Rectangle ABCD has vertex coordinates A(–1, –1), B(–1, –3), C(–4, –3), and D(–4, –1). It is translated 4 units to the right and
1 answer:
You might be interested in
General Idea:
If we have a quadratic function of the form f(x)=ax^{2} +bx+c , then the function will attain its maximum value only if a < 0 & its maximum value will be at x=-\frac{b}{2a} .
Applying the concept:
The height h is modeled by h = −16t^2 + vt + c, where v is the initial velocity, and c is the beginning height of the firecracker above the ground. The firecracker is placed on the roof of a building of height 15 feet and is fired at an initial velocity of 100 feet per second. Substituting 15 for c and 100 for v, we get the function as .
Comparing the function f(x)=ax^{2} +bx+c with the given function , we get
,
and
.
The maximum height of the soccer ball will occur at t=\frac{-b}{2a}=\frac{-100}{2(-16)} = \frac{-100}{-32}=3.125 seconds
The maximum height is found by substituting in the function as below:
Conclusion:
<u>Yes !</u> The firecracker reaches a height of 100 feet before it bursts.
Answer:
Weight of dog: 34 pounds,
Weight of cat: 12 pounds.
Step-by-step explanation:
Let d represent weight of dog and c represent weight of cat.
We have been given that a dog weighs two pounds less than three times the weight of a cat.
3 times weight of cat:
We can represent the given information in an equation as:
We are also told that the dog also weights twenty-two more pounds than the cat. We can represent the given information in an equation as:
Equate both equations:
Therefore, the weight of cat is 12 pounds.
Substitute in equation (2)
Therefore, the weight of dog is 34 pounds.