Find the y-intercept and the axis of symmetry of f(x)=ax2+2ax+3.

Answers

Answer 1

Answer:

[tex] y= cx^2 +dx +e[/tex]

We see that:

[tex] c = a, d= 2a , e= 3[/tex]

The axis of symmetry is defined by this formula:

[tex] X= - \frac{d}{2c}[/tex]

And replacing we got:

[tex] X= -\frac{2a}{2a}= -1[/tex]

Thn the axis of symmetry would be X=-1

Step-by-step explanation:

For this case we have the following function:

[tex] y = ax^2 +2ax +3[/tex]

If we compare this function with the general expression of a quadratic formula given by:

[tex] y= cx^2 +dx +e[/tex]

We see that:

[tex] c = a, d= 2a , e= 3[/tex]

The axis of symmetry is defined by this formula:

[tex] X= - \frac{d}{2c}[/tex]

And replacing we got:

[tex] X= -\frac{2a}{2a}= -1[/tex]

Thn the axis of symmetry would be X=-1


Related Questions

To find the number of units that gives break-even for the product, solve the equation R C. Round your answer to the nearest whole unit A manufacturer has total revenue given by the function R = 90x and has total cost given by C 35x + 17,000, where x is the number of units produced and sold. A, 55 units
B. 125 units
C. 136 units
D. 309 units

Answers

Answer:

The correct answer is D.

Step-by-step explanation:

Giving the following information:

R = 90x

Total cost= 35x + 17,000

x= is the number of units produced and sold

Now, we know that:

Unitary variable cost= 35

Fixed costs= 17,000

Selling price per unit= 90

To calculate the break-even point in units, we need to use the following formula:

Break-even point in units= fixed costs/ contribution margin per unit

Break-even point in units= 17,000 / (90 - 35)

Break-even point in units= 309 units

Each square in the grid is a unit square with an area of 1 square unit.
What is the area of the figure?
square units

Answers

Answer:

6 square units

Step-by-step explanation:

Simply count the number of squares:

There are 4 squares aligned in a vertical column, and one to the right of that column (so up to this point you have 5 full squares). Then notice that you have two half squares in the shape of triangles. So two halves give us another full square. That totals 6 square units.

Someone pls help if you want more points just go to my other questions and answer them pls

Answers

Answer:

I would say the answer is C.

Last week Perry ran 24.9 miles more than Mike. Perry ran 40.5 miles. How many miles did Mike run? LAST ONE LOL

Answers

Answer:

15.5mi

Step-by-step explanation:

S refers to the distance covered

Given:

Last week Perry ran 24.9 miles more than Mike. Perry ran 40.5 miles.

Required:

How many miles did Mike run=?

Formula:

40.5mi-S(Perry)=S(Mike)

Solution:

40.5mi-S(Perry)=S(Mike)

40.5mi-24.9mi=S(Mike)

15.6mi=S(Mike)

Hope this helps.

Answer:

15.6 miles

Step-by-step explanation:

40.5 mi - 24.9 = 15.6 mi

Mike ran 15.6 miles

Please can someone help me asap

Answers

Answer:

48

Step-by-step explanation:

Because you add 20 cm, 15 cm, and lastly 13 cm. Then you add it all together and get the answer.

I REALLY NEED HELP PLZZZ. I WILL MARK YOU AS THE BRAINLIEST ANSWER IF U GIVE A GOOD RESPONSE TO THE QUESTIONS!!!!

Answers

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Hope this helped you.

