MATHEMATICS HIGH SCHOOL

Tanya kicks a ball into the air. The function that models this scenario is f(t) = –16t2 + 96t, where h is the height of the ball in feet and t is the time seconds.When will the ball hit the ground?

Answers

Answer 1
Answer:

Answer:

the ball hit the ground at t=6\ sec

Step-by-step explanation:

we have

h(t)=-16t^(2) +96t

This is the equation of a vertical parabola open downward

The vertex is a maximum

we know that

The x-intercept of the function is the value of t when the value of h(t) is equal to zero

The ball hit the ground when h(t) is equal to zero

equate the function to zero  and solve for t

0=-16t^(2) +96t

Factor the leading coefficient

-16t(t -6)=0

The solutions are

t=0, t=6\ sec

therefore

the ball hit the ground at t=6\ sec
Answer 2
Answer: I guess the function is h(t) = -16t^2 + 96t (instead of f(t) )

When the ball hits the groung h(t) = 0

Then solve the equation for t

- 16t^2 + 96 t = 0

Divide by -16

t^2 - 6t = 0

t(t-6) = 0

t =0  is when the ball is kicked off

t = 6 is the answer.

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Which statements accurately describe the function f(x) = 3√18^x? Check all that apply. A. The domain is all real numbers.
B. The range is y > 3.
C. The initial value is 3.
D. The initial value is 9.
E. The simplified base is √2.
F. The simplified base is 3√2.

Answers

Option A is correct: the domain is all real numbers for there is no real value of x for which f(x) does not have a value.

Option B is incorrect: the range is not y > 3, because, for negative values of x, f(x) < 3, e.g. for x = -1, f(x) = 3 * sqrt(18^(-1)) = 3*sqrt(1/18) = 3*0.2357 = 0.7071 < 3.

Option C is correct: f(0) = 3*sqrt(18^0) = 3*sqrt(1) = 3 * 1 = 3

Option D is incorrest: (see working for option C)
The correct options are:

A) The domain is all real numbers;
C) The initial value is 3; and 
F) The simplified base is 3√2.

Explanation:

A) The domain is the set of numbers that can be use for x.  In this function, there are no domain restrictions; this means there are no values for x that will not give you a value for y.  This means that all numbers work, which we say is "the set of all real numbers."

C) To find the initial value (starting point), substitute 0 for x:
f(x) = 3(√18)ˣ
f(0) = 3(√18)⁰
f(0) = 3(1) = 3

Thus the initial value is 3.

F)  The base of the current function is √18; this is because that is what is raised to a power.  If we simplify this, we find the prime factorization of 18, looking for pairs of factors to take out.

The prime factorization of 18:
18 = 2*9
9 = 3*3

This means 18 = 2*3*3; it gives us √18 = √(2*3*3).  We have a pair of 3's under the radical, so we take a 3 out; this leaves a 2 under the radical:
√18 = √(2*3*3) = 3√2.

Round 10.065 correct to 1 decimal place​

Answers

Answer:10.1

Step by step explanation:

Round up to ten
6 rounds up so it’s just 10.1
the answer is 10.1 because 6 is greater than 5

Convert 4 years to months​

Answers

Answer:

48 months

Step-by-step explanation:

12 times 4 48

Answer:

48 months

There's 12 months in 1 year.

So we would multiply 12 months by 4 years to get 48 months

Please help. Due soon.

Answers

The function represents exponential growth (since the exponent is positive).

The percentage increase is, if I'm not mistaken, 181.3% (since 710 is just a constant, we don't need to worry about that - it won't affect the growth rate of the function)

3. Kendall is going to a store that sells abottle of iced tea for $1.99 and a pack of
six bottles for $9.65. Kendall buys five
bottles of iced tea. Is Kendall being
financially responsible or financially irresponsible? Explain.

Answers

Answer: financially irresponsible

Step-by-step explanation:

Kendall is buying 5 for $9.95 when she could buy 6 for $9.65 which would get her another bottle and save 30 cents

Which equation does not have the same solution as the others?x/4 = 2,
x - 9 = 17,
x + 12 = 20,
2x = 16.

Answers

If you would like to know which equation doesn't have the same solution as the others, you can calculate this using the following steps:

x/4 = 2 ... x = 4 * 2 = 8

x - 9 = 17 ... x = 17 + 9 = 26

x + 12 = 20 ... x = 20 - 12 = 8

2 * x = 16 ... x = 16/2 = 8

The correct result would be x - 9 = 17.
(x)/(4)=2\nMultiply\ by\ 4\ on\ both\ sides.\nx=2*4\n{\boxed{x=8}


\n\nx-9=17\nAdd\ 9\ on\ both\ sides.\nx=17+9\n{\boxed{x=26}

x+12=20\nSubtract\ 12\ on\ both\ sides.\nx=20-12\n{\boxed{x=8}

2x=16\nDivide\ by\ 2\ on\ both\ sides.\nx=(16)/(2)\n{\boxed{x=8}


\sf\ The\ only\ equation\ that\ did\ not\ have\ the\ same\ solution\ as\ the\nothers\ was\n {\boxed{x-9=17}
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