What is the standard form of the parabola whose vertex form is y= 2(x+4)^2+5
A. y = 2x2 +16x - 37
B. y=-2x² + 4x - 25
C. y = 2x° +16x +37
D. y = 2x² + 4x - 25

Answers

Answer 1

[tex]y = 2(x+4)^2+5\implies y = 2(x+4)(x+4)+5 \\\\\\ y = 2(\stackrel{\mathbb{USING~FOIL}}{x^2+8x+16})+5\implies y= 2x^2+16x+32+5 \\\\[-0.35em] ~\dotfill\\\\ ~\hfill y = 2x^2+16x+37~\hfill[/tex]


Related Questions

If a ∥ b and b ⊥ y, then _____

Answers

Answer:

a ⊥ y

Step-by-step explanation:

since b is parallel to a & perpendicular to y , line y will eventually cut across line a at a 90 degree angle as well

Answer:

a ⊥ y

Step-by-step explanation:

Look at the image given below.

Which expression is equivalent to
R^9/r^3?

Answers

Answer:

r^9/r^3 = r^9-3 = r^6

Step-by-step explanation:

Hi there!  

»»————- ★ ————-««

I believe your answer is:  

[tex]r^6[/tex]

»»————- ★ ————-««  

Here’s why:  

⸻⸻⸻⸻

[tex]\boxed{\text{Simplifying...}}\\\\\frac{r^9}{r^3} \\--------------\\\\\text{Recall the quotient rule:}} \frac{a^x}{a^y}=a^{x-y}\\\\\rightarrow \frac{r^9}{r^3}\\\\\rightarrow r^{9-3}\\\\\rightarrow \boxed{r^6}[/tex]

⸻⸻⸻⸻

»»————- ★ ————-««  

Hope this helps you. I apologize if it’s incorrect.  

 

Simplify the following expression by using these values:
m = −6; n = 2; p = 4
[tex]-3m^{2}[/tex]+4n-p

Answers

Hi there!

Given the expression below:-

[tex] \large{ - 3 {m}^{2} + 4n - p}[/tex]

We are also given these three values below:

m = -6n = 2p = 4

Simply substitute these values in:-

[tex] \large{ - 3 {( - 6)}^{2} + 4(2) - 4}[/tex]

Any negative numbers squared would result in positive.

[tex] \large{ - 3(36) + 8 - 4} \\ \large{ - 108 + 4} \\ \large \boxed{ - 104}[/tex]

Hence, the answer is -104 when substituting values in the expression.

Let me know if you have any questions!

[tex]\huge\text{Hey there!}[/tex]

[tex]\large\textsf{-3m}\mathsf{^2}\large\textsf{ + 4n - p}\\\large\textsf{= -3(-6)}\mathsf{^2}\large\textsf{ + 4(2) - 4}\\\\\large\textsf{(-6)}^2\\\large\textsf{= (-6)(-6)}\\\large\textsf{= \bf 36}\\\\\large\textsf{= -3(36) + 4(2) - 4}\\\\\large\text{-3(36)}\\\large\textsf{= \bf -108}\\\\\large\textsf{= -108 + 4(2) - 4}\\\\\large\textsf{4(2)}\\\large\textsf{= \bf 8}\\\\\large\textsf{= -108 + 8 - 4}\\\\\large\textsf{-108 + 8}\\\large\textsf{= \bf -100}\\\\\large\textsf{-100 - 4}\\\large\text{ = \bf -104}[/tex]

[tex]\boxed{\boxed{\huge\text{Therefore, your answer is: \boxed{\bf -104}}}}\huge\checkmark[/tex]

~[tex]\frak{Amphitrite1040:)}[/tex]  

5x + 2y + 19 = 0 3x + 4y + 17 = 0​

Answers

Answer:

x = -3; y = 2

Step-by-step explanation:

