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Aloiza [94]
3 years ago
8

Factor the trionomial x^2+15x+14

Mathematics
1 answer:
uysha [10]3 years ago
8 0

Answer:(x+1)(x+14)


Step-by-step explanation:


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Let's calculate Charlie swimming distance. Assume Charlie swimming distance is D.
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The position of a ball after it is kicked can be determined by using the function f left parenthesis x right parenthesis equals
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Answer:

When kicked, the height of the ball is 1 feet. The highest point for the ball's trajectory is 12 feet.

Step-by-step explanation:

We are given that the height is given by f(x)=-0.11x^2+2.2x+1. The distance between the ball to the point where it was kicked is 0 right at the moment the ball was kicked. So, the height of the ball, when it was kicked is f(0) = -0.11*0 + 2.2*0 +1  = 1.

To determine the highest point, we will proceed as follows. Given a parabola of the form x^2+bx + c, we can complete the square by adding and substracting the factor b^2/4. So, we get that

x^2+bx+c = x^2+bx+\frac{b^2}{4} - \frac{b^2}{4} +c = (x+\frac{b}{2})^2+c-\frac{b^2}{4}.

In this scenario, the highest/lowest points is c-\frac{b^2}{4}[/tex} (It depends on the coefficient that multiplies x^2. If it is positive, then it is the lowest point, and it is the highest otherwise). Then, we can proceed as follows. [tex] f(x) = -0.11x^2+2.2x+1 = -0.11(x^2-20x)+1

We will complete the square for x^2-20x. In this case b=-20, so

f(x) = -0.11(x^2-20x+\frac{400}{4}-\frac{400}{4})+1 = -0.11(x^2-20x+100-100)+1

We can distribute -0.11 to the number -100, so we can take it out of the parenthesis, then

f(x) = -0.11(x^2-20x+100)+1+100*0.11 = -0.11(x^2-20x+100)+1+11 = -0.11(x-10)^2+12

So, the highest point in the ball's trajectory is 12 feet.

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