Complete the square to determine the minimum or maximum value of the function defined by the expression. −x2 − 14x + 1

Answers

Answer 1

Answer:

Answer:

maximum: 50

Step-by-step explanation:

The negative coefficient of x^2 tells you the parabola opens downward. (Any even-degree polynomial with a negative leading coefficient will open downward.)

Going through the steps for completing the square, we ...

1. Factor out the leading coefficient from the x-terms

-1(x^2 +14x) +1

2. Add the square of half the x-coefficient inside parentheses, subtract the same amount outside parentheses.

-1(x^2 +14x +49) -(-1·49) +1

3. Simplify, expressing the content of parentheses as a square.

-(x +7)^2 +50

4. Compare to the vertex form to find the vertex. For vertex (h, k), the form is

a(x -h)^2 +k

so your vertex is ...

(h, k) = (-7, 50) . . . . . . . . . a = -1 < 0, so the curve opens downward. The vertex is a maximum.

The maximum value of the expression is 50.

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Find three consecutive numbers whose sum is 612

Answers

Answer: 203, 204, 205

Step-by-step explanation:

Consecutive numbers are numbers that are right next to each other. An example would be 1,2,3 or 67,68,69. Since this problem is asking for three consecutive numbers where the sum is equal to 612, we need to find the numbers that will be greater than 200.

Since we know that the sum is 612, we know that the numbers will be in the 2 hundreds. All we need to do is find 3 numbers that equal to 12.

3+4+5=12

Now that we have the three numbers, let's add 200.

203+204+205=612

Therefore, the three numbers are 203, 204, 205.

Answer: 203, 204, 205

Step-by-step explanation:

Let's say the number is x.

So the three consecutive numbers are: x, x + 1, and x+ 2

3x + 3 = 612

3x = 609

x = 203

Plug in x.

203, 204, and 205

Shipping box that is length=3 3/4ft width=3ft height=3 1/4 what is the volume and how to work it out

Answers

Answer:

36 9/16 ft^3

Step-by-step explanation:

volume = length * width * height

volume = 3 3/4 ft * 3 ft * 3 1/4 ft

Change all mixed numerals to fractions.

volume = 15/4 * 3/1 * 13/4 ft^3

volume = 585/16 ft^3

volume = 36 9/16 ft^3

Given the digits 2,5,7,9, 4, and 1, how many 4-digit codes can be made if 4 pointsthe first digit must be even and the last digit must be greater than 6?
80
120
48
144

Answers

Answer:

144

Step-by-step explanation:

first digit of the code: only 2 and 4 are the only even numbers availible, so only 2 possibilities for the first digit.

2nd digit of code: 2,5,7,9,1 so 6 possibilities for the 2nd digit.

3rd digit of code: 2,5,7,9,1 so 6 possibilities for the 3rd digit.

4th digit of code: only 7 and 9 are greater tyhan 6 so only 2 possibilities for the 4th digit.

SO...

2 x 6 x 6 x 2 = 144

Determine the solution for x2 + 36 > 12x

Answers

$\huge\text{Hey there!}$

$\large\boxed{\mathsf{x^2 + 36 > 12x}}$

$\large\text{SUBTRACT 12x to BOTH SIDES.}$

$\large\boxed{\mathsf{\rightarrow x^2 + 36 - 12x = 12x - 12x}}$

$\large\text{SIMPLIFY IT!}$

$\large\text{NEW EQUATION: }\large\boxed{\mathsf{x^2 - 12x + 36 = 0}}$

$\large\text{FACTOR the LEFT side: \boxed{\mathsf{(x - 6)(x - 6) = 0}}}$

$\large\text{We get: \boxed{\mathsf{x = 6}}}$

$\large\text{CHECK to make sure you have intervals with the equations.}$

$\large\text{Either of these inequalities should work with your given inequality}\downarrow$

$\large\text{YOUR ANSWERS..}$

$\large\boxed{\mathsf{x > 6}}\n\n\large\boxed{\mathsf{x < 6}}$

$\huge\text{Good luck on your assignment \& enjoy your day!}$

~ $\frak{Amphitrite1040:)}$

Answer:

its d

Step-by-step explanation: i just did it

-4 1/4 as a decimal number HELP!!!

Answers

Answer:

-4.25

−4 1/4 = −4 +1/4

= −4/1+1/4

=(−4/1×4/4)+1/4

=−16/4 + 1/4= −17/4

So, -17 divided by 4 equals

-4.25

Researchers are investigating the effect of pH level in water on the breeding habits of the moon jellyfish. As part of a laboratory experiment, they will randomly assign one of three treatments, low pH, medium pH, or high pH, to the water in the tanks that hold the jellyfish.Which of the following is the best reason for the random assignment of a treatment level to an experimental unit?

Answers

Answer:

A. Randomization tends to minimize the effects of uncontrolled variables, such as water temperature, so that such factors are not confounded with the treatment effects.

Step-by-step explanation:

---Researchers are investigating the effect of pH level in water on the breeding habits of the moon jellyfish. As part of a laboratory experiment, they will randomly assign one of three treatments, low pH, medium pH, or high pH, to the water in the tanks that hold the jellyfish.

Which of the following is the best reason for the random assignment of a treatment level to an experimental unit?

A. Randomization tends to minimize the effects of uncontrolled variables, such as water temperature, so that such factors are not confounded with the treatment effects.

B. Randomization will make up for improper experimental design, data collection, and analysis.

C. Randomization makes the analysis easier since the data can be entered into the computer in any order.

D. Randomization is required by statistical consultants before they will analyze the experiment.

E. Randomization means that the experiment would not need to be replicated---

Randomization is used to ensure that the results of a trial or an experiment are actually because if the treatment or hypothesis we are trying, instead of any other external factor that we can not control, or because it just always happens that way, if all of the jellyfish are affected or not in the same way, then the Ph had little to nothing to do with it, and if only one group of them is affected we can re-try the experiment to see if the difference in the Ph had anything to do with the change.

Answer:

A.Randomization tends to minimize the effects of uncontrolled variables, such as water temperature, so that such factors are not confounded with the treatment effects.

Step-by-step explanation:

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