math help plz
how to solve parabola and its vertex, how to understand easily and step by step with an example provided please

Answers

Answer 1

Answer:

The general equation for a parabola is:

y = f(x) = a*x^2 + b*x + c

And the vertex of the parabola will be a point (h, k)

Now, let's find the values of h and k in terms of a, b, and c.

First, we have that the vertex will be either at a critical point of the function.

Remember that the critical points are the zeros of the first derivate of the function.

So the critical points are when:

f'(x) = 2*a*x + b = 0

let's solve that for x:

2*a*x = -b

x = -b/(2*a)

this will be the x-value of the vertex, then we have:

h = -b/(2*a)

Now to find the y-value of the vertex, we just evaluate the function in this:

k = f(h) = a*(-b/(2*a))^2 + b*(-b/(2*a)) + c

k =  -b/(4*a) - b^2/(2a) + c

So we just found the two components of the vertex in terms of the coefficients of the quadratic function.

Now an example, for:

f(x) = 2*x^2 + 3*x + 4

The values of the vertex are:

h = -b/(2*a) = -3/(2*2) = -3/4

k = -b/(4*a) - b^2/(2a) + c

=  -3/(4*2) - (3)^2/(2*2) + 4 = -3/8 - 9/4 + 4 = (-3 - 18 + 32)/8 = 11/8


Related Questions

Need help please I don’t get it

Answers

the e-function stuff can be confusing sometimes, but notices that g(x) / the blue line, is just somewhat lower, rest is the same.

how much lower? look at the y-intercepts

f(0)= "about 5"

g(0)= "about -3"

with this y-intercept only option c can work

A cylinder with radius 3 meters and height 7 meters has its radius tripled. How many times greater is the volume of the larger cylinder than the smaller cylinder?
How many times greater is the volume of the larger cylinder than the smaller cylinder?


Please help :)

Answers

Answer:

9x

Step-by-step explanation:

Quick maths, I dont really have an explaination pls give me brainliest ;-;.

f(X) = 10x^3 find inverse

Answers

1000 is you answer
Or
10x10x10
Or
10/3

Answer: [tex]y=\sqrt[3]{\frac{x}{10} }[/tex]

Step-by-step explanation:

[tex]f(x)=10x^{3}\\y=10x^{3}[/tex]

switch the x and y:

[tex]x=10y^{3}[/tex]

Now solve for y:

[tex]x=10y^{3} \\\frac{x}{10} =y^{3} \\\sqrt[3]{\frac{x}{10} } =y\\[/tex]

Therefore, the inverse of that function is: [tex]y=\sqrt[3]{\frac{x}{10} }[/tex]

(c) Construct a 99% confidence interval for u if the sample
size, n, is 35.

Answers

Answer:

The confidence interval is [tex](\overline{x} - 1.99\frac{\sigma}{\sqrt{35}}, \overline{x} + 1.99\frac{\sigma}{\sqrt{35}})[/tex], in which [tex]\overline{x}[/tex] is the sample mean and [tex]\sigma[/tex] is the standard deviation for the population.

Step-by-step explanation:

We have that to find our [tex]\alpha[/tex] level, that is the subtraction of 1 by the confidence interval divided by 2. So:

[tex]\alpha = \frac{1 - 0.99}{2} = 0.005[/tex]

Now, we have to find z in the Z-table as such z has a p-value of [tex]1 - \alpha[/tex].

That is z with a pvalue of [tex]1 - 0.005 = 0.995[/tex], so Z = 2.575.

Now, find the margin of error M as such

[tex]M = z\frac{\sigma}{\sqrt{n}}[/tex]

In which [tex]\sigma[/tex] is the standard deviation of the population and n is the size of the sample.

In this question:

[tex]M = 1.99\frac{\sigma}{\sqrt{35}}[/tex]

The lower end of the interval is the sample mean subtracted by M, while upper end of the interval is the sample mean added to M. Thus, the confidence interval is [tex](\overline{x} - 1.99\frac{\sigma}{\sqrt{35}}, \overline{x} + 1.99\frac{\sigma}{\sqrt{35}})[/tex], in which [tex]\overline{x}[/tex] is the sample mean and [tex]\sigma[/tex] is the standard deviation for the population.

