Answer:
They answerd it
Step-by-step explanation: :(
Answer: FIRST OPTION
Step-by-step explanation:
According the quotient of powers property, when you have the division of two powers with the same base, then you must subtract the exponents.
Therefore, keeping the property above on mind, you have that the quotient is the shown below:
Answer:
(-∞, -4] ∪ [5, ∞)
Step-by-step explanation:
Hi!
Alright, so greater (or less) than or equal to is denoted with a bracket.
If x is less than or equal to -4, then the bracket is on the left side.
(___, -4]
Because x is <em>any</em> number under or equal to -4, x can range from negative infinity. However, we use a parentheses for infinity because infinity can never truly be reached.
So, x 
-4 = (-∞, -4]
X
5
Equal to = bracket
X is any number above 5, so
[5, ∞)
Because we want both of these, we use the union sign (∪)
so,
= (-∞, -4] ∪ [5, ∞)
Answer:
Sean's rocket lands 3 seconds after Kiara's rocket.
Step-by-step explanation:
Kiara: f(t)= -16t² + 80t
Sean: h(t) = -16t² + 120t + 64
Assume that both rockets launch at the same time. We need to be suspicious of Sean's rocket launch. His equation for height has "+64" at the end, whereas Kiara's has no such term. The +64 is the starting height iof Sean's rocket. So Kiara has a 64 foot disadvantage from the start. But if it is a race to the ground, then the 64 feet may be a disadvantage. [Turn the rocket upside down, in that case. :) ]
We want the time, t, at which f(t) and h(t) are both equal to 0 (ground). So we can set both equation to 0 and calculate t:
Kiara: f(t)= -16t² + 80t
0 = -16t² + 80t
Use the quadratic equation or solve by factoring. I'll factor:
0 = -16t(t - 5)
T can either be 0 or 5
We'll choose 5. Kiara's rocket lands in 5 seconds.
Sean: h(t) = -16t² + 120t + 64
0= -16t² + 120t + 64
We can also factor this equation (or solve with the quadratic equation):
0 = -8(t-8)(2t+1)
T can be 8 or -(1/2) seconds. We'll use 8 seconds. Sean's rocket lands in 8 seconds.
Sean's rocket lands 3 seconds after Kiara's rocket.
