Explain the steps necessary to convert a quadratic function in standard form to vertex form.

Answers

Answer 1

Step-by-step explanation:

A quadratic function in standard form is converted to vertex form by completing the square. The first two terms are used to create a perfect square trinomial after a zero pair is added. The zero pair is found by taking half of the x-term coefficient and squaring it.


Related Questions

You are an avid coin collector. You decide to start keeping better track of your coin collection:after 15 days you count and find out you have 155 coins. After 22 days,you have 218 coins. Write an equation in point-slope form

Answers

9514 1404 393

Answer:

  y - 155 = 9(x -15)

Step-by-step explanation:

The given points are ...

  (days, coins) = (15, 155) and (22, 218)

The slope is given by the slope formula:

  m = (y2 -y1)/(x2 -x1) = (218 -155)/(22 -15) = 63/7 = 9

The point-slope form is for a line with slope m through point (h, k) is ...

  y -k = m(x -h)

Here, we have m=9 and (h, k) = (15, 155), so the equation can be written ...

  y - 155 = 9(x -15)

when I add a number to another number four times as big, the result is 30. find the first number

Answers

Answer:

x = 6

Step-by-step explanation:

Let x = first number

x+4x = 30

5x = 30

Divide by 5

5x/5 =30/5

x = 6

Let's assume the number is N

According to the question,

when I add a number to another number four times as big, the result is 30.

[tex]x+4x=30\\\\5x=30\\\\x=\dfrac{30}{5}\\\\x=\frak{6}[/tex] 

Which inequality is true?

Answers

Answer:

[tex]\boxed{\sf Option \ C \ is \ correct .}[/tex]

Step-by-step explanation:

We need to tell which of the given inequality is true . The given inequalities are ,

[tex]\sf A)\pi + 8 <11\\\\\sf B) \dfrac{\pi}{8} > 2 \\\\\sf C) 3\pi > 9 \\\\\sf D) 2\pi - 1 < 5 [/tex]

Let's check the options one by one .

Option A :-

[tex]\sf\longrightarrow \pi + 8 < 11[/tex]

Subtract 8 to both sides ,

[tex]\sf\longrightarrow \pi < 11 - 8 [/tex]

Simplify ,

[tex]\sf\longrightarrow \pi < 3[/tex]

We know the approximate value of pi 3.14 . But the inequality says pi is less than 3 . Therefore the given inequality is incorrect .

______________________________________

Option B :-

[tex]\sf\longrightarrow \dfrac{\pi}{2} > 2 [/tex]

Multiply both sides by 2 ,

[tex]\sf\longrightarrow \pi > 4 [/tex]

We know the approximate value of pi 3.14 . But the inequality says pi is more than 4 . Therefore the given inequality is incorrect .

______________________________________

Option C :-

[tex]\sf\longrightarrow 3 \pi > 9[/tex]

Divide both sides by 3 ,

[tex]\sf\longrightarrow \pi < 9/3[/tex]

Simplify ,

[tex]\sf\longrightarrow \pi > 3 [/tex]

We know the approximate value of pi 3.14 .And the inequality says pi is more than 3 . Therefore the given inequality is correct .

Option C is correct .

Evaluate function from their graph

Answers

Answer:  5

This is because the point (0,5) is shown on the graph. This is the point on the y axis.

We can say that h(x) = 5 when x = 0.

Answer:

5

Step-by-step explanation:

The fellow who expalined it before before me expalined it correctly, so the answer should be 5.

Suppose that a recent article stated that the mean time spent in jail by a first-time convicted burglar is 2.5 years. A study was then done to see if the mean time has increased in the new century. A random sample of 26 first-time convicted burglars in a recent year was picked. The mean length of time in jail from the survey was 3 years with a standard deviation of 1.8 years.Suppose that it is somehow known that the population standard deviation is 1.5. If you were conducting a hypothesis test to determine if the mean length of jail time has increased, what would the null and alternative hypotheses be? The distribution of the population is normal.(a) null hypothesis H0: μ = 2.5 yearsH0: μ = 3 years H0: μ > 3 yearsH0: μ ≥ 2.5 yearsH0: μ = 1.8 years(b) alternative hypothesis Ha: μ ≠ 2.5 yearsHa: μ > 3 years Ha: μ ≥ 1.8 yearsHa: μ ≤ 3 yearsHa: μ > 2.5 years

Answers

Answer:

The null hypothesis is [tex]H_0: \mu = 2.5[/tex].

The alternative hypothesis is [tex]H_1: \mu > 2.5[/tex]

Step-by-step explanation:

Suppose that a recent article stated that the mean time spent in jail by a first-time convicted burglar is 2.5 years.

At the null hypothesis, we test if the mean is of 2.5 years, that is:

[tex]H_0: \mu = 2.5[/tex]

A study was then done to see if the mean time has increased in the new century.