For a data set of the pulse rates for a sample of adult​ females, the lowest pulse rate is 39 beats per​ minute, the mean of the listed pulse rates is x=76.0 beats per​ minute, and their standard deviation is s=13.8 beats per minute. a. What is the difference between the pulse rate of 39 beats per minute and the mean pulse rate of the​ females? b. How many standard deviations is that​ [the difference found in part​ (a)]? c. Convert the pulse rate of 39 beats per minutes to a z score. d. If we consider pulse rates that convert to z scores between −2 and 2 to be neither significantly low nor significantly​ high, is the pulse rate of 39 beats per minute​ significant

Answers

Answer:

a) The difference is of -37, that is, this pulse rate is 37 beats per minute below the mean.

b) 2.68 standard deviations below the mean.

c) Z = -2.68.

d) Z-score below -2, so a pulse rate of 39 beats per minute is significantly low.

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.

a. What is the difference between the pulse rate of 39 beats per minute and the mean pulse rate of the​ females?

Difference between 39 and 76, so 39 - 76 = -37.

The difference is of -37, that is, this pulse rate is 37 beats per minute below the mean.

b. How many standard deviations is that​ [the difference found in part​ (a)]

Standard deviation of 13.8, so:

-37/13.8 = -2.68

So 2.68 standard deviations below the mean.

c. Convert the pulse rate of 39 beats per minutes to a z score.

2.68 standard deviations below the mean, so Z = -2.68.

d. If we consider pulse rates that convert to z scores between −2 and 2 to be neither significantly low nor significantly​ high, is the pulse rate of 39 beats per minute​ significant?

Z-score below -2, so a pulse rate of 39 beats per minute is significantly low.

8. Solve the system using elimination.
3x - 4y = 9
- 3x + 2y = 9

Answers

Answer:

3x−4y=9 −3x+2y=9

Add these equations to eliminate x: −2y=18

Then solve−2y=18

for y: −2y=18 −2y −2 = 18 −2 (Divide both sides by -2)

y=−9

Now that we've found y let's plug it back in to solve for x.

Write down an original equation: 3x−4y=9

Substitute−9for y in 3x−4y=9: 3x−(4)(−9)=9

3x+36=9(Simplify both sides of the equation)

3x+36+−36=9+−36(Add -36 to both sides)

3x=−27 3x 3 = −27 3 (Divide both sides by 3) x=−9

Answer: x=−9 and y=−9

Hope This Helps!!!

Z varies directly as Square x and inversely as y. If z = 187 when x = 64 and y = 6, find z if and 9. (Round off your answer to the nearest hundredth.)

Answers

Answer:

Z = 50

Step-by-step explanation:

Given the following data;

Z = 187

x = 64

y = 6

Translating the word problem into an algebraic expression, we have;

Z = k√x/y

First of all, we would find the constant of proportionality, k;

187 = k√64/6

187 * 6 = k√64

1122 = 8k

k = 1122/8

k = 140.25

To find z, when x and y = 9

Z = 140.25√9/9

Z = (140.25 * 3)/9

Z = 420.75/9

Z = 46.75 ≈ 50

Note: The values in the latter part of the question isn't explicitly stated, so I assumed a value of 9 for both x and y.

Please help me on this real quick

Answers

Answer: x=17


Step 1: Write an equation

To start solving this problem, we will need to first write an equation. We can do so by adding together all of the angles, and having them equal 180, since this is the sum of the angles in a triangle. Let’s do so now.

4x+3+x+7+5x+0=180

Step 2: Combine like terms

The next step will be to combine like terms. To do this, we need to combine the terms with the same variable, or lack of. In this case, the like terms with the same variable are 4x, x, and 5x. The like terms with no variable are 3, 7, and 0. Let’s add these together now.

4x+3+x+7+5x+0=180
10x+10=180

Step 3: Get 10x alone on the left side

Before we find x, we need to get 10x alone on the left side. To do this, we need to move the constant to the right side.

