Answer:
6 days
Step-by-step explanation:
Step one:
Given data
For Ray
He has 16 pages already
Now he is writing 2 pages per day
let x be the number of days
and y be the total number of pages writen
the linear function for the situation is given as
y=2x+16-------------1
For Claudia
He has 2 pages already
Now he is writing 4 pages per day
let x be the number of days
and y be the total number of pages writen
the linear function for the situation is given as
y=4x+2-------------2
Step two:
let us equate equation 1 and 2 to find x
2x+16=4x+2
collect like terms
2x-4x=2-16
-2x=-12
divide both sides by -2
x=12/2
x=6
Therefore it will take 6 days for them to have the same number of pages
Answer:
a = 2/27
b = 13/27
Step-by-step explanation:
The given polynomial is presented as follows;
f(x) = a·x³ + b·x² + x + 2/3
Given that x + 3 is a factor, we have;
f(-3) = 0 = a·(-3)³ + b·(-3)² - 3 +2/3 = 0
-27·a + 9·b - 3 + 2/3 = 0
-27·a + 9·b = 7/3........(1)
Also we have
(a·x³ + b·x² + x + 2/3) ÷ (x + 2) the remainder = 5
Therefore;
a·(-2)³ + b·(-2)² + (-2) + 2/3 = 5
-8·a + 4·b - 2 + 2/3 = 5
-8·a + 4·b = 2 - 2/3 = 4/3........(2)
Multiplying equation (1) by 4/9 and subtracting it from equation (2), we have;
-8·a + 4·b - 4/9×(-27·a + 9·b) = 4/3 - 4/9 × 7/3
-8·a + 12·a = 8/27
4·a = 8/27
a = 2/27 ≈ 0.0741
imputing the a value in equation (1) gives;
-27×2/27 + 9·b = 7/3
-2 + 9·b = 7/3
9·b = 7/3 + 2 = 13/3
b = 13/27 ≈ 0.481.