At the alternative hypothesis, we test if the mean has increased, that is, if it is above 2.5 years. So

[tex]H_1: \mu > 2.5[/tex]

For what values of x does 25^x = 5^x^2^-3?

Answers

Answer:

The correct option is Second Option

#CarryOnLearning

❦︎Park Hana Moon

PLS HELP 10 POINTS!!!

Identify the term whose coefficient is -12 in the expression:
98x – 12xy2 - 15xy2

Answers

Answer:

[tex] - 12xy {}^{2} [/tex]

Step-by-step explanation:

A coefficient is a rational number in front of multiple consecutive terms.

which of the following is equivalent to 18-
[tex] \sqrt{ - 25} [/tex]
a 5i
b 18-5i
c 18+5i
d 23​

Answers

Answer:

[tex]18-\sqrt{-25}[/tex]

[tex]\sqrt{-25} =5i[/tex]

[tex]=18-5i[/tex]

OAmalOHopeO

(b) If n(U)= 300, n(M) = 150, n(T) = 144 and n( MT)= 33. Find the value of n(MUT). (ii) Present the above information in a Venn diagram. ​

Answers

Answer:

Step-by-step explanation:

n(M ∪ T) = n(M) + n(T) - n(M∩T)

               = 150 + 144 - 33

               = 294 - 33

               = 261

Please help I don’t understand how to solve this !

Answers

Answer:

x = 30

Step-by-step explanation:

x + 2x + 3x = 180

             6x = 180

              6       6

               x =  30

guys, please help its graph-related. please i will dieeee

Answers

(a) Dilation is the process of extending the line segment AB to the longer one A'B'. The scale factor has to be larger than 1, and also it has to be positive.

(b) To get the dilation factor, you should first compute the length of AB, then compare it to the length of A'B'.

A is the point (-4, 2), and B is the point (2, -4). So the length of AB is

√((-4 - 2)² + (2 - (-4))²) = √((-6)² + 6²) = √72

A' is the point (-8, 4) and B' is (4, -8). The coordinates of A' and B' are twice the coordinates of A and B, so the distance is

√((2(-4) - 2(2))² + (2(2) - 2(-4))²) = √(2²×72) = 2√72

Then the dilation factor is

(2√72) / √72 = 2

As for dying, don't worry about it. It happens to everyone.

A locker combination has three nonzero digits, with no repeated digits. If the first digit is a 2, what is the probability the second digit is also even?
A. 1/2
B. 1/3
C. 3/7
D. 3/8

Answers

I think it would be 3/8 :))

two similar triangular prisms have surface areas of 64cm2 and 144cm2(the 2 means square) respectively. a.find the ratio of their heights. b. The height of the smaller prism is 49cm,find the height of the larger prism.​

Answers

Answer:

a.The ratio of the heights is the square roots of the both of them √64 and √144

which is 8 and 12

b.To find the height of the larger prism you use the ratio of the heights,in a ratio and proportion

8 - 49

12-x

8x/8=588/8

x=73.5

I hope this helps

If 4 over 7 ton of concrete covers 7 over 8 of a bridge, how many tons of concrete are required to cover the entire bridge?

Answers

Answer:

Your answer would be 32/49.

Step-by-step explanation:

4/7 tons = 7/8 x

4/7 / 7/8

32/49

The tons of concrete are required to cover the entire bridge is 32/49 tons.

What are fractions?

A fraction is a non-integer that is made up of a numerator and a denominator. An example of a fraction is 4/7.

How many tons is needed to cover the whole bridge?

To determine this value, divide 4/7 by 7/8

4/7 ÷ 7/8

4/7 x 8/7 = 32/49 tons

To learn more about the division of fractions, please check: https://brainly.com/question/25779356

verify a(b-c)=ab-ac for a=1.6;b=1/-2;& c=-5/-7​

Answers

Given:

[tex]a=1.6,b=\dfrac{1}{-2},c=\dfrac{-5}{-7}[/tex]

To verify:

[tex]a(b-c)=ab-ac[/tex] for the given values.

Solution:

We have,

[tex]a=1.6,b=\dfrac{1}{-2},c=\dfrac{-5}{-7}[/tex]

We need to verify [tex]a(b-c)=ab-ac[/tex].

