Rationalize the denominator, divide by 4, add 2.
Anything times 1 = the same number so 696969x1=696969
The base is a triangle, so the formula for finding the area of a triangle is b x h / 2
2 x 3 = 6 / 2 = 3
and the formula for finding the volume of a triangular prism is b x h
3 x 14.4 =43.2 and rounded to the nearest whole number would be 43
so A is your answer
Answer:
(x, y) = (1, 1/3)
Step-by-step explanation:
The x-coefficient in the first equation is -2 times that in the second equation, so adding twice the second equation to the first will eliminate x:
(4x -9y) +2(-2x +3y) = (1) +2(-1)
-3y = -1 . . . . simplify
y = 1/3 . . . . . divide by -3
The y-coefficient in the first equation is -3 times the y-coefficient in the second equation, so adding 3 times the second equation to the first will eliminate y:
(4x -9y) +3(-2x +3y) = (1) +3(-1)
-2x = -2 . . . . . . simplify
x = 1 . . . . . . . . . divide by -3
The solution is (x, y) = (1, 1/3).
The answers will be:
- (4, 5)
- remain constant and increase
- g(x) exceeds the value of f(x)
<h3>What is Slope and curve?</h3>
a) The slope of the curve g(x) roughly matches that of f(x) at about x=4. Above that point, the curve g(x) is steeper than f(x), so its average rate of change will exceed that of f(x). An appropriate choice of interval is (4, 5).
b) As x increases, the slope of f(x) remains constant (equal to 4). The slope of g(x) keeps increasing as x increases. An appropriate choice of rate of change descriptors is (remain constant and increase).
c) The curves are not shown in the problem statement for x = 8. The graph below shows that g(x) has already exceeded f(x) by x=7. It remains higher than f(x) for all values of x more than that. We can also evaluate the functions to see which is greater:
f(8) = 4·8 +3 = 35
g(8) = (5/3)^8 ≈ 59.54 . . . . this is greater than 35
g(8) > f(8)
d) Realizing that an exponential function with a base greater than 1 will have increasing slope throughout its domain, it seems reasonable to speculate that it will always eventually exceed any linear function (or any polynomial function, for that matter).
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