Answer:
x+4 = 8
(❁´◡`❁)(❁´◡`❁)(❁´◡`❁)
Step-by-step explanation:
An example would be x+4 = 8
(❁´◡`❁)(❁´◡`❁)(❁´◡`❁)
When you divide by a fraction all you have to is multiply by the reciprocal. The reciprocal of 3/8 is 8/3.
<span>The real problem is 2/3 TIMES 8/3. Multiply the numerators across 2 X 8 = 16. Then multiply the denominators across 3 X 3 = 9. The answer is 16/9. If you need to simplify then the answer is 1 7/9.</span>
The empty jug weighs 0.75 lb
With the 3c, the total weighs 2.25 lb. That means:
3c + empty jug = 3c + 0.75 = 2.25
3c = 2.25 - 0.75
3c = 1.5
and 1c = 0.5 (so c is a constant -or the slope-)
Then the equation is:
y = 0.5x + 0.75
Answer:
-2, 8/3
Step-by-step explanation:
You can consider the area to be that of a trapezoid with parallel bases f(a) and f(4), and width (4-a). The area of that trapezoid is ...
A = (1/2)(f(a) +f(4))(4 -a)
= (1/2)((3a -1) +(3·4 -1))(4 -a)
= (1/2)(3a +10)(4 -a)
We want this area to be 12, so we can substitute that value for A and solve for "a".
12 = (1/2)(3a +10)(4 -a)
24 = (3a +10)(4 -a) = -3a² +2a +40
3a² -2a -16 = 0 . . . . . . subtract the right side
(3a -8)(a +2) = 0 . . . . . factor
Values of "a" that make these factors zero are ...
a = 8/3, a = -2
The values of "a" that make the area under the curve equal to 12 are -2 and 8/3.
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<em>Alternate solution</em>
The attachment shows a solution using the numerical integration function of a graphing calculator. The area under the curve of function f(x) on the interval [a, 4] is the integral of f(x) on that interval. Perhaps confusingly, we have called that area f(a). As we have seen above, the area is a quadratic function of "a". I find it convenient to use a calculator's functions to solve problems like this where possible.