10x+10=180
10x=170

Step 4: Find x

Now let’s solve the last step of the equation. We need to get x alone to find its value. To do so, we need to get rid of the coefficient next to it. We can do this by dividing each term by 10. Let’s do this now.

10x=170
x=17


Hope this helps! Comment below for more questions.

What is the effect of X on Y?

Answers

Answer:

GMM,pooled OLC,even cross country OLC are most variables not difficult panel data analysis

2x+2y=38 y=x+3 solve by the solution

Answers

Answer:

x = 8 , y = 11

Step-by-step explanation:

[tex]2x + 2y = 38 => x + y = 19 - -- ( 1 ) \\\\y = x + 3 ---- ( 2 ) \\\\Substitute \ ( 2 ) \ in \ ( 1) :\\\\ x + y = 19\\\\x + ( x+ 3) = 19\\\\2x + 3 = 19\\\\2x = 19 - 3 \\\\2x = 16 \\\\x = \frac{16}{2} = 8\\\\Substitute \ x = 8 \ in \ ( 1 ) : \\\\x + y = 19\\\\8 + y = 19\\\\y = 19 - 8 = 11[/tex]

Time Remaining 59 minutes 49 seconds00:59:49 PrintItem 1 Time Remaining 59 minutes 49 seconds00:59:49 At the end of Year 2, retained earnings for the Baker Company was $2,950. Revenue earned by the company in Year 2 was $3,200, expenses paid during the period were $1,700, and dividends paid during the period were $1,100. Based on this information alone, what was the amount of retained earnings at the beginning of Year 2?

Answers

Answer:

$2550

Step-by-step explanation:

Calculation to determine the amount of retained earnings at the beginning of Year 2

Using this formula

Beginning Retained Earnings + Revenue − Expenses − Dividends = Ending Retained Earnings

Let plug in the formula

Beginning Retained Earnings + $3,200 − $1,700 − $1,100 = $2950

Beginning Retained Earnings= $2,950-$400

Beginning Retained Earnings = $2,550

Therefore the amount of retained earnings at the beginning of Year 2 is $2550

Help asap! Lia can rent a van for either $90 per day with unlimited mileage or $50 per day with 250 free miles and an extra 25¢ for each mile over 250. For what number of miles traveled in one day would the unlimited mileage plan save Lia money? (Show work)

Answers

Answer:

The unlimited mileage plan would save money for Lia from 410 miles onwards.

Step-by-step explanation:

Since Lia can rent a van for either $ 90 per day with unlimited mileage or $ 50 per day with 250 free miles and an extra 25 ¢ for each mile over 250, to determine for what number of miles traveled in one day would the unlimited mileage plan save Lia money, the following calculation must be performed:

90.25 - 50 = 40.25

40.25 / 0.25 = 161

161 + 250 = 411

Therefore, the unlimited mileage plan would save money for Lia from 410 miles onwards.

Jose bought 217 shares of Darien Electric for $21.96 apiece. His broker charged him a commission of $106.12 for the
purchase. If the yearly dividend on Darien Electric is 77 cents per share, what is the annual yield on Jose's stock? Show
work.

Answers

Answer:

what is photosynthic ..

p.l.e.a.s.e join eti-fgdd-xjs

why do plant need it

Suppose the age that children learn to walk is normally distributed with mean 12 months and standard deviation 2.5 month. 34 randomly selected people were asked what age they learned to walk. Round all answers to 4 decimal places where possible.

Answers

Answer:

Step-by-step explanation:

a.) it's just mean, variance

so here it's just 12,6.25

b.) For the x bar thing just divide the variance by the number of people (mean stay the same)

the variance is then (2.5²/34)= .1838

which makes it (12,.1838)

c.) here we don't use x bar (and so it's normal (12,2.5²))

p(11.6) = (11.6-12)/(2.5)= -.16 = .4364

p(12.4)= (12.4-12)/2.5 = .16= .5636

.5636-.4364= .1272

d.) here we use x bar because it's asking for an average so it's normal (12, .1838)

same deal

p(11.6)=(11.6-12)/√.1838= -.93295= .1762

p(12.4)= (12.4-12)/√.1838= .93295= .8238

.8238-.1762= .6476

d.) no because they're probably IID

f.) It's average so here we use x bar

q1 is just the 25th percentile

the 25th percentile is -.6745

-.6745=(x-12)/(√.1838)= 11.711

q3 is the 75th percentile

.6745=(x-12)/√.1838

x=12.289

The interquartile range is just the difference between the two

12.289-11.711= .5784

Solve the inequality 5x + 3 2 >48

Answers

Answer:

[tex]{ \tt{5x + 3 \geqslant 48}} \\ { \tt{5x \geqslant 45}} \\ { \tt{x \geqslant 9}}[/tex]

Answer:

x[tex]\geq[/tex]9

Step-by-step explanation:

5x+3[tex]\geq \\[/tex]48  /-3

5x[tex]\geq[/tex]45   //5

x[tex]\geq[/tex]9

What is the probability of drawing 1 red marble out of a bag containing 4 red marbles, 3 green marbles, 2 blue marbles, and 1 purple marble?

Answers

Answer:

2/5

Step-by-step explanation:

There are a total of 4+3+2+1=10 marbles in the bag. Since there is an equal chance of drawing any marble from the bag, the chances of drawing a red marble is equal to the number of red marbles divided by the total number of marbles.

What we're given:

4 red marbles10 total marbles

Therefore, the probability of drawing a red marble is:

[tex]\frac{4}{10}=\boxed{\frac{2}{5}}[/tex]

Answer: Most probably

Step-by-step explanation:

I need help please and thank you.

Answers

Answer:

option a.

[tex] + - \frac{13}{5} [/tex]

Step-by-step explanation:

[tex]25x^2\: - \:169 = 0 [/tex]

[tex]25x^2 = 169[/tex]

[tex] {x}^{2} = \frac{169}{25} [/tex]

[tex]x = + - \sqrt{ \frac{169}{25} } [/tex]

[tex]x = + - \frac{13}{5} [/tex]

Need help please....

Answers

Answer:

-14 x²

Step-by-step explanation:

10 x² - 24 x² = -14 x²

The answer is 14

if you multiply both P(x) and Q(x), the third part becomes 14x², so the coefficient of x² becomes 14.

Answered by GAUTHMATH

1 red marble 4 blue marbles 3 green marbles probability of drawing 2 blue marbles

Answers

Answer:

3/14

Step-by-step explanation:

Assuming you draw one after the other without replacement, you have a 1/2 chance of drawing blue the first time, and after one is taken out, you have 7 left. In order to draw 2 blues you would have to have a blue the first time, so there would be 3 blue left. Multiplying the 2 probabilities gets 1/2*3/7= 3/14. Double check that though.

Choose the algebraic description that maps the image ABC onto A'B'C'.

Answers

(X,Y-4) this is the answer to the question since the y value of the translated image is moved down from the preimage

: Find absolute minimum and maximum values of (, ) = 2
2 +
4 + 4
On the close triangular region R bounded by the lines = −2, = 0, = 2

Answers

f(x , y) = x + y - xy, D is the closed triangular region with vertices (0, 0), (0 , 2) , and (4 , 0)

A car took 6 minutes to travel between two stations that are 3 miles apart find the average speed of the car in mph

Answers

Answer: 30 mph is the answer.

Step-by-step explanation:

s = 3 miles

t = 6 minutes

so,

60 minute = 1 hour

1 minute = 1/60 hour

6 minutes = 1/60 * 6 = 0.1 hour

so

average speed = s/t

= 3/0.1 = 30 mph

Mathematics I need help

Answers

(X-3)^2 +4. Is the answer

1/4+3+11/2=
NEEED ANSWER ASAP BTW

Answers

Answer:

8.75 or 8 3/4

Step-by-step explanation:

To do this question, many do it differently. But for now, we will convert the fractions into decimals.

1/4 = 0.25

11/2= 5.5

0.25 + 3 + 5.5

3.25 + 5.5 =

8.75

The answer is 8.75 or 8 3/4

Answer:

[tex] \frac{35}{4} \: \: \: or \: \: \: 8 \frac{3}{4} [/tex]

Decimal form :

8.75

Step-by-step explanation:

Hope it is helpful....


