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Peter => x

x + 7x/3 + 1/2(7x/3) = 999

x = 222

1/3 of the 6 dozen fruits in a fruit seller's cost are apples. If 1/4 of all the fruits are oranges & the rest are bananas, how many dozen bananas are there in the fruit seller cart?     

So, rewording the problem,      1/3 • 6 dozen fruits  =  2.0 dozen fruits are apples  

                                                 1/4 • 6 dozen fruits  =  1.5 dozen fruits are oranges  

We see that the apples + the oranges  =  3.5 dozen fruits that are not bananas  

Therefore, the bananas are (6.0 dozen – 3.5 dozen)  =  2.5 dozen that are bananas  

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Setting Joe has 3x, Alex has 8x, Sean has 5x,

3x + (1 - 1/5) * 5x * 3/8 = 8x + (1 - 1/5) * 5x * 5/8 - 96

x = 16

∴ 3x + 16 + (1 - 1/5) * 5 * 16 * 3/8 = 72

∴ Joe have 72 stamps in the end.

In this case, me look up the apply math. 

Triangle ABC is isosceles with angle B congruent to angle C. The measure of angle C is five times the measure of angle A. What is the number of degrees in the measure of angle B?     

The sum of the three interior angles of any triangle is 180^o. 

So A + B + C  =  180^o  

and B = C  

and C = 5A  

Since B = C and C = 5A, then B = 5A   

Use substitution to get A + B + C all in terms of A  

A + 5A + 5A  =  180^o   

[At this point I realized where it was going, and started having misgivings about my solution.  Usually, problems this easy are constructed to that the answer comes out even.  I've checked and double checked and doubled that again, and I can't see that I'm doing anything wrong.  So, I'm going to continue to the end.  But I'd feel a whole lot better if the problem had said that C is four times A.] 

So 11A = 180^o  which means that A = 180/11 degrees  

Since B = 5A, then B = 900/11 degrees  or in decimal form, approximately 81.82 degrees   

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2x/(x + 2) = -6/(x + 4) + 5

Hello Guest!

\(x\notin \mathbb R\)

  !

The first equation is:  3a + 4b  =  7

The second equation is:    6a + 4b  =  k - 3a - 8b

which becomes:              9a + 12b  =  k

Multiplying the first equation by 3:  9a + 12b  =  21

For these to have infinitely many solutions, these must be two forms for the same equation; so  k = 21

Two points on this line are  (0,-3)  and  (1,-5).

The solpe is  (-5 - -3) / (1 - 0)  =  -2

The y-intercept is  (0, -3)

The equation is:  y  =  -2x - 3

It appears to be a hyperbola whose center is (3,-1)  --->   y + 1  =  1/(x - 3)

This becomes:  y  =  (-x + 4) / (x - 3)  =  (x - 4) / (-x + 3)

Solve for x:
3^(2 x - 1) = 9 2^(-x + 3)

Take the natural logarithm of both sides and use the identities log(a b) = log(a) + log(b) and log(a^b) = b log(a):
log(3) (2 x - 1) = log(2) (-x + 3) + 2 log(3)

Expand out terms of the left hand side:
2 log(3) x - log(3) = log(2) (-x + 3) + 2 log(3)

Expand out terms of the right hand side:
2 log(3) x - log(3) = -log(2) x + 3 log(2) + 2 log(3)

Add x log(2) + log(3) to both sides:
(log(2) + 2 log(3)) x = 3 log(2) + 3 log(3)

Divide both sides by log(2) + 2 log(3):

x = (3 log(2) + 3 log(3))/(log(2) + 2 log(3))==~1.85972

NEW area   5 * 9 = 45  in²

Original area  6*10 = 60

(60 - 45) / 60 * 100% = 25 % decrease

Nice logic Guinevere  

You should give yourself a point  

Would you please explain how you got this answer?

If it takes four painters 1.25 days to finish a job, it would take one person 5 days to finish the same job. If this five days is divided into 3 people, it will take 5/3 days for them to complete the job.

since a two-pound cake requires 1.5 cups of flower, a one-pound cake would take 0.75 cups of flower.

