Answer:
b=4
Step-by-step explanation:
So, we have the function 
. We need to find b such that the average rate of change or the slope is -1/8 between the intervel [2, b]. First, let's find f(2).
f(2) = 1/(2) = 1/2
So, we have the point (2, 1/2)
At point b, f(b) = 1/b.
Let's plug this into the slope formula:
Now, we just need to solve for b. First, let's multiply both the numerator and denominator by b (to get rid of the annoying fraction in the numerator).
Now, cross multiply.
Solve for b. Factor using the numbers -4 and -2.
Thus, b=4 or b=2.
However, b=2 is not a possible solution since the interval [2,2] means nothing. Thus, b=4.
Answers:
The area for the square on the left is 81m^2. This is found because all sides of this square are the same, so the length and width are the same. Just multiply 9 x 9.
The area for the triangle is 31.5m^2. We find the left side is 9 meters because the triangle shares the same side as the square on the left side. We also find the bottom side is 7 because that is the length of each side of that square because all sides on a square is the same. We then multiply 9 times 7, getting 63, we divide this by 2 because it’s a triangle.
The square on the right has the area of 225 because both length and width is 15.
Answer:
3cm+2cm+5cm=10cm
%=100
10*10=100
2cm*10=20%
Step-by-step explanation:
the shaded area is width of 2 2/10 or 20/100
W=4L/9
A=LW, using W found above gives us
A=L(4L/9)
A=4L^2/9 and we were told that A=576 so
4L^2/9=576 multiply both sides by 9
4L^2=5184 divide both sides by 4
L^2=1296 take the square root of both sides
L=36, and we know that W=4L/9 so
W=4(36/9)=16
So the dimensions are: width=16in and length=36in
Answer:
B. r + l = 45; 2r + 3l = 96
39 regular; 6 long-distance
Step-by-step explanation:
There were 45 baskets, so
(1) r + l = 45
There were 96 points in the game, so
(2) 2r + 3l = 96
Solve equation (1) for l
l = 45 – r Substitute the value for l in Equation (2)
2r + 3(45 – r) = 96 Remove parentheses
2r + 135 - 3r = 96 Combine like terms
-r + 135 = 96 Subtract 135 from each side
-r = -39 Multiply each side by -1
r = 39 Substitute the value of r in Equation (1)
39 + l = 45 Subtract 39 from each side
l = 6
===============
Check:
(1) 39 + 6 = 45
45 = 45
(2) 2×39 + 3×6 = 96
78 + 18 = 96
96 = 96
