If your asking for a standard deck of cards the probability is 1/8
She was correct to multiply .75 by .15 to get .1125, but she forgot to add that value to .75 to get the total amount of fabric needed.
1.1 Factoring: 4x2+9y2+16z2-6xy-12yz-8xz
Thoughtfully split the expression at hand into groups, each group having two terms :
Group 1: -6xy-12yz
Group 2: 16z2-8xz
Group 3: 4x2+9y2
Pull out from each group separately :
Group 1: (x+2z) • (-6y)
Group 2: (x-2z) • (-8z)
Group 3: (4x2+9y2) • (1)
Looking for common sub-expressions :
Group 1: (x+2z) • (-6y)
Group 3: (4x2+9y2) • (1)
Group 2: (x-2z) • (-8z)
Answer: 44%
Step-by-step explanation:
For a circle of radius R, the area is written as:
A = pi*R^2
Where pi = 3.14
If we increase the radius by 20%, the new radius will be:
R´ = R + 0.20*R = 1.20*R
The new area will be:
A´ = pi*(1.20*R)^2 = (1.20)^2*pi*R^2
= 1.44*pi*R^2
And pi*R^2 = A, the original area, then_
A´ = 1.44*A = A + 0.44*A
This means that the percentage in which the area increased is:
0.44*100% = 44%
You can't solve it because it isn't equal anything
but we can factor
since the quadratic coefient (number in front of y^2 term) is 1
we can do this
for ax^2+bx+c
when a=1
what 2 numbers multiply to c and add to b
what 2 numbers multiply to -16 and add to -8
no numbers
if you had y^2-8y+16 then that would be (x-4)(x-4)
but no
ok, so we need to complete the squaer
so
y^2-8y-16
take 1/2 of linear coefient and square it
-8/2=-4, -4^1=16
add negative and poisitve to it
y^2-8y+16-16-16
factor
(y-4)^2-16-16
(y-4)^2-32
then we can force factor again
remember difference of 2 perfect square
a^2-b^2=(a+b)(a-b)
√32=4√2
so
(y-4)^2-(4√2)^2=(y-4+4√2)(y-4-4√2)
the factore form would be (y-4+4√2)(y-4-4√2)
not equal to anything tho so we can't solve