0.75*12=9

\(\sqrt(x\sqrt(x))\) on the inside of the parenthesis, move the x to the inside of the other sqrt, so that

\(\sqrt(\sqrt(x^3))\) the inside sqrt can be combined with the 3 on the inside, so that
\(\sqrt(x^{3/2})\). This is also the answer.

It can also be expressed as \(x^{3/4}\)

Each hour is 60 minutes, so convert the second value to minutes.

3*60+30=210 (for converting to minutes)

If she can eat 1 popsicle per 15 minutes, divide 210 by 15. This comes out to 14, so she can eat 14 popsicles in 3 hours and 30 minutes.

To simplify radicals such as these, there are multiple methods. One method is to find the prime factorization of the number and edit it from there.

(2*2*2*2*7) is the prime factorization for 112. You can pull out pairs of numbers to the front of the sqrt, although cancel one in the process. this would then be \(2*2\sqrt7\) this is then simplified to \(4\sqrt7\), which is the answer.

To find the perimeter, we must first find the distance from (1, -2) to  (4, -10). To do this, we can use the distance formula.

\(\sqrt((x\delta)^2+(y\delta)^2),\) where \(\delta\)=the change in positioning for the point.

We can plug in for this equation to get \(\sqrt((4-1)^2+(-10--2)^2)\)

Simplifying this, we get \(\sqrt(3^2+(-8)^2)\), then \(\sqrt(9+64)\), and finally \(\sqrt73\)

Since there are 4 sides to a square, multiply \(\sqrt73\) by 4 to account for all sides.

The final answer should be \(4\sqrt73\) since 73 is prime.

First, we set each person to a variable.

If Peter=x, or (6/6)x

    Ned=2 1/3 x, or (7/3)x, or (14/6)x,

 Morris= (7/6)x

Since the total number of apples was 999, (6/6)x+(14/6)x+(7/6)x=999

Adding the x coefficients together, we get (27/6)x=999.

To get rid of the fraction, multiply both sides by (6/27).

This results in x=999*(6/27)

999*(6/27)=222

If we plug this in for each person, we get

  Peter=222,

    Ned=518,

Morris=259

It is also helpful to make a graph (as shown below) for convenience:

 (obviously the 3rd column would not be needed for this problem)

The minute hand of a clock, while moving, creates an arc that is some part of a circle.

Since the minute hand is only moving for 45 minutes, it moves 3/4 of an entire circle.

This circle would have radius of 4.5 inches.
The circumference of a circle is πd, where d is 2r.

We can substitute 2*4.5 for d.

The circumference of a circle with radius of 4.5 is 9π.

Since only 3/4 of the entire circumference is travelled, multiply 9π by 3/4.

(3/4)*9π=27π/4, or ≈21.206

Would you please explain how you got 625 as the answer?

If on the sixth day Annie has 5/8 of the bag left, that means she ate 3/8 in 6 days. (3/8)/6=1/16, so Annie eats 1/16 of the bag per day.

By the 9th day, she will have eaten 9/16 of the bag, meaning 7/16 of the bag is left.

Let x=the number of sweets in the bag.

(7/16)x=63. To get rid of the coefficient of x, multiply both sides by (16/7), resulting in

x=63*(16/7), which also is x=144

Therefore, the number of sweets in the bag at the start is 144.

Would you please explain how you got 92 degrees as the answer?

To find the angle of the circle graph, we must first find how many total people are accounted for in this graph. 

Plugging in from the given information, 53+8+155+17+145+10+98+2=488

Since circles are made up of 360 total degrees, we divide 360/488 for the degrees per person. This also simplifies to 45/61.

Since 145 people are in the "45-54 year-old Males" sector, we multiply 145*(45/61).

145*(45-61)≈106.967
106.967 to the nearest whole number is 107, so the answer is 107.

Instead of using "snake" and "fish", we will set snake and fish equal to s and f, respectively.

The equation s=2f is true.

Since 9 fish are left in the shop after 5 are sold, the original number of fish was 14.

If you substitute this into the first equation, s=2*14, so s=28.