a mistake in your question! Make sure you didn't reverse the numbers for juniors and seniors!

Where are the "numbers" in your question? Did you check it before posting it??

umm... it says that it is incorrect... what should i do?

C + B + P==103, 

B/P ==4/5, 

[C - 1/2C + B - 1/2B + P]==79, solve for B, C, P

Use substitution to get:

B==44 erasers - what Brandon started with

C ==4 erasers - what Caden started with

P ==55 erasers - what Perry started with.

44 - (44/2) ==22 erasers - Brandon had in the end.

55 - 0 ==55 erasers - what Perry had in the end.

22 + 55==77 total erasers of Brandon and Perry at the end.

4 - (4/2) ==2 erasers - what Caden had in the end.

Check: 22 + 55 + 2 ==79 total of all erasers at the end. 

The perimeter of a rectangular field is 330 yards.  

If the width of the field is 72 yards, what is its length?  

The perimeter is the Length + Width + Length + Width.  

You can also express this as 2L + 2W.  

So,                                P  =  2L + 2W  

                                  330  =  (2)(L) + (2)(72)  

                                  330  =  2L + 144  

                                  330 – 144  =  2L  

                                      2L  =  186  

                                        L  =  93  

_.

Hi Melody,

Thanks for your feedback...well, the question how I gave it is preceisely how it is on the paper...They give the graph, you can clearly see "a" is 1, yet they ask to calculate "a" for 4 mnarks...anycase, thanks for your time...always appreciated...stay well..

Do the following:

Franklin can move a maximum of 6 steps to the right, 6 steps to the left, 6 steps up, or 6 steps down. If he moves a maximum in any one direction, he can end up at 6^2 = 36 different points. However, he could also move 5 steps to the right, 5 steps up, and 2 steps to the left. This would give him a different point than if he had moved 6 steps to the right and 6 steps up. In other words, Franklin can end up at 6^2 * 4 = 96 different points.

However, this is not the final answer. Franklin can also end up at the origin after 12 steps. He can do this by taking 6 steps to the right, 6 steps to the left, 6 steps up, and 6 steps down. This gives us a total of 96 + 1 = 97 possible points.

We can solve this problem by casework.

Case 1: The first square is red.

The second square must be yellow, and the third square must be blue. The fourth square can be red, yellow, or blue, and the fifth square can be the color that was not used in the first three squares. This gives us 3×3=9 possible arrangements.

Case 2: The first square is yellow.

The second square must be red, and the third square must be blue. The fourth square can be red, yellow, or blue, and the fifth square can be the color that was not used in the first three squares. This gives us 3×3=9 possible arrangements.

Case 3: The first square is blue.

The second square must be yellow, and the third square must be red. The fourth square can be red, yellow, or blue, and the fifth square can be the color that was not used in the first three squares. This gives us 3×3=9 possible arrangements.

Therefore, there are 9+9+9=27​ ways to color the five squares.

How many erasers did Brandon and Perry have in the end?

Hello Guest!

\(c+b+p=103\\ b:p=4:5\\ \dfrac{c}{2}+\dfrac{b}{2}+p=79\\ p=\dfrac{5b}{4}\\ c+b+\dfrac{5b}{4}=103\\ \dfrac{c}{2}+\dfrac{b}{2}+\dfrac{5b}{4}=79\)

\(c+b+\dfrac{5b}{2}=158\\ 158-b-\dfrac{5b}{2}=103-b-\dfrac{5b}{4}\\ 55=\dfrac{5b}{2}-\dfrac{5b}{4}\\ 55=\dfrac{5b}{4}\\ \color{blue}b=44\\ Brandon\ has\ 44\ erasers\ at\ the\ beginning.\\ b:p=4:5\\ p=\dfrac{5b}{4}=\dfrac{5\cdot 44}{4}\\ \color{blue}p=55\\Perry\ has\ 55\ erasers\ at\ the\ beginning.\)

\(c=103-44-55\\ c=4\\ Caden\ has\ 4\ erasers\ at\ the\ beginning.\\ Brandon\ and\ Caden\ gave\ up\ half\ of\ their\ erasers.\\b-\dfrac{b}{2}+p= 44-\dfrac{44}{2}+55=\color{blue}77\)

77 erasers did Brandon and Perry have in the end.

  !

I do not think your question is complete Juriemagic.

Anyway your question is presumably in degrees.

the amplitude is 'a', the wavelength is 720 degrees  (2pi radians)

and the diplacement is 30 degrees to the right

The other guy gave the right answer, but, heck, you

could get that from the answers in the back of the book. 

That doesn't help you with the "how" of solving the problem. 

Here's the way I answered this problem several days ago.  

A bag contains yellow, green, blue, and white marbles.  The ratio of yellow, green, blue, and white marbles is 1:2:3:4.  If the bag contains 180 marbles, then how many blue marbles are there?  

Consider:  "The ratio of yellow, green, blue, and white marbles is 1:2:3:4."  

Call the number of yellow marbles X.  

So the number of green marbles is 2X. 

And the number of blue marbles is 3X.  

And the number of white marbles is 4X.  

Add up all the marbles and you have     10X  =  180  

Therefore                                                   X  =  18 yellow marbles  

                                                                 2X  =  36 green marbles  

                                                                 3X  =  54 blue marbles  

                                                                 4X  =  72 white marbles  

_.

54 blue marbles

incorrect