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The area of triangle ACE is 120.

one s. is -14.

We know AX = 2, now solve for CX

2 = CX * 4      | : 4

CX = 0.5

BX/2 = 0.5/BX   | * BX

BX = 1

my bad.

so (- m)² - 4 * 3 * 21 < 0    calculate

     m² - 252 < 0                + 252

     m² < 252                    sqrt both sides

     m < 15.87...               round to the nearest integer (16)

m = 16

16 is the answer.

Ooops !   c = 21

Hint: For b² - 4ac < 0 it has no real solutions,

then a = 3, b = -m and c = 7.

Area = height * median

60 = 6 * median

60 / 6 = median

\(\frac{\mbox{Total number of all possible solutions}}{\mbox{Total number of all solutions}}\)

You can choose 100 numbers so 

\(\frac{n}{100}\) .

There are 50 numbers that are divisible by 2 in the set { 1, 2, 3, ..., 100 }.

In the set { 1, 2, 3, ..., 100 } there are 12 numbers divisible by 8.

Every multiple of 8 is divisible by 2, so (50 - 12 =) 38 possible solutions. (n = 38)

\(\frac{38}{100} = \frac{19}{50} = 0.38 = 38\%\)

(x, y, z) = (1, 16, 25) is a valid answer.

BC = 5.

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chancery bb?

Monomials are algebraic expressions consisting only of one term.

A) x^23 is a monomial

B) 2x + 2 is NOT a monomial; it has 2 terms

C) 19 is a monomial

D) 13^9 + 12 is NOT a monomial; there are two terms but they can be combined into one single number

E) x^9 + y^9 is NOT a monomial- it has 2 terms

F) y is a monomial

Let the original number of friends==F
Let the share of each friend ==S

F * S ==63,  
[F - 2]*S + [F - 2] * 2==63, solve for F, S

Use the quadratic formula to get:

F ==9 - original number of friends
S==$7 - original share of each friend.

By the quadratic formula, the only k that works is k = 12.

I wrote a computer program, and found that there were 684 ways.

Christian made a list of five different kinds of brownies: chocolate chip brownies, Rocky Road brownies, brownies with walnuts, peanut butter swirl brownies, and butterscotch brownies. He asked seventy-eight students to choose their favorite brownie from the last.  8/39 of the students liked peanut butter swirl brownies the best.  Three-thirteenths of the students preferred Rocky Road brownies. Chocolate chip brownies were the favorite of two-thirteenths of the students.  7/39 of the students just loved brownies with walnuts and the rest of the students liked butterscotch brownies best. How many students preferred butterscotch brownies?  

Convert each fraction so that they all have a common denominator

peanut butter     8 / 39  =  16 / 78  

rocky road          3 / 13  =    9 / 78  

chocolate chip    2 / 13  =    6 / 78  

brownies             7 / 39  =  14 / 78  

total fraction of students who did not prefer butterscotch   45 / 78  =>  45 students 

total number of students who did prefer butterscotch         78 – 45  =  33 students  

_.

Add all the equations: 

\(10a+10b+10c+10d=28\)

Divide by 10

\(a + b+c+d=\color{brown}\boxed{2.8}\)

Katherine divided her pie into eighths. Savannah divided her pie into fourths. Katherine's family ate six eighths of her pie. How many fourths of Savannah's pie would have to be eaten to result in an equivalent amount of pie being eaten? 

Three.    6 / 8  =  3 / 4   

Convert the times to minutes   10  = 600     7 = 420

600 -x = 420 + 5x

x = 30                   600 - 30 = 570   ====>        so     36 minutes ago it was 9:30    making the time now  =  10:06

its 10,5

Let the cost of 1 mango==M
Then the cost of 1 pear==1/3M

4M  +  1/3M*12 ==4/11
8M ==4/11, solve for M

M ==1/22 - cost of 1 mango
Cost of 1 pear==1/3 * 1/22=1/66

1 - 4/11 ==7/11 of his money left
[7/11] / [1/66] ==[7/11 x 66] ==462 / 11==42 pears - he could buy with the rest of his money.

First let's try and factor what we can first. Since the coefficient of m is -6, then we know that the first part of the parenthesis when factored should look something like this:

(3m _ _)(n _ _)

Then we can plug in some values, since we know that the coefficient of m is -6, we divide -6 by 3, and get -2. Then the expression is:

(3m _ _)(n - 2)

Since the coefficient of n is 7, then the expression is:

(3m + 7)(n - 2).

When done factoring, the expression should look like:

\((3m+7)(n-2)\)

Once the parenthesis are opened, you will see that the constant is -14.

6x³ - 15x² + 21x