Christian is rewriting an expression of the form y = ax2 + bx + c in the form y = a(x – h)2 + k. Which of the following must be true?

Answers

Answer 1

Answer:

The Value Remains the Same

Step-by-step explanation:

Trust

Answer 2

The value of a remains unchanged. Therefore, option C is the correct answer.

Given that, Christian is rewriting an expression of the form y = ax² + bx + c in the form y = a(x – h)² + k.

We need to find from the option which is true for the given statement.

What is a vertex form?

The Vertex formula of a parabola is used to find the coordinates of the point where the parabola crosses its axis of symmetry. The vertex is the point (h,k). As we know the standard equation of a parabola is y = ax²+bx+c. The vertex form of the parabola y = a(x - h)²+ k. There are two ways in which we can determine the vertex (h, k).

Now,

The original expression is given as y = ax²+bx+c and Christian rewritten as y = a(x - h)²+ k.

Simplify the equation y = a(x - h)²+ k, that is y = a(x²-2xh+h²)+k.

⇒y=ax²-2axh+ah²+k

Compare the equation y=ax²-2axh+ah²+k with y = ax²+bx+c.

That is ax²=ax²

bx=-2xh and c=ah²+k

Analyzing the above equations ax²=ax²

Now, divide both sides by x², and we get a=a.

So, the value of a remains unchanged.

Therefore, option C is the correct answer.

To learn more about the vertex form visit:

https://brainly.com/question/22649174.

#SPJ6

Christian is rewriting an expression of the form y = ax² + bx + c in the form y = a(x – h)² + k. Which of the following must be true?

h and k cannot both equal zero

k and c have the same value

the value of a remains the same

h is equal to one half –b


Related Questions

what do you think of france

Answers

Answer:

Baguette is very important

Step-by-step explanation:

they don't have bidet but baguette

Answer:

honestly i think its a pretty country, its pretty nice and wish i could go.  

Step-by-step explanation:

find 150 of 28 by writing the percent as a decimal

Answers

Answer:

28 / 150 = 18.666666666667%

Step-by-step explanation:

28 / 150 = 18.666666666667%

4.45 / 100 = 4.45%

143 / 165 = 86.666666666667%

127,998 / 1,609,008 = 7.955087855374%

Please hurry I am being timed!

The three angles of a triangle have equal measures. The sum of their measures is 180º. What is the measure of each angle?
A. 45º
B. 30º
C. 60º
D. 55º


Please select the best answer from the choices provided

Sorry if this is easy for you I'm bad at math

Answers

The angle of each measure is 60 degrees

The table shows the location of four cities relative to sea level.
Which city is closest to sea level? Explain.

Answers

Answer:its citc (C)

Step-by-step explanation:

Calculate the circumference of the following circles. Give your answers to 1 decimal place.​

Answers

Answer:

a) 31.4 cm b) 22.0 cm c) 9.4 mm d) 18.8 m e) 1.6 m f) 28.3 cm g) 78.5 cm h) 9.7 m

Step-by-step explanation:

All it really is multiply the diameter which is the straight line through the center of the circle

C = d × \pi

The circumference of the circles is A. 31.4 cm, B. 22cm approx,

C. 9.4 mm, D. 18.88 m, E. 1.6 m, F. 28.3 cm, G. 78.5 cm, H. 4.1 m.

What is a circle?

A circle is a closed, two-dimensional object where every point in the plane is equally spaced from a central point. The line of reflection symmetry is formed by all lines that traverse the circle. Additionally, every angle has rotational symmetry around the center.

Given circles,

circumference  of circle is 2πr in form of diameter = πd

where d is diameter,

A. given d = 10 cm

circumference   = c = πd

c = 3.14 x 10

c = 31.4 cm

B. given, d = 7 cm

c= πd

c = 3.14 x 7

c = 21.98 cm = 22 cm approx

C.given, d= 3 mm

c = πd

c = 3.14 x 3

c = 9.4 mm

D. given d = 6 m

c = πd

c = 3.14 x 6

c = 18.8 m

E. given c = 0.5 m

c = πd

c = 3.14 x 0.5

c = 1.6 m

F. given d = 9 cm

c = πd

c = 3.14 x 9

c = 28.3 cm

G. given d = 25 cm

c = πd

c = 3.14 x 25

c = 78.5 cm

H. given d = 1.3 m

c = πd

c = 3.14 x 1.3

c = 4.1 m

Hence the circumference is as follows.

Learn more about circles;

https://brainly.com/question/29142813

#SPJ5

You were given a Starbucks gift card for your birthday. One day, you used the gift card to order 3 drinks that cost $5.20 each. When you looked at your receipt, you noticed that there was a remaining balance of $26.00 on the gift card.

