I need help with this

Determine the vertex of the function f(x) = 2(x-4)^2+5

spayn [35]

Answer:

(4,5)

Step-by-step explanation:

The vertex is written in vertex form.

y = a(x - b)^2 + c

Vertex: (b,c) Notice the sign change on b.

So for your equation, you get (4,5) No sign change on the 5.

5 0

3 years ago

Simplify: 4(r + 1) + 3r A. 4r + 4 B. 5r + 1 C. 7r + 1 D. 7r + 4

klasskru [66]

Answer:

look in the explanation, it is in there

Step-by-step explanation:

i don't know if you are distributing or just using PEMDAS .

if you are distributing then: do in the equation 4(r + 1) + 3r.. do 4 x r and 4 x 1 , now you have 4r + 4 + 3r

7r +4

is what i got!

If you are doing PEMDAS then: first you do what is inside the perenthisis ()

4(r + 1) +3r changes into

4( r1 ) + 3r now you do multipulcation because that in the "M" in pemdas

4r + 3r, then if you are using like terms you would add them

7r

i hope this helps you out!

6 0

3 years ago

Read 2 more answers

C. How long is 10% of a 24-hour day?

shutvik [7]

Answer:

2.4 hours

Step-by-step explanation:

3 0

3 years ago

Read 2 more answers

A random sample of 30 households was selected as part of a study on electricity usage, and the number of kilowatt-hours (kWh) wa

grin007 [14]

Answer:

The 98% confidence interval for the mean usage in the March quarter of 2006, in kWh, was (333.87, 416.13).

Step-by-step explanation:

We have the standard deviation for the sample, which means that the t-distribution is used to solve this question.

The first step to solve this problem is finding how many degrees of freedom, we have. This is the sample size subtracted by 1. So

df = 30 - 1 = 29

98% confidence interval

Now, we have to find a value of T, which is found looking at the t table, with 29 degrees of freedom(y-axis) and a confidence level of $1 - \frac{1 - 0.98}{2} = 0.99$ . So we have T = 2.462

The margin of error is:

$M = T\frac{s}{\sqrt{n}} = 2.462\frac{91.5}{\sqrt{30}} = 41.13$

In which s is the standard deviation of the sample and n is the size of the sample.

The lower end of the interval is the sample mean subtracted by M. So it is 375 - 41.13 = 333.87 kWh

The upper end of the interval is the sample mean added to M. So it is 375 + 41.13 = 416.13 kWh

The 98% confidence interval for the mean usage in the March quarter of 2006, in kWh, was (333.87, 416.13).

6 0

3 years ago

You are planning to give you're a regale birthday surprise this coming 12 of July as she about to celebrate her 50th birthday. T

velikii [3]

All functions have an inverse expression.

The cost function is: $\mathbf{C(x) = 40000 + 100x}$ .
The inverse function is: $\mathbf{C'(x) = 0.01x - 400 }$

From the question, we have the following observations:

Base fare = 50000 pesos for first 100
Additional guest = 100 pesos

So, the cost function would be:

$\mathbf{C(x) = 50000 + (x - 100) \times 100}$

Where: x represents the number of guests, and C(x) represents the cost function

Expand

$\mathbf{C(x) = 50000 + 100x - 10000}$

Evaluate like terms

$\mathbf{C(x) = 40000 + 100x}$

To calculate the inverse function, we have:

$\mathbf{C(x) = 40000 + 100x}$

Replace C(x) with y

$\mathbf{y = 40000 + 100x}$

Swap x and y

$\mathbf{x = 40000 + 100y}$

Subtract 40000 from both sides

$\mathbf{x - 40000 = 100y}$

Divide both sides by 100

$\mathbf{\frac{x - 40000}{100} = y}$

Rewrite as:

$\mathbf{y= \frac{x - 40000}{100} }$

Split

$\mathbf{y= \frac{x}{100} - \frac{40000}{100} }$

$\mathbf{y= 0.01x - 400 }$

Hence, the inverse function is: $\mathbf{C'(x) = 0.01x - 400 }$

Read more about functions and inverse at:

brainly.com/question/10300045

3 0

3 years ago

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