Let's put this in terms of a system of equations. Let's call the numbers x and y, with x being the larger integer and y the smaller one. Since they are consecutive odd integers, we know that:
x = y + 2
The constraint is:
xy= 3(x+y) + 71 Simplify
xy = 3x + 3y + 71 Plug in (y+2) for x:
(y + 2) y = 3(y + 2) + 3y + 71 Simplify
y² + 2y = 3y + 6 + 3y + 71 Subtract 6y from both sides, add 71+6
y² -4y = 77
y² - 4y - 77 = 0
Factor:
(y - 11) (y+7) = 0
y = 11 or y=-7
When y = 11, x = 13, since x = y+2
Plug in to make sure:
xy = 3(x+y) + 71
11*13 = 3 (11 + 13) + 71
143 = 3 (24) + 71
143 = 72 + 71
143 = 143
Our values work!
Answer: 11, 13
The domain of this function is x = all real numbers.
The range of this function is that y ≥ 0.
To find the domain, you need to look for exclusions. The only numbers that you exclude are when you can't divide by 0 or have a negative square root. Since this problem has no square root symbol or fractions, it is all real numbers.
For the range, we need to find the smallest value of y. y can get no smaller in this problem than when x = 0. In that case y also = 0. Because the lead coefficient is positive (4), we know that the graph is increasing. Therefore, we know that y must always be bigger than 0.
Answer:
The correct option is B
Step-by-step explanation:
The equation of a line in point-slope form is:
y-y1 = m(x-x1)
where m is the slope and (x1,y1) a point on the line
here m=2 and (x1,y1)=(2,3)
substitute these values into the equation.
y-3 =2(x-2)
Thus the correct opttion is B....
In exponential form: 10^2=3(x+5)
If we were to solve, x=85/3