Write an equation in point-slope form that represents the total balance left on the gift card, y, in terms of the number of drinks ordered, x.

Answers

Answer:

The card had 41.60 originally

Step-by-step explanation:

3 x 5.20 = 15.60

15.60 + 26.00 = 41.60

unless there is tax

please help im struggling​

Answers

Answer:

a = 6

b = 3

c = 2

Step-by-step explanation:

Since n(P) = a+b = 9

and n(Q) = b+c = 5

and b is given to be 3

a and b follow easily.

a is 9-b = 9-3 = 6

c is 5-b = 5-3 = 2

A shop sells chocolate, vanilla, and strawberry ice cream cones. If 45% of the ice cream sold is chocolate and 17% is strawberry, what percent that is sold is vanilla?

Answers

Answer:

38 %

Step-by-step explanation:

45 + 17 is 62. Soif you add 38% + 62% you'll get 100% !

Hope this helps! ^O^

(-4c2+7cd+8d)+(-3d+8c2+4cd)=

Answers

Answer:

4c² + 11cd + 5d

Step-by-step explanation:

To add monomials, you have to look at the variables that are accompanied by their coefficients. In the given problem, (–4c2 + 7cd + 8d) + (–3d + 8c2 + 4cd), you can combine both cd ut nt cd and c² and cd and d and d and c² because they have different variables.

(–4c2 + 7cd + 8d) + (–3d + 8c2 + 4cd)  

(-4c² + 8c²) + (7cd + 4cd) + (8d - 3d)

4c² + 11cd + 5d

Answer:

4,11,5

Step-by-step explanation:

Find the slope and a point on the line. y-9=-1/3(x-4)

Answers

Answer:

slope- -1/3

a point: (0, [tex]\frac{31}{3}[/tex])

Step-by-step explanation:

y-9= -1/3(x-4)

y-9= -1/3x+4/3

y= -1/3x+31/3

to find a point:

y= -1/3(0)+31/3

y=31/3

(this happens when x= 0, so the point is (0,31/3)

Answer:

m=-1/3

Point: (4,9)

Step-by-step explanation:

i just took the question and got it right on ed2020

While Justin is in training he has to drink 500 ml of water per day. How many liters will that be for one week?

Answers

Answer:

3.5 Liters

Step-by-step explanation:

Since 500 ml is equal to 0.5 liters and there are 7 days in a single week you just need to multiple the number of liters (0.5) by the 7 days to get a total of 3.5 liters

What are two coordinates on this graph?

Answers

Answer:

(0,5) and (6,0)

Step-by-step explanation:

please helppppppp :(((

Answers

Answer:

y = 1/2x - 1

General Formulas and Concepts:

Pre-Algebra

Order of Operations: BPEMDASEquality Properties

Algebra I

Slope Formula: [tex]m=\frac{y_2-y_1}{x_2-x_1}[/tex]

Slope-Intercept Form: y = mx + b

m - slope b - y-intercept

Step-by-step explanation:

Step 1: Define

Find points from the graph.

x-intercept (2, 0)

y-intercept (0, -1)

Step 2: Find slope m

Substitute:                    [tex]m=\frac{-1-0}{0-2}[/tex]Subtract:                       [tex]m=\frac{-1}{-2}[/tex]Simplify:                        [tex]m=\frac{1}{2}[/tex]

Step 3: Write linear equation

y = 1/2x - 1

Answer:

its y = 1/2 x - 1

Step-by-step explanation:

why did math tutor delete my question?!?!??!

In the metric system, which prefix would you use for "1/100"?
A. Kilo-
B. Milli-
C. Centi-
O D. Hecto-

Answers

Answer:

C

Step-by-step explanation:

Centi means 1/100.

Answer:  C. Centi-

Step-by-step explanation:

It comes from Latin. You can remember that 0ne Cent is 1/100 of a dollar.

which is an equation of the line parallel to 4y-7x=8 and passes through (-4,0)

Answers

Answer:

The correct option is; A. [tex]y = \dfrac{7}{4} x + 7[/tex]

Step-by-step explanation:

The given equation is 4·y - 7·x = 8

The coordinates of the point the line passes = (-4, 0)

By dividing the given equation by 4, we have;

4·y/4 - 7/4·x = 8/4

Which gives;

y  - 7/4·x = 2

y   = 7/4·x + 2

Which is the equation of a straight line in slope and intercept form, y = m·x + c, with the slope, m = 7/4, and the y-intercept = 2