5x + 2y + 19 = 0

3x + 4y + 17 = 0​

-10x - 4y - 38 = 0

3x + 4y + 17 = 0

-7x - 21 = 0

x = -3

5(-3) + 2y = -19

2y = -4

y = -2

Answer: x = -3; y = 2

Twelve different video games showing drug use were observed. The duration times of drug use were​ recorded, with the times​ (seconds) listed below. Assume that these sample data are used with a 0.05 significance level in a test of the claim that the population mean is greater than 85 sec. If we want to construct a confidence interval to be used for testing that​ claim, what confidence level should be used for a confidence​ interval? If the confidence interval is found to be −1.8 sec<μ<213.5 ​sec, what should we conclude about the​ claim? The given confidence interval ▼ does not contain contains the value of 85 ​sec, so there ▼ is is not sufficient evidence to support the claim that the mean is greater than 85 sec

Answers

Answer:

95% confidence level should be used for a confidence​ interval.

The given confidence interval contains the value of 85 ​sec, so there is not sufficient evidence to support the claim that the mean is greater than 85 sec.

Step-by-step explanation:

0.05 significance level

1 - 0.05 = 0.95

0.95*100% = 95%

This means that a 95% confidence level should be used for a confidence​ interval.

Confidence interval is found to be −1.8 sec<μ<213.5 ​sec, what should we conclude about the​ claim?

Contains the value of 85 sec, thus there is not sufficient evidence to support the claim that the mean is greater than 85 sec.

Find the value of x on this triangle

Answers

Answer:

x = 35

Step-by-step explanation:

We can use the Pythagorean theorem since this is a right triangle

a^2 + b^2 = c^2  where a and b are the legs and c is the hypotenuse

x^2 + 12^2 = (x+2)^2

FOIL

x^2+144=x^2+4x+4

Subtract x^2 from each side

144= 4x+4

Subtract 4 from each side

140 = 4x

Divide by 4

35 =x

The pie chart shows the favorite type of book of the more than 50,000 high school students. About what percent of favorite type of book is drama? About what percent is mystery?


Complete the statements based on the information.


About

% of high school students chose dramas as their favorite type of book.


About

% of high school student chose mysteries as their favorite type of book.

Ans:
50%

25%

Answers

Answer:

About 50% of high school student chose dramas as their favorite type of book.

About 25% of high school student chose mysteries as their favorite type of book.

Thus, 50% of high school students chose dramas as their favorite type of book and 25% of high school students chose mysteries as their favorite type of book.

What is the percentage?

It's the ratio of two integers stated as a fraction of a hundred parts. It is a metric for comparing two sets of data, and it is expressed as a percentage using the percent symbol.

It is given that:

The pie chart shows the favorite type of book of more than 50,000 high school students.

As we know,

A circular statistical visual with slices illustrating a normal probability plot is named a pie chart. Each slice's arc length in a pie chart matches to the quantity it displays.

Thus, 50% of high school students chose dramas as their favorite type of book and 25% of high school students chose mysteries as their favorite type of book.

Learn more about the percentage here:

brainly.com/question/8011401

#SPJ2

x^ 3 +x^ 2 +4x/x^ 2 +x-2
into partial
fractions​

Answers

Answer:

x + (4/ x-2) + (2/ x-1)

Step-by-step explanation:

x + (6x/ x^2 + 2x - x -2)

x + (6x/ (x + 2) X (x - 1))

(6x/ (x + 2) X (x - 1))

(A/ x+2) + (B/ x-1)

(6x/ (x + 2) X (x - 1)) = (A/ x+2) + (B/ x-1)

6x = Ax + Bx - A + 2B

6x = (A+B)x + (-A+2b)

{0 = -A+2B

{6 = A+B

(A,B) = (4, 2)

(4/ x+2) + (2/ x-1)

x + (4/ x-2) + (2/ x-1)

Im new, and i hope someone tells me the right answers!