Solve the expression using the correct order of operations.
0.75x3.2+ (9.1)2-((-2.3)-(-0.9))2

Answers

Answer:

[tex]0.75 * 3.2+ (9.1)^2-((-2.3)-(-0.9))^2 = 83.25[/tex]

Step-by-step explanation:

Given

[tex]0.75 * 3.2+ (9.1)^2-((-2.3)-(-0.9))^2[/tex]

Required

Solve

Start with the bracket

[tex]0.75 * 3.2+ (9.1)^2-((-2.3)-(-0.9))^2 = 0.75 * 3.2+ (9.1)^2-(-1.4)^2[/tex]

Evaluate all exponents

[tex]0.75 * 3.2+ (9.1)^2-((-2.3)-(-0.9))^2 = 0.75 * 3.2+ 82.81-1.96[/tex]

Evaluate all products

[tex]0.75 * 3.2+ (9.1)^2-((-2.3)-(-0.9))^2 = 2.4+ 82.81-1.96[/tex]

[tex]0.75 * 3.2+ (9.1)^2-((-2.3)-(-0.9))^2 = 83.25[/tex]

what is the value of -3^2+(4+7)(2)?​

Answers

Answer:

[tex] { - 3}^{2} + (4 + 7)(2) \\ = - 9 + 22 \\ = 13[/tex]

Find the length of CE

Answers

Answer:

C. 37.8 units

Step-by-step explanation:

ED = 17/ cos(38°) = 17 / 0.7880 = 21.6 units

DF = 17× tan (38°) = 17× 0.7813 = 13.3 units

CD = 10/13.3 × 21.6 = 16.2 units

so, the length of CE = 21.6+16.2 = 37.8 units

U have to work out the value of a by the way

Answers

Answer:

Step-by-step explanation:

180-90=2b+b

90=3b

90/3=b

30=b

2b=2*30

   =60

180-90=a+a

90=2a

a=90/2

a=45

the answer is 45 degrees

hope it helps!!let me know if it does

Answer:

a= 15°

Step-by-step explanation:

> use the fact that the sum of angles in a triangle is 180°

> based on the picture in the small right triangle we have b° +2b° +90° =180°

b +2b +90 =180° , combine like terms

3b +90 = 180, subtract 90 from both sides of the equation

3b = 90, divide by 3 both sides of the equation

b = 30°

> angle b has a ray that continues as a line so it makes an 180° angle and we have the acute triangle so we can write that

a + a+ (180-b) =180, substitute b

2a + 180-30 =180, subtract 180 from both sides, and add 30 to both sides

2a=30, divide by 2 both sides

a= 15°

I need help with this math problem not sure what to do?​

Answers

Answer:

B. 14

Step-by-step explanation:

It's asking for function f + function g. Then it wants you to use 2 as the x value. So you have:

(f+g)(x) = 2x^2 + 3x + x - 2

(f+g)(x) = 2x^2 + 4x -2

Then using 2 as x:

(f+g)(2) = 2(2^2) + 4* 2 -2

(f+g)(2) = 8 + 8 - 2

(f+g)(2) = 14

Hope that helps, and let me know if I did any of that wrong.

I need some help please!

Answers

Answer:

See below

Step-by-step explanation:

Given :-

y || z

To Prove :-

m∠5 + m∠2 + m∠6 = 180°

Proof :-

Here we are required to prove that ,

[tex]\rm\implies m\angle 5 + m\angle 6 + m\angle 2 = 180^o [/tex]

And here it's given that , y || z . Therefore ,

∠3 = ∠6 ( alternate interior angles )∠1 = ∠5 ( alternate interior angles )

Now we know that the measure of a straight line is 180°. Therefore ,

[tex]\rm\implies m\angle 1 + m\angle 2 + m\angle 3 = 180^o \\\\\implies\boxed{\rm m\angle 5 + m\angle 6 + m\angle 2 = 180^o} [/tex]

From 1 and 2 .

Hence Proved !

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