C is the answer, looking at point N, after it is reflected across the y 1, you will see the point ends up at (4,1)
This is simple algebra :)
First, we can write the question as an algebraic equation.
Given that Doug spent 40 more hours than Laura, we can represent Laura as (x) and Doug as (x+40).
"Doug and Laura spent a combined 250 hours." So we can write this as
(x) + (x+40) = 250
Now simplify:
2x + 40 = 250
Solve x by subtracting 40 from both sides of the equation:
2x = 210
Therefore:
x = 210/2
= 105
So Laura (x) spent 105 hours!
The answer to that question is the sum of the hours he studied for on both days, which will be 1/4 + 3/8.
However, we cannot add fractions with different denominators. In this case, it's 4 and 8.
So if we want to add them, we must make the denominators similar to each other. How to make 4 into 8? We multiply it by 2: 4 x 2 = 8.
BUT when we multiply fractions, we must multiply both the numerator and the denominator by the same number to keep its original value. In this case, if you want to multiply 4 by 2, you must also multiply 1 by 2.
=> SO to make 1/4 into y/8, we will multiply it like this (1 x 2) / (4 x 2) = 2/8
Now we can add the 2 fractions together. 2/8 + 3/8 = (2 + 3)/8 = 5/8. THIS IS YOUR ANSWER.
TL;DR: He studied 5/8 (or 0.625) hour altogether on both days.
Answer:
5−x²+2xy−y²
Step-by-step explanation:
5 - (x-y)²
Rewrite
(x−y)² as (x−y)(x−y) so
5−((x−y)(x−y))
Expand (x−y)(x−y) using the FOIL Method
Apply the distributive property.
5−(x(x−y)−y(x−y))
Apply the distributive property
5−(x⋅x+x(−y)−y(x−y))
Apply the distributive property
5−(x⋅x+x(−y)−yx−y(−y))
Simplify and combine like terms
Simplify each term
5−(x²−xy−yx+y²)
Subtract yx from −xy
5−(x²−2xy+y²)
Apply the distributive property
5−x²−(−2xy)−y²
Multiply −2 by −1
5−x²+2xy−y²
Corner points in this graph are: ( 0,0 ) ( 0,8 ) ( 5,6 ) and ( 8, 0 ).
If we plug those values in : P = 2 x + 3 y
P ( 0,0 )= 0
P ( 0,8 ) = 2 * 0 + 3 * 8 = 24
P ( 6 , 5 ) = 2 * 6 + 3 * 5 = 12 + 15 = 27
P ( 8 , 0 ) = 2 * 8 + 3 * 0 = 16
The maximum value is:
P max ( 6 , 5 ) = 27