Taking left hand side, we get

[tex]a(b-c)=1.6\left(\dfrac{1}{-2}-\dfrac{-5}{-7}\right)[/tex]

[tex]a(b-c)=1.6\left(-\dfrac{1}{2}-\dfrac{5}{7}\right)[/tex]

Taking LCM, we get

[tex]a(b-c)=1.6\left(\dfrac{-7-10}{14}\right)[/tex]

[tex]a(b-c)=\dfrac{16}{10}\left(\dfrac{-17}{14}\right)[/tex]

[tex]a(b-c)=\dfrac{8}{5}\left(\dfrac{-17}{14}\right)[/tex]

[tex]a(b-c)=-\dfrac{68}{35}\right)[/tex]

Taking right hand side, we get

[tex]ab-ac=1.6\times \dfrac{1}{-2}-1.6\times \dfrac{-5}{-7}[/tex]

[tex]ab-ac=-\dfrac{16}{20}-\dfrac{8}{7}[/tex]

[tex]ab-ac=-\dfrac{4}{5}-\dfrac{8}{7}[/tex]

Taking LCM, we get

[tex]ab-ac=\dfrac{-28-40}{35}[/tex]

[tex]ab-ac=\dfrac{-68}{35}[/tex]

Now,

[tex]LHS=RHS[/tex]

Hence proved.

(Question is in the image)

please I really need help

Answers

Answer:

c

Step-by-step explanation:

The period is 1 complete cycle of the wave, before repeating.

1 cycle is from - 6 to - 2 , then

period = 4  → c


Changing some of the values in a data set is called transforming the data.
A. True
B. False

Answers

The answer is a. True

Answer:

The answers is False

Step-by-step explanation:

If the product of two numbers is 1800 and its H.C.F. Is 30, find the L.C.M.​

Answers

Answer:

LCM = 60

Step-by-step explanation:

Product = HCF × LCM

1800 = 30 × LCM

LCM = 1800/30

∴ LCM = 60

12X12= ___+144-88=___

Answers

12x12=144+144-88=200 good luck!
200
Explanation. After you get the 12×12 and get the answer you add the answer to 144 and subtract 88 and that’s your answer

What is the surface area of a sphere with a diameter of 14 cm?
Question 6 options:


175.84 cm^2


351.68 cm^2


615.44 cm^2


2461.76 cm^2

Show your work:

Answers

9514 1404 393

Answer:

  (c)  615.44 cm^2

Step-by-step explanation:

The surface area of a sphere is given by ...

  A = 4πr² . . . . where r is the radius, half the diameter

  A = 4(3.14)(7 cm)² = 196(3.14) cm² = 615.44 cm²

A coffee distributor needs to mix a(n) Rift Valley coffee blend that normally sells for $10.20 per pound with a Terraza coffee blend that normally sells for $13.50 per pound to create 40 pounds of a coffee that can sell for $10.37 per pound. How many pounds of each kind of coffee should they mix

Answers

Answer:

Rift =37.92 pounds

Terraza=2.08 pounds

9514 1404 393

Answer:

Rift Valley: 37 31/33 ≈ 37.94 lbTerraza: 2 2/33 ≈ 2.06 lb

Step-by-step explanation:

Let t represent the number of pounds of Terraza blend required. Then 40-t is the number of pounds of Rift Valley blend needed. The cost of the mix will be ...

  13.50t +10.20(40 -t) = 10.37(40)

  3.30t = 6.8 . . . . . . . . . . . . . . . . . . . . subtract 408

  t = 6.8/3.30 = 68/33 = 2 2/33 ≈ 2.06061 . . . . pounds of Terraza

Then the quantity of Rift Valley blend required is ...

  40 -2 2/33 = 37 31/33 ≈ 37.93939 . . . . pounds of Rift Valley

What is the surface area of the cylinder? Express the answer in terms of pi
d = 8 cm
h = 18 cm

Answers

bonjour,

answer ≈ 522.92

working
A= 2πrh+2πr^2
=2 x π x 4 x 18+2 x π x 4^2
≈552.92031

Find the measure of FG.

Answers

Answer:

Choice D, x = 9

Answer:

Step-by-step explanation:

EG = EF + FG = 9 + x - 3 = 6 + x

AG = AH + HG = 6 +x - 2 =  4 + x

Intersecting secant theorem,

FG * EG = HG * AG

(x - 3)*(6 +x) = (x -2)(x + 4)

Use Foil method

6x + x²  - 18 - 3x = x² + 4x - 2x - 8

x² + 3x  - 18 = x² + 2x - 8

x² - x² + 3x - 2x = -8 + 18

               x = 10

The sum of two numbers is 90. The larger number is 14 more than 3 times the smaller number. Find the numbers.

[ x + y = 90 ; x = 14 + 3y ]

Answers

Answer:

fourteen times six equals eighty-four, eighty-four plus six equals 90

What is the value of x in the triangle below?

A. 18

B. 15

C. 6

D. 45

Answers

Answer:

it is b I already took it I just checked again

When do we use the AC Test?

Answers

Ummmm…… let me guess when your ac is damaged?

Instructions: Find the measure of the indicated angle to the nearest degree.
?