Answers

A factor is a natural number that can be multiplied by another natural number to get a value. The greatest common factor refers to when one compares the factors of two numbers, the largest natural number that both numbers have in common is the number's greatest common factor.

In the case of ([tex]m^2[/tex]) and ([tex]m^4[/tex]), the greatest common factor is ([tex]m^2[/tex]) because there are no factors of ([tex]m^2[/tex]) that are larger than it. No number can have a factor larger than itself. Since ([tex]m^2[/tex]) is also a factor of ([tex]m^4[/tex]) it is the greatest common factor of the two numbers.

Find the equation for the line that passes through the points ( - 1, - 10) and ( - 6,9). Give your
answer in point-slope form. You do not need to simplify.

Answers

Answer:

The point slope form of the equation is,

[tex]y + 10 = - \frac{19(x + 6)}{5} [/tex]

m = (y2-y1)/(x2-x1) = (9-(-10))/((-6)-(-1)) = -19/5

b = y1-mx1 = -69/5

Answered by GAUTHMATH

Find the sum of the geometric series given a1=2, r=−3, and n=8.

Answers

Answer:

S₈ = - 3280

Step-by-step explanation:

The sum to n terms of a geometric series is

[tex]S_{n}[/tex] = [tex]\frac{a_{}(r^{n}-1) }{r-1}[/tex]

Here a₁ = 2, r = - 3 and n = 8 , then

S₈ = [tex]\frac{2((-3)^{8}-1) }{-3-1}[/tex]

   = [tex]\frac{2(6561-1)}{-4}[/tex]

   = [tex]\frac{2(6560)}{-4}[/tex]

   = [tex]\frac{13120}{-4}[/tex]

   = - 3280

 

What is the best point estimate for the population's standard deviation if the sample standard deviation is 37.3

Answers

Answer:

The best point estimate for the population's standard deviation is 37.3.

Step-by-step explanation:

Best point estimate:

The best point estimate for the population mean is the sample mean.

The best point estimate for the population standard deviation is the sample standard deviation.

In this question:

Sample standard deviation of 37.3, and thus, the best point estimate for the population's standard deviation is 37.3.

Given a mean score of 1150, standard deviation of 90, and 500 participants, solve the following problem. Using this data and the z-score distribution provided in class. Be sure to give your answer in the units requested. Only place your answer in the box.
1. What is the score for someone in the 15th percentile?
2. What is the percentile rank of someone with a score of 1100?
3. How many students have scores of 1060 or greater?
4. How many students scored between 1200 and 1250?

Answers

Answer:

1. 1056.67

2. 29th percentile.

3. 79

4. 77

Step-by-step explanation:

Normal Probability Distribution

Problems of normal distributions can be solved using the z-score formula.

In a set with mean [tex]\mu[/tex] and standard deviation [tex]\sigma[/tex], the z-score of a measure X is given by:

[tex]Z = \frac{X - \mu}{\sigma}[/tex]

The Z-score measures how many standard deviations the measure is from the mean. After finding the Z-score, we look at the z-score table and find the p-value associated with this z-score. This p-value is the probability that the value of the measure is smaller than X, that is, the percentile of X. Subtracting 1 by the p-value, we get the probability that the value of the measure is greater than X.

Mean score of 1150, standard deviation of 90

This means that [tex]\mu = 1150, \sigma = 90[/tex]

1. What is the score for someone in the 15th percentile?

This is X when Z has a p-value of 0.15, so X when Z = -1.037.

[tex]Z = \frac{X - \mu}{\sigma}[/tex]

[tex]-1.037 = \frac{X - 1150}{90}[/tex]

[tex]X - 1150 = -1.037*90[/tex]

[tex]X = 1056.67[/tex]

2. What is the percentile rank of someone with a score of 1100?

This is the p-value of Z when X = 1100. So

[tex]Z = \frac{X - \mu}{\sigma}[/tex]

[tex]Z = \frac{1100 - 1150}{90}[/tex]

[tex]Z = -0.555[/tex]

[tex]Z = -0.555[/tex] has a p-value of 0.29, so 29th percentile.

