I got (-6.28, -0.76).
Step 1.) Write out the problems
-2x=8-6y
-15x=21-6y
Step 2.) Pick a problem and solve for X
-2x=8-6y = x=-4-3y
Step 3.) Plug in the x
(-15)(-4-3y)= 21-6y
60 + 45y= 21-6y
Step 4.) Solve for y
y=-0.76
Step 5.) Plug in the y value into one of the equations
-2x= 8- 6(-0.76)
-2x= 8 + 4.56
x= -6.28
Step 6.) Check your answers
-2(-6.28)=8-6(-0.76)
12.56=12.56
Step 7.) Write it out
(-6.28,-0.76)
It will be 16[tex] 16^{2} = 256
There are 6 other positions in the string, each with 26 choices. So if you fix BO as the first two letters, there are
possible strings that you can make.
If BO is at the end of the string, you still have
possible strings.
Together, then, you have
possible strings.
To find the area of the curve subject to these constraints, we must take the integral of y = x ^ (1/2) + 2 from x=1 to x=4
Take the antiderivative: Remember that this what the original function would be if our derivative was x^(1/2) + 2
antiderivative (x ^(1/2) + 2) = (2/3) x^(3/2) + 2x
* To check that this is correct, take the derivative of our anti-derivative and make sure it equals x^(1/2) + 2
To find integral from 1 to 4:
Find anti-derivative at x=4, and subtract from the anti-derivative at x=1
2/3 * 4 ^ (3/2) + 2(4) - (2/3) *1 - 2*1
2/3 (8) + 8 - 2/3 - 2 Collect like terms
2/3 (7) + 6 Express 6 in terms of 2/3
2/3 (7) + 2/3 (9)
2/3 (16) = 32/3 = 10 2/3 Answer is B
Let small cups = S
Large cups = L
They bought a total of 8 cups, so S + L = 8
Rewrite as S = 8-L (1st equation)
Then you also have
$3S + $5L = $30 (2nd equation)
Replace the S in the second equation with the first equation:
$3(8-L) + $5L = $30
Simplify:
24 - 3L + 5L = 30
Combine like terms:
24+2L = 30
Subtract 24 from both sides:
2L = 6
Divide both sides by 2:
L = 3
They bought 3 large cups
Since they bought a total of 8 cups, that means they bought 5 small cups ( 8-3=5)
Large = 3 cups, Small = 5 cups