Answers

Answer:

? = 14

Step-by-step explanation:

Since this is a right triangle, we can use trig functions

tan theta = opp /adj

tan ? = 8/33

Taking the inverse tan of each side

tan ^-1 ( tan ?) = tan ^-1 ( 8/33)

? =13.62699

To the nearest degree

? = 14

Answer:

14

Step-by-step explanation:

We can solve for either x or y first, but we will choose to solve for x first. The side with length of 8 is opposite the angle x and the side with length of 33 is adjacent. Since we have opposite and adjacent sides, we will use the tangent ratio.

tan(x)= opposite/adjacent

tan(x)= 8/33

To find the measure of angle x, we will use the inverse tan function.

x=tan⁻¹(8/33)= 14

PLEASE HELP WILL GIVE BRAINSLIST

Answers

Answer: 3. 55° 2. 225° 1. 125°

Step-by-step explanation: don't want brainliest

write a inequality phrase: you have to be at least 21 years of age

Answers

Answer:

[tex]a\geq 21[/tex]

Step-by-step explanation:

"At least" is inclusive, so you can be 21 years old.

Answer:

a≥ 21

Step-by-step explanation:

Let a = age

At least means greater than or equal to

a≥ 21

Select all that apply.
The slope of the graph of a direct variation function is -3. Which of the following is true?

The equation is y = -3x.
The function is linear.
The equation of the function is y = -x .
The point (2, -6) is on the graph of the function.

Answers

a and b are correct

c is wrong

d can't be decided, because it can be true for one case, but not for others.

so only go for a and b

Answer:

B. The function is linear. (A and D COULD work)

Step-by-step explanation:

If the graph of a direct variation function has a slope of -3, then we know that the function is linear, and that m in the equation y = mx + b is -3. However, option A could be incorrect since we don't know if there is a y-intercept or not. C is wrong because of -3 being the slope, and D would only be true if A was also correct. So that leaves B. (If you know that there is more than one option, then A, B, and D are correct.)

Other Questions
Louise has a hard time keeping her workspace clean at her job. She tries, but it just ends up getting messy again. Which of the following is a likely outcome of her consistent messiness? O a) She will have fewer safety issues. b) She will feel more productive. c) Customers will think she is very busy. O d) She will have a hard time focusing. a peace above all earthly dignities a still and quiet conscience explanation Are 5-x=y and x-5=y the same ? Sun Smarts Solar installs solar panels in large newly constructed buildings. The company employs several expert installers who work on a full-time basis. Although the installation team works every day, the company pays them at the end of the month, for the previous month's work. Employee salaries are recorded as __________ on Sun Smarts's balance sheet.A. capital cash flows B. current liabilities C. retained earnings D. long-term liabilities i don't understand this, can someone help please?? Find the line integral with respect to arc length C(9x+5y)ds, where C is the line segment in the xy-plane with endpoints P=(2,0) and Q=(0,7).(a) Find a vector parametric equation r (t) for the line segment C so that points P and Q correspond to t=0 and t=1, respectively(b) Rewrite integral using parametrization found in part a(c) Evaluate the line integral with respect to arc length in part b what are the useful of carbon dioxide? PLEASE help me ASAP. Social studies question.1. How can we make proper use of electricity? present any six ways. What is the surface area of this figure in square centimeters?A.96B.75C.84D.60 Phn tch nguyn tc xc nh thm quyn x pht vi phm hnh chnh quy nh ti iu 52 Lut x l vi phm hnh chnh nm 2012. Ly v d cho tng khon Which equation is the inverse of y = 16+ 1?Choices made this question if you can able to make Factor the polynomial expression 3x4 + 24x. Find the length of the third side. If necessary, round to the nearest tenth.1520Submit AnswerAnswer:attempt 1 out of 2PLS HELP ASAP ASAP ITS TIMED What is the following sum? Assume x20 and 20.W x + 2 / x 374 + xy y0 x 7 y- 2xy?0 2xy y + 2xy x0 4xy dxo 2xyxy in a 5 liter milk jar water and milk are in the ratio 2:3. If 1 liter of milk and 1 liter of water is added. what will be the new ratio.Give me answer with steps . and the answer is 3:4. but how I want to know Who does the Time Traveller meet when he lands in the future in The Time Machine?A. People dressed in purpleB. Wild lifecougars and lionsC. A group of masked figuresD. Green aliens the more beautiful or handsome you are the more problem you have.argue for or against this statement What group of people might the Medical Man represent in The Time Machine?A. DoctorsB. LawyersC. PoliticiansD. Teenagers A sample from a stock of a bacterial colony in liquid media was diluted by a factor of 106, and 2 ml of this dilution was spread on a Petri dish of solidified media. 56 colonies were observed. What was the concentration of bacteria of the initial stock?