3. How many students have scores of 1060 or greater?

The proportion is 1 subtracted by the p-value of Z when X = 1060. So

[tex]Z = \frac{X - \mu}{\sigma}[/tex]

[tex]Z = \frac{1060 - 1150}{90}[/tex]

[tex]Z = -1[/tex]

[tex]Z = -1[/tex] has a p-value of 0.1587.

Out of 500:

0.1587*500 = 79

79 is the answer.

4. How many students scored between 1200 and 1250?

The proportion is the p-value of Z when X = 1250 subtracted by the p-value of Z when X = 1200. So

X = 1250

[tex]Z = \frac{X - \mu}{\sigma}[/tex]

[tex]Z = \frac{1250 - 1150}{90}[/tex]

[tex]Z = 1.1[/tex]

[tex]Z = 1.1[/tex] has a p-value of 0.8643.

X = 1200

[tex]Z = \frac{X - \mu}{\sigma}[/tex]

[tex]Z = \frac{1200 - 1150}{90}[/tex]

[tex]Z = 0.555[/tex]

[tex]Z = 0.555[/tex] has a p-value of 0.7106

0.8643 - 0.7106 = 0.1537

Out of 500:

0.1537*500 = 77

77 is the answer.

What information is NOT necessary to find the area of a circle?
a.
pi
c.
diameter
b.
radius
d.
height

Answers

Answer:

D. Height

General Formulas and Concepts:

Geometry

Area of a Circle: A = πr²

r is radius

Step-by-step explanation:

In order to find the area of a circle, we must follow the formula. Out of all the options given, height is not incorporated into the formula.

It wouldn't make sense to use height anyways since it would be 3-dimenional and we're talking 2-dimensional.

∴ our answer is D.

A warehouse contains ten printing machines, two of which are defective. A company selects seven of the machines at random, thinking all are in working condition. What is the probability that all seven machines are nondefective?

Answers

Answer:

0.0667 = 6.67% probability that all seven machines are nondefective.

Step-by-step explanation:

The machines are chosen from the sample without replacement, which means that the hypergeometric distribution is used to solve this question.

Hypergeometric distribution:

The probability of x successes is given by the following formula:

[tex]P(X = x) = h(x,N,n,k) = \frac{C_{k,x}*C_{N-k,n-x}}{C_{N,n}}[/tex]

In which:

x is the number of successes.

N is the size of the population.

n is the size of the sample.

k is the total number of desired outcomes.

Combinations formula:

[tex]C_{n,x}[/tex] is the number of different combinations of x objects from a set of n elements, given by the following formula.

[tex]C_{n,x} = \frac{n!}{x!(n-x)!}[/tex]

In this question:

10 machines means that [tex]n = 10[/tex]

2 defective, so 10 - 2 = 8 work correctly, which means that [tex]k = 8[/tex]

Seven are selected, which means that [tex]n = 7[/tex]

What is the probability that all seven machines are nondefective?

This is P(X = 7). So

[tex]P(X = x) = h(x,N,n,k) = \frac{C_{k,x}*C_{N-k,n-x}}{C_{N,n}}[/tex]

[tex]P(X = 7) = h(7,10,7,8) = \frac{C_{8,7}*C_{2,0}}{C_{10,7}} = 0.0667[/tex]

0.0667 = 6.67% probability that all seven machines are nondefective.

