Given the functions f(x) = 3x2, g(x) = x2 − 4x + 5, and h(x) = –2x2 + 4x + 1, rank them from least to greatest based on their axis of symmetry.

Answers

Answer 1

Answer: f(x) = 3x^2 : axis of symmetry is x = 0.
g(x) = x^2 - 4x + 5 = (x - 2)^2 + 1 : axis of symmetry is x = 2
h(x) = -2x^2 + 4x + 1 = -2(x - 1)^2 + 3 : axis of symmetry is x = 1

Therefore, based on their axis of symmetry, f(x) < h(x) < g(x)

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A nurse mixes 50 cc of a 60% saline solution with a 10% saline solution to produce a 20% saline solution. How much of the 10% solution should he use?

Answers

Answer:

The nurse should use 200cc of the 10% saline solution in order to produce a 20% saline solution.

Step-by-step explanation:

to the given mix we add a quantity of a lower mix to generate another.

50cc at 60% + Xcc at 10% = (50 + X)cc at 20%

50 x 60% + X x 10% = (50 + X) x 20%

30 + 0.1X = 10 + 0.2X

30 - 10 = 0.2X - 0.1X

20 = 0.1X

20/0.1 = X

X = 200

Final answer:

To produce a 20% saline solution, the nurse should use 200 cc of the 10% saline solution.

Explanation:

To find out how much of the 10% saline solution the nurse should use, we can set up an equation using the idea that the amount of saline in the mixture is equal to the sum of the amounts of saline in each solution.

Let's say the nurse uses x cc of the 10% saline solution. The amount of saline in the 60% saline solution will be 0.6 * 50 cc = 30 cc. The amount of saline in the 10% saline solution will be 0.1 * x cc = 0.1x cc.

Since the resulting solution is 20% saline, the total amount of saline in the mixture will be 0.2 * (50 + x) cc. Setting up the equation, we have 30 + 0.1x = 0.2 * (50 + x).

Simplifying the equation, we get 30 + 0.1x = 10 + 0.2x. Solving for x, we find that x = 200 cc.

Learn more about the Saline solution here:

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Which of following is true? Net cash flow -cash outflow=cash inflow

Answers

The correct formula is Net cash flow + cash outflow = cash inflow.

The following information should be considered:

The cash inflow refers to the term where the cash should be received. It increased the cash balance.

The cash outflow refers to the term where the cash is to be paid. It decreased the cash balance.
The net cash flow = Cash inflow - cash outflow,

Therefore we can conclude that The correct formula is Net cash flow + cash outflow = cash inflow.

Learn more about the cash outflow here: brainly.com/question/10714011

Micah takes a job with a starting salary of $78,000 for the first year. He earns a 4% increase each year. How much does Micah make over seven years?

Answers

Answer:

Micah make 616066.97 $ over seven years

Step-by-step explanation:

This increase is in the form of a geometric progression.

Micah takes a job with a starting salary of $78,000

First term of GP = $78,000

He earns a 4% increase each year

Common ratio $=1+(4)/(100)=1.04$

Sum of n terms of GP with first term a and common ratio r.

$s_n=(a(r^n-1))/(r-1)$

How much does Micah make over seven years, so wee need to find sum of GP when n = 7.

$s_7=(78000(1.04^7-1))/(1.04-1)=616066.97\$$

Micah make 616066.97 $ over seven years

So his job has a starting salary of $78,000 and he gets a 4% increase each year. 4% of 78,000 is 3120 since 3120 divided by .04 equals 78,000, and 78,000+3120 = 81120 x 7= 567,840. So every year he can make $81120 and multiply that by 7, Mica would earn $567,840 every 7 years with the 4% increase in his salary every year.

-2.678 + 4.5 + (-0.69)

Answers

1.132isthe correct answer of this question

Find two condecutive odd integers such that the smaller one is twelve more than one-third the larger

Answers

Let be x and x + 2 two consecutive odd integers;
You have the equation : x = 12 + ( x + 2 ) / 3 ;
(3x) / 3 = 36 / 3 + ( x + 2 ) / 3 ;
(3x) / 3 = ( 38 + x ) / 3 ;
3x = 38 + x ;
2x = 38 ;
x = 19 ;
The numbers are 19 and 21 .

Write y = –2/3x + 7 in standard form using integers. 2x + 3y = 21
3x – 2y = 21
–2x – 3y = 21
–2x + 3y = 7

Answers

The standard form of an equation of a line is written as:

Ax + By = C

where A, B and C are constants.

y = –2/3x + 7
2/3x + y = 7
(2/3x + y = 7)3
2x + 3y = 21

Therefore the correct answer is the first option.

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