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3 years ago

Y=x² + 16x + 64

Mathematics

1 answer:

motikmotik3 years ago

8 0

I'll do the first one to get you started

The equation y = x^2+16x+64 is the same as y = 1x^2+16x+64

Compare that to y = ax^2+bx+c and we see that

a = 1

b = 16

c = 64

Use the values of 'a' and b to get the value of h as shown below

h = -b/(2a)

h = -16/(2*1)

h = -8

This is the x coordinate of the vertex.

Plug this x value into the original equation to find the corresponding y value of the vertex.

y = x^2+16x+64

y = (-8)^2 + 16(-8) + 64

y = 0

Since the y coordinate of the vertex is 0, this means k = 0.

The vertex is (h,k) = (-8, 0)

---------------------

So we found that a = 1, h = -8 and k = 0

Therefore,

f(x) = a(x-h)^2 + k

f(x) = 1(x-(-8))^2 + 0

f(x) = (x+8)^2

is the vertex form

---------------------

<h3>Final answer to problem 1 is f(x) = (x+8)^2 </h3>

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A bacteria colony doubles in 8 hours. How long does it take to triple? Use N=No2^t/T

Volgvan

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4 years ago

Answer all questions, your combing like terms. Show ALL of you work! Thank you!!

Elanso [62]

Answer:

1. -12x - 9y - 6

2. -12x + 36

3. -240

4. -2

5. x = -57

6. x = -6

7. x = 48

8. x = 20

9. x = -288

10. n = 8

Step-by-step explanation:

-5x - 13 + 3y - 7x - 12y + 7

-12x - 13 + 3y - 12y + 7

-12x - 6 + 3y - 12y

-12x - 6 - 9y

-12x - 9y - 6

-3(4x - 12)

-3(4x) + (-3)(-12)

-12x + 36

6x - 282

6(7) - 282

42 - 282

-240

6x + 2(y + x)

6(-2) + 2(7 + (-2))

-12 + 2(7 - 2)

-12 + 2(5)

-12 + 10

-2

x - 23 = -80

+ 23 +23

x = -57

12x = -72

/12 /12

x = -6

x/4 = 12

* 4 * 4

x = 48

3x + 12 = 72

- 12 - 12

3x = 60

/3 /3

x = 20

x/4 - 8 = -80

+ 8 + 8

x/4 = -72

* 4 * 4

x = -288

10.

-4(1 - 5n) - 8n = 92

-4 + (-4)(-5n) - 8n = 92

-4 + 20n - 8n = 92

-4 + 12n = 92

12n - 4 = 92

+ 4 + 4

12n = 96

/12 /12

n = 8

6 0

3 years ago

Please show me how you got the answer. Will give brainliest.

umka21 [38]

Answer: 410 possible points

To solve for the possible points in the course, use a proportion and cross multiply.

<h2>What is a proportion?</h2>

A proportion is two fractions that are equal to each other. For the fractions to be equal, they are proportionate. In our math problem, percentage is proportionate the the number of points.

The fractions represent information you have, and one variable will represent what you are solving for.

<h2 /><h3>Given</h3>

Your points = 361

Points to get an 'A' = your points + 8

'A' = 90% of possible points

<h3>Find the points needed for an 'A' at 90%</h3>

Points to get an 'A' = your points + 8

= 361 + 8

= 369

<h3>State variables</h3>

let <em>x</em> be the amount of possible points

<h3 /><h3>Write a proportion</h3>

We know the number of points for 90% is 369 points. Remember that 90% is the same as 90/100.

Keep the information with the same units inside the same fraction. Here, percentage is represented by the first fraction. Points is represented by the second fraction.

$\displaystyle{\frac{90}{100}=\frac{369}{x}}$

<h3>Solve</h3>

We can solve using cross multiplication. This is when we multiply each numerator by the denominator from the other fraction.

$90x = 369*100$ Simplify by multiplying.

$90x = 36,900$ Isolate the variable <em>x</em>.

$\displaystyle{\frac{90x}{90} = \frac{36,900}{90}}$ Divide both sides by 90 to cancel out 90 on the left.

$\displaystyle{x = \frac{36,900}{90}}$ Divide.

$x = 410$ Solved for <em>x</em>, representing the possible points.

∴ The possible points in the art course is 410.

Learn more about finding a missing number given percentage here: brainly.com/question/26535441

4 0

1 year ago

Identify the property being shown here, assuming that a + 2 = y. <br> (a + 2)/3 = y/3

allochka39001 [22]

Assuming that <em>a + 2 = y</em>, the property that was applied to arrived at <em>(a + 2)/3 = y/3</em> is the: division property of equality.

<em><u>Recall:</u></em>

What is done to both sides of an equation will determine what property of equality was applied to the equation.

Thus, given the equation:

a + 2 = y

The following was obtained:

(a + 2)/3 = y/3

Observing the equation stated above, we will see that both sides of the equation was divided by three. This makes both sides equal.

Therefore, assuming that <em>a + 2 = y</em>, the property that was applied to arrived at <em>(a + 2)/3 = y/3</em> is the: division property of equality.

Learn more here:

brainly.com/question/13260378

4 0

3 years ago

Scores on the SAT Mathematics test are believed to be normally distributed. The scores of a simple random sample of five student

AysviL [449]

Answer:

The mean calculated for this case is $\bar X=584$

And the 95% confidence interval is given by:

$584-2.776\frac{86.776}{\sqrt{5}}=476.271$

$584+2.776\frac{86.776}{\sqrt{5}}=691.729$

So on this case the 95% confidence interval would be given by (476.271;691.729)

Step-by-step explanation:

Previous concepts

A confidence interval is "a range of values that’s likely to include a population value with a certain degree of confidence. It is often expressed a % whereby a population means lies between an upper and lower interval".

The margin of error is the range of values below and above the sample statistic in a confidence interval.

Normal distribution, is a "probability distribution that is symmetric about the mean, showing that data near the mean are more frequent in occurrence than data far from the mean".

$\bar X$ represent the sample mean for the sample

$\mu$ population mean (variable of interest)

s represent the sample standard deviation

n represent the sample size

Solution to the problem

The confidence interval for the mean is given by the following formula:

$\bar X \pm t_{\alpha/2}\frac{s}{\sqrt{n}}$ (1)

In order to calculate the mean and the sample deviation we can use the following formulas:

$\bar X= \sum_{i=1}^n \frac{x_i}{n}$ (2)

$s=\sqrt{\frac{\sum_{i=1}^n (x_i-\bar X)}{n-1}}$ (3)

The mean calculated for this case is $\bar X=584$

The sample deviation calculated $s=86.776$

In order to calculate the critical value $t_{\alpha/2}$ we need to find first the degrees of freedom, given by:

$df=n-1=5-1=4$

Since the Confidence is 0.95 or 95%, the value of $\alpha=0.05$ and $\alpha/2 =0.025$ , and we can use excel, a calculator or a tabel to find the critical value. The excel command would be: "=-T.INV(0.025,4)".And we see that $t_{\alpha/2}=2.776$

Now we have everything in order to replace into formula (1):

$584-2.776\frac{86.776}{\sqrt{5}}=476.271$

$584+2.776\frac{86.776}{\sqrt{5}}=691.729$

So on this case the 95% confidence interval would be given by (476.271;691.729)

3 0

3 years ago