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Real numbers a and b satisfy

a + ab = 250

a - ab = -240

Enter all possible values of a, separated by commas.

If you add the two equations together                a + ab  =   250  

                                                                           a – ab  = –240  

                                                                          ————————  

you get                                                              2a         =  10  

from which                                                                  a  =  5  

The problem doesn't ask for b,  

but ... find b by substituting  

a back into a + ab = 250                                    5 + 5b  =  250  

                                                                                5b  =  245  

                                                                                  b  =  49  

check b by substituting  

a back into a – ab = –240                                  5 – 5b  =  –240  

                                                                              –5b  =  –245  

                                                                                  b  =  49  

_.

Do not post a link like that again or you will be banned from the forum.

I did this question using same of the same logic as you but I did get a different answer.

I have not checked my answer , or yours.

But one of them is wrong.

72% AS a decimal  

The % sign is called percent. 

Percent is short for per centum.  

Centum means hundred.  It's Latin. 

When they want to say something important,

they say it in Latin.  Lawyers do this a lot. 

Nobody knows why.  

And in math, "per" means "divided by".

Anyway, 72 percent is 72 per hundred, written as 0.72.  

_.

I may have tried to help but the writing is too small.  

Find the sum 1/8 + 1/3 enter your answer in simplest term  

The requisite for adding or subtracting fractions, is to  

determine a common denominator.  

One way you can always find a common denominator  

is by multiplying the denominators together. 

                                              1         1            3          8  

                                             ––   +   ––    =    ––   +   ––  

                                              8          3           24        24  

Should be easy for you now.  

                                                                       11 

                                                                       ––  

                                                                       24  

_.

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?  

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)  

_.

sorry, but that is wrong

Let the number be 10x+y     where x and y are single digit numbers and x is not 0

10y+x=10x+y-45       and     x=2y-1   or     y=2x-1

10y+x=10x+y-45

9y-9x=-45

y-x=-5

y=x-5

now

x=2y-1        or        y=2x-1

x=2(x-5)-1        or        y=2x-1

x=2x-11       or        x-5=2x-1

-x=-11             or        -x=4

x=11              or           x=-4

x is a one digit number so x=-4

y=x-5

y=-9

-40-9

=-49

check

-40-9 = -90-4   + 45

rhs = -45-4=-49 = lhs    true.

-9=2*-4-1   true

This is the second time this has been answered in the last few days.

Circumference of the tire = 11 * 2 * 3.14 =69.08 inches

69.08  *  15 =  1,036.2 - inches - total distance travelled.

1,036.12 inches / 12 inches per foot =86.35 feet - total distance travelled. 

the big one has side length    27

the next has sidelength    27*2/3 = 18       the difference between the 2 is 9

the next has sidelength    18*2/3 = 12        the difference between the 2 is 6

etc

put all the lengths on the pic and work out the perimeter and area.

The probability that the distance will be MORE than 1.5cm   will be 

the area of the solid red section / the area of the unit circle.

The prob that it will be LESS than 1.5cm will be 1 - the answer you just got.

The answer will be way higher than the  47%  acyclics figured.

If you want me to explain further how I figure this then ask me in a continuing post.

Answered here: https://web2.0calc.com/questions/even-more-more-more-geometric-series-and-sequences#r3

To solve this problem, we first need to find the area of triangle XYZ. Since triangle XYZ is a right triangle, we can use the formula for the area of a triangle:

Area = (1/2) * base * height

The base of triangle XYZ is XY, which has a length of 12, and the height is YZ, which has a length of 6. Therefore, the area of triangle XYZ is:

Area(XYZ) = (1/2) * 12 * 6 = 36

Now, we need to find the probability that the area of triangle XYD is at most 20. Since point D is chosen randomly within triangle XYZ, any point within the triangle is equally likely to be chosen. So, we can consider the ratio of the areas.  link deleted by Melody

To find the probability, we compare the area of triangle XYD to the area of triangle XYZ. The probability is given by:

Probability = Area(XYD) / Area(XYZ)

To find the area of triangle XYD, we need to determine the base and height of this triangle. The base is still XY, which is 12. The height can be found by considering that the area of triangle XYD is half the area of rectangle XYZD.

Since XYD is a right triangle, the height is the altitude from the right angle to the hypotenuse YD. We can use the formula for the area of a triangle to find the height:

Area(XYD) = (1/2) * base * height

20 = (1/2) * 12 * height

height = (2 * 20) / 12 = 40 / 12 = 10 / 3 ≈ 3.33

Therefore, the height of triangle XYD is approximately 3.33.

Now we can calculate the area of triangle XYD:

Area(XYD) = (1/2) * 12 * 3.33 ≈ 19.98

Now we can calculate the probability:

Probability = Area(XYD) / Area(XYZ) = 19.98 / 36 ≈ 0.555

So the probability that the area of triangle XYD is at most 20 is approximately 0.555, or 55.5%.  

What diagram?

Think about these two equations and what they mean:

(D is Dad & G is Grogg)

D - 7 = 6(G - 7)

D - 4 = 4(G - 4)

Ahhh yes, I failed to consider the combinations with 1s in them. Thank you so much, and I now understand.

Um... Franklin can either go to the right, left, up or down, so there are four points he can be at after 1 step? Not sure if this is what you mean but-

Thanks Tiggsy,

I'll take your word that my answer is flawed.

If the question asker bothers to respond I will do it over :))

Hi Tiggsy, 

You are probably correct ,  either way the instructions are poor.

It is not equal to 11/6

Six cards problem:

There are C(6,3) = 20 ways to distribute the cards to the couples. For each of these ways, there is one way to distribute the cards within each couple so that both people have the same card number. Therefore, there are 20 ways to distribute the cards so that both people in each couple have the same card number. The total number of ways to distribute the cards is C(9,6) = 84, so the probability is 20/84​ = 5/21​​.

Solve 3a + 4b = 5a - 6b + 24 - 3a for a in terms of b.  

                                                                         3a + 4b = 5a - 6b + 24 - 3a  

Put all the a's on one side of the  

equals sign and everything else  

on the other side                                              3a – 5a + 3a  =  –6b – 4b + 24  

Total the like terms                                                             a  =  –10b + 24  

_.

0.8 = y/(186 + x),

148.8 + 0.8x = y.

 y is to be an integer, so 0.8x has to be something point 2.

The smallest value of that fits is x = 4, then 148.8 + 3.2 =152.