Given that the required line is parallel to the graph of the equation, 4·y - 7·x = 8, the slopes of both equations are equal we have;

Slope of required line = 7/4, point on the line = (-4, 0), which gives the following point and slope form equation of a straight line;

y - 0 = 7/4 × (x - (-4))

y = 7/4·x + 7/4 × 4 = 7/4·x + 7

The equation of the line is therefore;

y = 7/4·x + 7

HELP ME PLEASE I NEED HELP I BEG OF U WILL MARK AND 5 STARS

Answers

x=43 because the whole triangle is 180 degrees so you simply just add the 25 and 112 together and minus that answer by 180

graph the function -4x + 3y = 15

Answers

Y=10 X=3.75 is the answer

Quinton bought n number of shares for d dollars and paid a 1% commission. He sold the stock for y dollars and paid a flat fee of

$7. Which expression below models Quinton's net proceeds algebraically?

oyn(1.01d - 7).

(1.01nd + 7) - Y

y - 1.01(nd - 7)

y (1.01nd + 7)

Answers

Answer:

y - (1.01nd + 7)

Step-by-step explanation:

Quinton bought n number of shares for d dollars and paid a 1% commission. It means he bought [tex]\dfrac{1}{100}nd=0.01nd[/tex]

He sold the stock for y dollars and paid a flat fee of  $7. It means he sold y-7.

We need to find Quinton's net proceeds algebraically. It will be given as :

[tex]y-7-0.01nd\\\\=y-(0.01nd+7)[/tex]

Hence, the correct option is (d) i.e. y - (1.01nd + 7)

Solve for X
-18x + 21 > - 15 OR 20x - 13 greater than or equal to 27
answers:
-x< -2 or x greater than or equal to 2
-x = -2
-x greater than or equal to 2
-There are no solutions
-All values of x are solutions

Answers

C, x is greater than or equal to 2

Step-by-step explanation:

Both equations have X equaling to 2

The table of values represents a linear function g(x), where x is the number of days that have passed and g(x) is the balance in the bank account:


x g(x)
0 $600
3 $720
6 $840
Part D: What is the balance in the bank account after 7 days? (2 points)

Answers

Answer:

880

Step-by-step explanation: Every three days the balance increases by 120 so you would divide 120 by 3 to get 40. This would mean that the balance increases by 40 everyday so after seven days the balance would be 880

Hello Guys it’s FreeGiftCardCodes I’ll be posting PS4 Xbox apple And Nintendo switch Gift cards ILL send a 2 when I get to 5 followers so add me if you want one And thank me also

Answers

Answer:

alright bet

Step-by-step explanation: ayyyeeeee

Answer:

Alright bro I will add you and thank you

Step-by-step explanation:

Find the total surface area of this square based
pyramid.
10ft
10 ft
[? ]ft?

Answers

Answer:

300 [tex]ft^{2}[/tex]

Step-by-step explanation:

area of triangle= [tex]\frac{b*h}{2}[/tex]

[tex]\frac{10*10}{2}[/tex] = 50

4 sides of the triangle

4*50=200

area of square= l*w

10*10=100

area of square+area of triangles

200+100=300

_[tex]ft^{2}[/tex]=300[tex]ft^{2}[/tex]

Answer: 300

Step-by-step explanation:

A pentagon has angle measures of 100, 105, 110, and 115. Find the fifth angle measure.

Answers

Answer:

110

Step-by-step explanation:

f(x)= x^2 + 10f(x)=x

2

+10f, left parenthesis, x, right parenthesis, equals, x, squared, plus, 10

Over which interval does fff have a positive average rate of change?

Choose 1 answer:

Choose 1 answer:


(Choice A)

A

[-3,3][−3,3]open bracket, minus, 3, comma, 3, close bracket


(Choice B)

B

[-4,-1][−4,−1]open bracket, minus, 4, comma, minus, 1, close bracket


(Choice C)

C

[-3,1][−3,1]open bracket, minus, 3, comma, 1, close bracket


(Choice D)

D

[-1,2][−1,2]

Answers

Answer:

The option D represents an interval with a positive average rate of change.

Step-by-step explanation:

Let [tex]f(x) = x^{2}+10[/tex], the average rate of change on the interval [tex][a,b][/tex] is represented by the definition of the secant line:

[tex]\bar f = \frac{f(b) -f(a)}{b-a}[/tex] (1)

Where:

[tex]a[/tex], [tex]b[/tex] - Lower and upper bounds, dimensionless.

[tex]f(a)[/tex], [tex]f(b)[/tex] - Function evaluated at lower and upper bounds, dimensionless.