What is (4n + 3n2 + 2) - (n - 6n
+1) simplified?
A -3n2 + 3n-2 C 9n2 + 3 + 2
B 3n2 + 3n + 2 D 9n2 + 3n + 1
C 9n2 + 3n + 2
D 9n2 + 3n + 1

Answers

Step-by-step explanation:

4n + 3n2 + 2 + n + 6n – 1 Expand with – 1

3n2 + 4n + n + 6n + 2 – 1 Grouped liked terms

3n2 + 11n – 1

of its employees based on the number of sales per hour. One employee had the following sales for the last 20 hours 3 4 5 5 6 7 What is the median for the distribution of number of sales per hour? ____________ Express as a number

Answers

Answer: I believe is 5

Explanation:
So they have given you the numbers 3, 4, 5, 5, 6, and 7. To find the median you have to put the numbers in numerical (which you already have) and then you cross each number out starting from either end, and then the number left in the middle , 5 is the median.

I hope this helps

Knowing that AQPT = AARZ, a congruent side pair is:

Answers

Answer:

A. QT ≅ AZ

Step-by-step explanation:

When writing a congruence statement of two triangles, the order of arrangement of the letters used in naming the triangles are carefully considered. Corresponding sides and angles of both triangles are arranged accordingly in the order they appear.

Given that ∆QPT ≅ ∆ARZ, we have the following sides that correspond and are congruent to each other:

QP ≅ AR

PT ≅ RZ

QT ≅ AZ

The only correct one given in the options given above is QT ≅ AZ

Logan has $1.95 in dimes and quarters in his pocket. He has 2 more dimes than quarters. (Keep in mind that dimes are worth 10c and quarters 25c.)

1. Write an equation that will help you determine the number of quarters.
2. Solve the equation showing all your steps.
3. Tell how many quarters and dimes he has.

Answers

Answer:

17 dimes 1 quarter

Step-by-step explanation:

logan has 1.95

step by step explanation:

a dime can not be more than 10 c

and less than 10c

a quarter can not be more than 25c

and less than 25 c

so logan must have 17 dimes and 1 quarter

key = 1 dime = 10c, 1 quarter = 25c

$1.70 + 25c = $1.95

hope this helps!!

2√3x+1 - √4x+5 =3

show your steps please

Answers

Answer:

x = 5

Step-by-step explanation:

I'm assuming that 3x +1 & 4x + 5 are all underneath the square root

2 √3x + 1  - √4x + 5 = 3

2 √3x + 1 = 3 + √4x + 5

4 (3x+1) = 9 + 6 √4x + 5 + 4x + 5

12x + 4 = 14 + 6√4x + 5 + 4x

-6 √4x + 5 = 14 + 4x - 12x - 4

-6 √4x + 5 = 10 - 8x

3 √4x + 5 = -5 + 4x  (divided both sides by - 2)

9 (4x +5) = 16x^2 - 40x + 25

36x + 45 = 16x^2 - 40x + 25

36x + 45 - 16x^2 + 40x - 25 = 0

76x + 20 - 16x^2 = 0

-16x^2 + 76x + 20 = 0

4x^2 - 19x -5 = 0  (dividied by -4)

4x^2 + x - 20x -5 = 0

x (4x + 1) -5 (4x +1) = 0

(4x +1) (x-5) = 0

Possible answers:

4x + 1 = 0

x - 5 = 0

x = -1/4

x =5

Now we will check which one satisfies the equation

2√3x+1 - √4x+5  

Substitue 5 for x and we get 3

Thus we know that 5 is the correct answer

Answered by Gauthmath

The answer to your question is 5

A tire manufacturer has a 60,000 mile warranty for tread life. The company wants to make sure the average tire lasts longer than 60,000 miles. The manufacturer tests 250 tires and finds the mean life for these tires to be 64,500 miles.What is the alternative hypothesis being tested in this example

Answers

Answer:

The alternative hypothesis being tested in this example is that the tire life is of more than 60,000 miles, that is:

[tex]H_1: \mu > 60,000[/tex]

Step-by-step explanation:

A tire manufacturer has a 60,000 mile warranty for tread life. The company wants to make sure the average tire lasts longer than 60,000 miles.

