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3 years ago

Let F(X) = x^2-16x+71. What is the vertex and minimum value of F(X)?

1 answer:

7 0

The veretx is normally the minimum value
hack:
for f(x)=ax²+bx+c
the x value of the vertex is -b/2a
so
f(x)=1x²-16x+71
x value is -(-16)/(2*1)=16/2=8
find f(8) to find y value of vertex

f(8)=8²-16(8)+71
f(8)=64-128+71
f(8)=7

the vertex is (8,7)
the minimum value is 7

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The Hawks are starting a babysitting business. They charge an initial deposit of $25 and a rate of $4 an hour. A linear model is

Sauron [17]

What’s the question so I can answer it.

7 0

3 years ago

If 3,000 bacteria, with a growth constant (k) of 2.8 per hour, are present at the beginning of an experiment, in how many hours

Ivenika [448]

Given:

Initial number of bacteria = 3000

With a growth constant (k) of 2.8 per hour.

To find:

The number of hours it will take to be 15,000 bacteria.

Solution:

Let P(t) be the number of bacteria after t number of hours.

The exponential growth model (continuously) is:

$P(t)=P_0e^{kt}$

Where, $P_0$ is the initial value, k is the growth constant and t is the number of years.

Putting $P(t)=15000,P_0=3000, k=2.8$ in the above formula, we get

$15000=3000e^{2.8t}$

$\dfrac{15000}{3000}=e^{2.8t}$

$5=e^{2.8t}$

Taking ln on both sides, we get

$\ln 5=\ln e^{2.8t}$

$1.609438=2.8t$ $[\because \ln e^x=x]$

$\dfrac{1.609438}{2.8}=t$

$0.574799=t$

$t\approx 0.575$

Therefore, the number of bacteria will be 15,000 after 0.575 hours.

4 0

2 years ago

Solve by using proper methods. Show your work.

NeX [460]

Answer:

$70,201.38

Step-by-step explanation:

To determine the principal amount, we can use the formula:

$P=\dfrac{A}{(1+\frac{r}{n})^{nt}}$

A = $200,000

r = 7% or 0.07

t = 15 years

n = 12

Now let's substitute our values.

$P=\dfrac{200,000}{(1+\frac{0.07}{12})^{12(15)}}$

$P=\dfrac{200,000}{(1.00583333333)^{12(15)}}$

$P=70,201.38$

So the principal needed to get 200,000 in 15 years is $70,201.38.

7 0

2 years ago

For each value of y , determine whether it is a solution to -21=6y-9 . A -5, B 3 , C -2, D 9

Nezavi [6.7K]

Option C

For each value of y, -2 is a solution of -21 = 6y - 9

Solution:

Given, equation is – 21 = 6y – 9

We have to find that whether given set of options can satisfy the above equation or not

Now, let us check one by one option

Option A)

Given option is -5

Let us substitute -5 in given equation

- 21 = 6(-5) – 9

- 21 = -30 – 9

- 21 = - 39

L.H.S ≠ R.H.S ⇒ not a solution

Option B)

Given option is 3

- 21 = 6(3) – 9

- 21 = 18 – 9

- 21 = 9

L.H.S ≠ R.H.S ⇒ not a solution

Option C)

Given option is -2

- 21 = 6(-2) – 9

- 21 = - 12 – 9

- 21 = - 21

L.H.S = R.H.S ⇒ yes a solution

Option D)

- 21 = 6(9) – 9

- 21 = 54 – 9

- 21 = 45

L.H.S ≠ R.H.S ⇒ not a solution

Hence, the solution for the given equation is – 2, so option c is correct

6 0

3 years ago

If f(x) = 2(x)^2 + 5 square root (x+2), complete the following statement (round your answer to the nearest hundredth): f(2) =

mojhsa [17]

$f(x) = 2(x)^{2} +5 \sqrt{x+2}$

$f(2) = 2(2)^{2} + 5 \sqrt{(2)+2}$

$f(2) = 2(4) + 5\sqrt{4}$

$f(2) = 8 + 5(2)$

$f(2)= 8+10$

f(2) = 18

3 0

2 years ago