Now we proceed to check each option:

A. [tex]a = -3[/tex], [tex]b = 3[/tex]

[tex]\bar f = \frac{19-19}{3-(-3)}[/tex]

[tex]\bar f = 0[/tex]

B. [tex]a = -4[/tex], [tex]b = -1[/tex]

[tex]\bar f = \frac{11-26}{(-1)-(-4)}[/tex]

[tex]\bar f = -5[/tex]

C. [tex]a = -3[/tex], [tex]b = 1[/tex]

[tex]\bar f = \frac{11-19}{1-(-3)}[/tex]

[tex]\bar f = -2[/tex]

D. [tex]a = -1[/tex]. [tex]b = 2[/tex]

[tex]\bar f = \frac{14-11}{2-(-1)}[/tex]

[tex]\bar f = 1[/tex]

The option D represents an interval with a positive average rate of change.

Answer:

It would be D

Step-by-step explanation:

A grocery store offers a 10% discount on your entire purchase when you spend more than $50. You have $117 to spend on groceries and the cost of the groceries in your cart is currently $50. The inequality 0.9(a+50)≤117 represents the cost a (in dollars) of groceries that you can add to your cart.

Answers

Answer:

a≤80

Step-by-step explanation:

Answer:

a≤80

Step-by-step explanation:

The graph represents this system of equations. A system of equations. y equals 4. y equals 3 minus StartFraction on-half EndFraction x. A coordinate grid with 2 lines. The first line passes through (negative 2, 4) and (0, 3). The second line passes through (negative 2, 4) and (0, 4). What is the solution to the system of equations?

Answers

Answer:

A coordinate grid with 2 lines. The first line passes through (negative 4, negative 3), (0, negative 3), and (4, negative 3). The second line passes through (0, negative 5) and (2, 4). The lines appear to intersect at about one-half, negative 3.

Solve the system of equations algebraically. Verify your answer using the graph.

y = 4x – 5

y = –3

What is the solution to the system of equations?

((StartFraction one-fourth EndFraction, negative 3), –3)

((StartFraction one-half EndFraction, negative 3), –3)

(–3, (negative 3, StartFraction 2 over 3 EndFraction))

Step-by-step explanation:

Answer:

its a

Step-by-step explanation:

i just did it

The length of the day in Lagos, Nigeria (in minutes), ttt days since the beginning of the year can be estimated by this formula: \qquad L(t) = 727+22\sin \left(\dfrac{2\pi (t - 80.75)}{365}\right)L(t)=727+22sin( 365 2π(t−80.75) ​ )L, left parenthesis, t, right parenthesis, equals, 727, plus, 22, sine, left parenthesis, start fraction, 2, pi, left parenthesis, t, minus, 80, point, 75, right parenthesis, divided by, 365, end fraction, right parenthesis. When is the longest day of the year? Give an exact answer.

Answers

Answer:

The longest day of the year is day 172  

Step-by-step explanation:

Since the length of day is L(t)=727+22sin[2π(t−80.75)/365], the maximum length of day is obtained when sin[2π(t−80.75)/365] is at its maximum value which is 1. So. sin[2π(t−80.75)/365] = 1

We now solve this to find the day at which this maximum value occurs.

sin[2π(t−80.75)/365] = 1

[2π(t−80.75)/365] = sin⁻¹(1)

[2π(t−80.75)/365] = π/2

dividing both sides by 2π/365, we have

[2π(t−80.75)/365] ÷ 2π/365 = π/2 ÷ 2π/365

t−80.75 = 365/4

t−80.75 = 91.25

t = 91.25 + 80.75

t = 172

The longest day of the year is day 172

Answer:

172

Step-by-step explanation:

Keep in mind, that when graphed one of the "tallest" points is 172,749. Using this, you'll find that 172 is the tallest

2/5+6/10
What is the answer

Answers

We have to make sure the denominators are equal.

10 goes into 5 evenly, so we only need to multiply one term to get a common denominator.

Multiply 2 by 2, and get 4, then we multiply 5 by 2 and get 10

Now the equation is 4/10 + 6/10

Since our denominators match, we can add the numerators.

4 + 6 = 10

That gives us the sum, which is 10/10 aka 1 whole

your welcome :) (btw can u please give brainly?)

Answer:

2/5 + 6/10 = 1

Step-by-step explanation:

first let’s change 2/5 so it has the same denominator as 6/10.

2/5 * 2/2 = 4/10

now add

4/10 + 6/10 = 1

The bus drives 66 km at an average speed of 24 km/h. How long does the journey take?