At the null hypothesis, we test if the tire life is of at most 60,000 miles, that is:

[tex]H_0: \mu \leq 60,000[/tex]

At the alternative hypothesis, we test if the tire life is of more than 60,000 miles, that is:

[tex]H_1: \mu > 60,000[/tex]

tìm tích phân tổng quát
xy'lny/x=x+ylny/x

Answers

Answer:

rhe

ehd

end

Step-by-step explanation:

jsu

uss

su

dj

dje

ej

e

at which value will the graph of y=csc x have a zero

Answers

Answer:

y = csc(x) does not have any zero.

Step-by-step explanation:

If we have:

y = f(x)

a zero of that function would be a value x' such that:

y = f(x') = 0

Here we basically want to solve:

y = csc(x) = 0

First, remember that:

csc(x) = 1/sin(x)

now, the values of sin(x) range from -1 to 1.

So we want to solve:

1/sin(x) = 0

notice that a fraction:

a/b = 0

only if a = 0.

Then is easy to see that for our equation:

1/sin(x) = 0

The numerator is different than zero, then the equation never will be equal to zero.

Then:

y = csc(x) = 1/sin(x)

Does not have a zero.

Hi !I need help with this question

Answers

The answer is 270 degrees

I have doubt it be 270 degrees.

Please help!! The question is the image below VVV
Answers are also images after the picture.

Answers

Step-by-step explanation:

When adding two fractions with different bases (bottom numbers), we can use this function:

[tex]\frac{a}{b} + \frac{c}{d} = \frac{ad + cb}{bd}[/tex]

So, to apply this to the given question:

[tex]\frac{x+3}{x-6} +\frac{1}{x-2}[/tex]

= [tex]\frac{(x+3)(x-2)+(1)(x-6)}{(x-6)(x-2)}[/tex]

From the given answers, we see we don't need to simplify the resulting base number, which makes things a lot easier.

Multiply top using: (a + b)(c + d) = ac + ad + bc + bd

= [tex]\frac{[(x*x) + (x*-2)+(3*x)+(3*-2)]+(x-6)}{(x-6)(x-2)}[/tex]

Simplify.

= [tex]\frac{[x^2 -2x+3x-6]+(x-6)}{(x-6)(x-2)}[/tex]

Remove parentheses.

= [tex]\frac{x^2 -2x+3x-6+x-6}{(x-6)(x-2)}[/tex]

Simplify again.

= [tex]\frac{x^2 +2x-12}{(x-6)(x-2)}[/tex]

Now if we wanna be a little smart, we can see that from here, the only answer that has x^2 and something else, is A. But, just for show, lets factor.

Factor.

= [tex]\frac{x(x+2)}{(x-6)(x-2)}[/tex]

Answer:

A) [tex]\frac{x(x+2)}{(x-6)(x-2)}[/tex]

In the figure, m<1= m<2 = 22 and m<3 = m<4 = 123. Find m

Answers

Answer:

35

Step-by-step explanation:

35 because the two angles are added 22 and 123 = 145. 145-180=35

Hello people can you please help me on this

Answers

Step-by-step explanation:

Step 1:  Complete the first equation

0.1 is a tenth, therefore if we have 15.3 then we have 153 tenths.

Step 2:  Complete the second equation

15.3 / 3 = 5.1  

0.1 is a tenth, therefore if we have 5.1 then we have 51 tenths.  

Step 3:  Complete the third equation

15.3 / 3 = 5.1

Im new to this app!
And im looking for help!!
Please help ASAP!!!
Please!!!!

Answers

y=x²-10x-7

a>0 so we will be looking for minimum

x=-b/2a=10/2=5

y=25-50-7=-32

Answer: (5;32)

What is 8% of 1125?

Answers

Answer:

90

Step-by-step explanation:

1125/100=11.25

11.25x8=90

find all the missing measurement​

Answers

Answer:

Hello,

|FD|=15

Step-by-step explanation:

Since the triangles are similar, the bissects are also.

k*35=21 ==> k=21/35

k*25=|FD|

|FD|=(21/35)*25=15

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