- Zero Product Property: if a × b = 0, then either a or b = 0 or both a and b = 0.
(Make sure to set f(x) to zero)
So for this equation, I will be factoring by grouping. Firstly, what two terms have a product of -5x^2 and a sum of 4x? That would be 5x and -x. Replace 4x with 5x - x:
Next, factor 5x^2 + 5x and -x - 1 separately. Make sure that they have the same quantity on the inside:
Now you can rewrite the equation as:
Now apply zero product property to the factors to solve for x:
<u>The x-intercepts are (1/5 ,0) and (-1,0).</u>
Here is the answer with an explanation!
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.
One JOB = 1 and 2 hours = 120 min
Tyler Rate per minute: 1/120 (in 1 minute he performes 1/120 of the job)
Dakota<span> Rate per minute: 1/90 (in 1 minute he performes 1/90 of the job)
Tyler's + Dakota's rate per 1 minute = 1/120 + 1/90 = 7/360 (Job/minutes)
7/360 of the job was performed in 1 minute
</span>a complete JOB =1 to be performed in x minutes (Rule of three)
x = 1x1/(7/360) that equals to 360/7 and x (time of both) = 51 min 42
ANSWER: h=1
EXPLANATION: I hope I help