Answers

Answer:

2.75 hours

Step-by-step explanation:

Speed is 24km per hour ([tex]\frac{24km}{1hour}[/tex]), and the bus covered 66km.

We need to get a value of km with the rate (24/1) and distance (66) given.

We get:  [tex]\frac{1hour}{24km} *66km[/tex].  

The km cancel out, leaving us with 66/24 hours, or 2.75 hours.

Which of the following statements must be true about this diagram? check all that apply.​

Answers

Answer:

F & B

Step-by-step explanation:

Answer:

C, D, E

Step-by-step explanation:

Remote angles theorem; when one side of a triangle is extended, the angle formed must equal the sum of the two angles in the triangle, that it isn't adjacent to.

C. (m<4) > (m<1), this has to be true because of remote angles theorem.

(m<4) must be greater than (m<1) because it is equal to (m<1) + (m<2)

D. (m<4) > (m<2), apply the same logic here, as was applied to the first problem.

E. (m<1) + (m<2) = (m<4), this is essentially remote angles theorem.

Other Questions
Read the legend titled "The Little Mice."Once upon a time, a prairie mouse busied herself all fall storing away a cache of beans. Every morning she was out early with her empty cast-off snakeskin, which she filled with ground beans and dragged home with her teeth.The little mouse had a cousin who was fond of dancing and talk but did not like to work. She was not careful to get her cache of beans, and the season was already well gone before she thought to bestir herself. When she came to realize her need, she found she had no packing bag. So she went to her hardworking cousin and said:"Cousin, I have no beans stored for winter and the season is nearly gone. But I have no snakeskin to gather the beans in. Will you lend me one?""But why have you no packing bag? Where were you in the moon when the snakes cast off their skins?""I was here.""What were you doing?""I was busy talking and dancing.""And now you are punished," said the other. "It is always so with lazy, careless people. But I will let you have the snakeskin. And now go, and by hard work and industry, try to recover your wasted time."Which statement best identifies the purpose and theme of this legend?The legend aims to teach readers a lesson about understanding, revealing the theme "honesty is greatly respected."The legend aims to teach readers a lesson about responsibility, revealing the theme "you get out of something what you put into it."The legend aims to teach readers a lesson about determination, revealing the theme "any job can be completed with effort and cooperation."The legend aims to teach readers a lesson about free time, revealing the theme "life's pleasures must equal life's work." Jose earns $3680 per month, of which 22% is taken out for federal and state income taxes and other required deductions. Last month he spent $775 for rent and 86.12 on clothing. What percent of his take-home pay did he spend on rent and clothing combined? What were the thirteen original colonies required to do in order to become a state of the United States of America? A. ratify the new constitution B. reach a population of five thousand C. join a confederation of states D. build a port on the Atlantic OceanThis is a question from buzz! Which of the following are only found in animal cells?chloroplastsBribosomesmitochondriaDlysosomes The sum of four consecutive integers is 74.What is the first integer?16171918 Which relation is a function?A. {(2, 3), (1, 5), (2, 7)}B. {(-1, 5), (-2, 6), (-3, 7)}C. {(11, 9), (11, 5), (9, 3)}D. {(3, 8), (0, 8), (3, -2)}Reset advantages and disadvantage of chemistry What is the middle term of the product of (3m - 1)(m + 9) whats the slope for 6,14 and 10,9 Vivaldi spent the bulk of his years as a priest, leading his congregants through theMass true or falsee Why did plantation owners of Saint Domingue use cruel and ruthless methods of treatment toward enslaved persons? to push the enslaved to produce more crops to render the enslaved powerless as to not revolt to provoke fear in the enslaved to repay their cost to harden the enslaved and ready them for auction Name one reason Philadelphia was chosen as the site of the Convention. The ratio of potatoes to turnips is 1:1, if there are 473 potatoes, how many turnips are there? Select which of the following is an example of a Jim Crow law? *a, indentured servitudeb. the exclusion of native Americans from the American politkal processc. debt peonageO d. requiring separate railroad cars for whites and for African Americans will give brainliest Which concept would states rights advocates have supported during the 1860 presidential election?the abolition of slaverythe idea of popular sovereigntythe candidacy of John Bellthe candidacy of Abraham Lincoln What is 1 1/3 minus 5/6 Help me please, ........ thanks, gracias What's an impact of the development of empires in Mesopotamia Empires made society less hierarchicalEmpires leased warfareEmpires decreased agricultural production.Empires sores Sumerian culture to a wider area. Choose the best Spanish translation.the Spanish classel clase de espaolla clase espaoluna clase de espaolla clase de espaol Evaluate 12.7 - x for x= 8.41