Answer:

Step-by-step explanation:
Before you add 2 fractions, the denominator needs to be the same. If they are the same, which they are, then add the 2 numerators.
1 plus 2 equals 3.
So the answer is 3 over 5.
For ease of solving, let's first find the rate of Mia and Luke per minute. Since Mia can do 4 pieces every 3 minutes, then she can do

of a piece per minute. Luke on the other hand can do

of a piece per minute.
To find how many pieces they made, we first need to find the time it took for them to make the pieces. We assign

as the time Mia spent making origami. Since Luke spent 5 more minutes, we can denote his time as

.
Putting this into an equation we'll get:




Therefore, Mia made pieces of origami for 39 minutes. Knowing this, we can find out the number of pieces of origami she made:
ANSWER: Mia made 52 pieces of origami.
Answer:
q=35
Step-by-step explanation:
x2 - 12x + q = 0
Let the two roots be r and r+2.
Factor the quadratic expression:
(x - r)[x - (r + 2)] = 0
Expand, simplify, group like terms, and get
x2 - 2(r + 1)x + r(r + 2) = 0
Compare to
x2 - 12x + q = 0
and set equal the coefficients of like terms:
Coefficient of x:
-2(r + 1) = -12 ⇒ r + 1 = 6 ⇒ r = 5
(Then the other root is r + 2 = 5 + 2 = 7)
Constant term:
r(r + 2) = q ⇒ 5(5 + 2) = q
q = 35
Test the solution:
(x - 5)(x - 7) = x2 - 12x + 35
With two roots differing by 2, you get an equation of the form
x2 - 12x + q = 0
with q = 35.
Answer look below
Step-by-step explanation:
Hope this helps