ChessChris

One Bagel costs 275 Cents 

t=#of toast 

b=#of bagels

m=#of muffins

2t+b=3.15

b+m=3.5

t+2b+3m=8.15

t=3.15-b                       ( b+m=3.5 which means two more muffins means its an extra 1.5 dollars so one muffin would be .75)

3.15-b+2b+3m=8.15 =  b+3m=5  

b=5-2.25

b=2.25 dollars which equals to 225 cents 

Using Pyhthagoreon Theorm we know that     the distance of the two cities=x

7.9^2+5.9^2=(the distance of the two cities)

62.41+32.49=x^2

100=x^2

x=10 

So the distance from arlington and manchester is 10 miles 

Lets call the first integer x 

Integer 1=x 

Integer 2= x+2 becuase it's a consecutive even integer (adding two takes it to the next even integer)

Integer 3=x+4

x+x+2+x+4=-36 

3x+6=-36

3x=-42

x=-14

Substitute x into the integer equation 

x=-14, x=-12, x=-10

The coordinate plane contains points A, B, and C. The constant k then changes to 32.

Let P be (x,y)

= Pa^2+Pb^2+pc^2

= (x-4)^2+(y+1)^2+(x-6)^2+(y-2)^2+(x+1)^2+(y-2)^2

= 3x^2+3y^2-18x-6y+64

= 3(x^2+y^2-6x-2y)+62

= 3((x-3)^2+(y-1)^2)+32

This shows that if Q = (3,1), Pq^2=(x-3)^2+(y-1)^2

And so pa^2+pb^2+pc^2=3pq^2+32

k = 32

x + y + 3z = 10      →   y =  10 - x - 3z

(we want to get y by itself0

-4x + 2y +5z = 7    →   -4x + 2(10 - x - 3z) + 5z = 7   →   -4x + 20 -2x - 6z + 5z  = 7  →  -6x - z = -13  →

6x + z  = 13

(substitute y into  the second equation)

Notice we have this system now 

k*x + z = 3

6x + z = 13 

And notice that, if k =6, we would have this system:

6x + z  = 3      and

6x + z  = 13       but this is impossible, because two things added together can't possibly have two different outcomes 

when k = 6, the system has no solution. 

(a + b)/2 - a/2 - b/2=

(a+b)/2-(a-b)/2=

(a+b-(a-b))/2=

2b/2=b 

First lets remeber the rule a*logb=logb^a

3log7= log7^3

2log5=log5^2

4log2=log2^4

we can write this as 

log7^3+log5^2-log2^4

log(7^3+5^2)/(log2^4) [we can do this becuase of these rules loga^x+loga^y=loga^(x*y) and loga^x-loga(y)=loga(x/y))

log(7^3+5^2)/(log2^4)= log(8575/16) which would be your solution in single log form. Hope this helped!

AD is the angle bisector of angle BAC, we have:

angle BAD = angle CAD = 30

Therefore, triangle ABD is a 30-60-90 triangle, which means that:

AD = BD / sqrt(3) = 8 * sqrt(3)

Now, since angle ABC = 60, triangle ABC is equilateral, which means that all sides are equal. Therefore, we have:

BC = AB

Let x be the length of AB. Then, using the law of cosines in triangle ABC, we have:

x^2 = 24^2 + (8 * sqrt(3))^2 - 2(24)(8 * sqrt(3))(cos 60)
x^2 = 576 + 192 - 384
x^2 = 384
x = 8 * sqrt(6)

Therefore, the area of triangle ABC is:
= (sqrt(3) / 4) * (8 * sqrt(6))^2
= 96 * sqrt(3)

Therefore, the area of triangle ABC is 96 * sqrt(3).

 a3−b3=(a−b)(a2+ab+b2) where a=ab+ac+b and b=ab

(substituting this into the equation we would get)

c(a+b)(3a2b2+3a2bc+3ab2c+a2c2+2abc2+b2c2)

Sales tax means you add whatver the percent of the cost is to the original price to get your final price in this example the solution would just be 

55*7%= 55*.07=3.85

know since we have the amount it costs with the tax we add 55 and 3.85 to get 58.85 after sales tax 

I don't know what you mean by this if its 3^2 than the answer would be 9 if it's 2 ^3 than the answer would be 8 

The equation of the parabola in the vertex form is y=a(x−h)^2+k

The vertex is given as (0,-2) and from the point given, we know that x = 4, and y = 1.

Plugging these points in the equation we get, 1=a(4-0)^2+2

1=4a+2

4a=-1

a=-1/4

So the equation of the proabola in vertex form would be y=-1/4(x-0)^2+2

AD is the angle bisector of angle BAC, we have:

angle BAD = angle CAD = 30

Therefore, triangle ABD is a 30-60-90 triangle, which means that:

AD = BD / sqrt(3) = 8 * sqrt(3)

Now, since angle ABC = 60, triangle ABC is equilateral, which means that all sides are equal. Therefore, we have:

BC = AB

Let x be the length of AB. Then, using the law of cosines in triangle ABC, we have:

x^2 = 24^2 + (8 * sqrt(3))^2 - 2(24)(8 * sqrt(3))(cos 60)
x^2 = 576 + 192 - 384
x^2 = 384
x = 8 * sqrt(6)

Therefore, the area of triangle ABC is:
= (sqrt(3) / 4) * (8 * sqrt(6))^2
= 96 * sqrt(3)

Therefore, the area of triangle ABC is 96 * sqrt(3).

Lets use x and y, x being your money and y being your brothers

(If I give my brother 5 dollars, then we will have the same amount of money.)

that means that x-5=y+5; x= y+10

( If instead he gives me 24 dollars, then I'll have twice as much money as he will have.)

using this information we can write the amount of money as 2(y-24)=x+24

(substitue y) 2(y-24)=y+34 =   2y-48=y+34 =  y=82

Since y stands for your brothers money that means your brother has 82 dollars and you have 92. Hope this helps! :)

x + y + 3z = 10      →   y =  10 - x - 3z

(we want to get y by itself0

-4x + 2y +5z = 7    →   -4x + 2(10 - x - 3z) + 5z = 7   →   -4x + 20 -2x - 6z + 5z  = 7  →  -6x - z = -13  →

6x + z  = 13

(substitute y into  the second equation)

Notice we have this system now 

k*x + z = 3

6x + z = 13 

And notice that, if k =6, we would have this system:

6x + z  = 3      and

6x + z  = 13       but this is impossible, because two things added together can't possibly have two different outcomes 

when k = 6, the system has no solution.