Answer:
Both air balloon and water balloon data are best modeled by an exponential function.
Step-by-step explanation:
Air balloon
Time (seconds) Volume (cubic centimeters)
0 95
3 69
6 50
9 37
12 27
The relation Volume variation/time is constant for lines, In this case, this value change from point to point, as can be seen next.
(69 - 95)/3 = -8.67
(50 - 69)/3 = -6.33
(37 - 50)/3 = -4.33
(27 - 37)/3 = -3.33
Water balloon
Time (seconds) Volume (cubic centimeters)
0 30
3 15.8
6 7.8
9 4
12 2
(30 - 15.8)/-3 = -4.73
(15.8 - 7.8)/-3 = -2.67
(7.8 - 4)/-3 = -1.27
(4 - 2)/-3 = -0.67
In this case, the relation Volume variation/time also change from point to point.
Then, both air balloon and water balloon data are best modeled by an exponential function.
Answer:17
Step-by-step explanation:Follow pemdas.
Start with parentheses which is (5+2) which gives you 7.
Now next in Pemdas is Exponents. SO do 2 to power of 2 which is 4 .Then do 3 to the power of 3 which is 27.Next add 4 to 27 which is 31.so now do 7 times 2 is 14.Then take 31 and subtarct it from 14 which gives you 17.
Look at pic to see clearly how it was solved and the steps. I color code it to show the steps.
Answer:
c would be the closest
Step-by-step explanation:
All triangles equal 180*. so if you combine the 2 angles, which adds up to 77* then that would leave the third angle to be 103* but since that isnt an option choose c since its the closest.
<h3>
Answer: -2w^2 + 25w = 25 or -2w^2 + 25w - 25 = 0</h3>
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Explanation:
Refer to the diagram below. The width is w. We have two opposite and parallel sides equal to this. The other two parallel congruent sides are L = 25-2w meters long. We start with the total amount of fencing, and then subtract off the two width values, so 25-w-w = 25-2w.
The area of the rectangle is
Area = length*width
Area = L*W
Area = (25-2w)*w
Area = 25w - 2w^2
Area = -2w^2 + 25w
Set this equal to the desired area (25 square meters) to get
-2w^2 + 25w = 25
and we can subtract 25 from both sides to get everything on one side
-2w^2 + 25w - 25 = 0
side note: The two approximate solutions of this equation are w = 1.0961 and w = 11.4039 (use the quadratic formula or a graphing calculator to find this)
f(g(-1)) = - 3
Evaluate g(-1) and substitute into f(x)
g(-1) = (-1)² -7(-1) - 9 = 1 + 7 - 9 = - 1
f(g(-1)) = (-1) - 2 = - 3