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Vlad1618 [11]
3 years ago
7

Figure ABCD is a parallelogram. A. 44 B. 14 C. 38 D. 49

Mathematics
1 answer:
Yuri [45]3 years ago
5 0

Answer:

44 units

Step-by-step explanation:

We know that in a parallelogram opposite sides are equal.

Therefore AB=CD and AD=BC

Consider AB=CD,

⇒4y-2=2y+6

⇒2y=8

⇒y=4

Now consider AD=BC,

⇒3x-1=2x+2

⇒x=3

now substituting values of x and y in the expressions of sides,

we get AB=CD=14 units and AD=BC=8 units

Therefore perimeter of parallelogram is 2*(AB+BC)=2*(14+8)=<u>44 units</u>

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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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Step-by-step explanation:

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