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3 8 3 ​ ÷9=3, start fraction, 3, divided by, 8, end fraction, divided by, 9, equals

Answers

Answer:

1/24

Step-by-step explanation:

In the above question, we are asked to solve for:

start fraction, 3, divided by, 8, end fraction, divided by, 9, equals

Mathematically, this is represented as:

(3/8) ÷ 9

= (3/8) × 1/9

= 3/72

= 1/24

Therefore, start fraction, 3, divided by, 8, end fraction, divided by, 9, equals 1/24

Find the width of a rectangle if the diagonal is 19 and the length is 16

Answers

Answer:

≈10.25

Step-by-step explanation:

use the Pythagorean Theorem: a² + b² = c²

c is the hypotenuse, the diagonal, or the longest side of the triangle

a = 16

b = ?

c = 19

(16)² + b² = (19)²

256 + b² = 361

b² = 105

b = √105 ≈ 10.25

T models the temperature (in degrees Celsius) in New York City when it's t hours after midnight on a given day. Match each statement with the feature of the graph that most closely corresponds to it.

Answers

Answer:

Y Intercept: It was 3C at the beginning of the day.

Positive or negative interval: The temperature was above zero between 8 am and 8 pm.

Increasing or decreasing interval: It was getting warmer between 2 am and 2 pm

Step-by-step explanation:

Features matching the correct statements are:

y intercept: It was ₋3°C at the beginning of the day.

Positive or negative interval: The temperature was above zero between 8 am and 8 pm.

Increasing or decreasing interval: It was getting warmer between 2am and 2 pm.

What is the temperature graph over time?

The x-axis in a time-temperature graph, sometimes known as a "x-y graph," depicts time, and the y-axis the temperature. The temperature's relationship to time is depicted on the graph.

we can notice in the given graph that T(t) represents the time and t represents the temperature of the city.

So we see when lowercase t when time is zero(0), zero hours after midnight the temperature in the New York city is negative 3°C(₋3°C) so it was ₋3°C at the beginning of the day since the true beginning of the day is right at midnight. Hence y intercept tells us that it was ₋3°C at the beginning of the day.  Then about the positive or negative interval we can notice from the graph that we have a negative interval from time equals zero to time equals eight which means the temperature is negative as it goes below zero and from 8 am to 8 pm we can see that the temperature goes positive and then it dips down to negative again. So a positive or negative interval tells us about when the temperature was above xero between 8 am and 8 pm.The increasing and decreasing interval, here we see that the function is increasing as t increases so does the temperature, all the way to 2 pm. Hence, we are just using the increasing interval to  match the statement that it was getting warmer between 2 am and 2 pm.

Hence we get the statements match to their features.

Learn more about"temperature problems" here-

https://brainly.com/question/24746268

#SPJ2

Please answer this question now

Answers

Answer:

[tex]\boxed{u = 6.0}[/tex]

Step-by-step explanation:

Using the cosine rule

[tex]c^2= a^2+b^2-2abCosC[/tex]

Here c = u , a = 11 , b = 12 and C = 30

[tex]u^2 = 11^2+12^2-2(11)(12)\ Cos 30\\u^2 = 121+144-2(132)(0.866)\\u^2 = 265-228.6\\u^2 = 36.37[/tex]

Taking sqrt on both sides

u = 6.0   (To nearest tenth)

This is really confusing I need help with this.

Answers

Answer:

Step-by-step explanation:

can you at least telllus what is in the drop box

The correct answer is

The y-axis is horizontal line , the slope of the line is zero


The x-axis is x=0 , the slope of the line is undefined

answer : horizontal line , zero
Answer: x=0 , undefined


The second step by step is below

Hopefully this help you

If you have any other questions let me know
Have a great day :)

If you have the answer pls screenshot and put each pare in one color pls

Answers

Step-by-step explanation:

(2 / 3)(-4)(9) = (2 / 3) * 9 * (-4) = 6 * (-4) = -24.

(-3 / 4)(7 / 8) = (-3 * 7) / (4 * 8) = -21 / 32.

(2 and 3/5)(7 / 9) = (10/5 + 3/5)(7/9) = (13/5)(7/9) = 91 / 45.

(5 / 16)(-2)(-4)(-4/5) = (5 / 16)(4 / 5)(2)(-4) = (1 / 4)(2)(-4) = (-1)(2) = -2.

Hope this helps!

hello:) i think that AB is longer than DC but I’m not sure if it’s correct :/ anyone able to help ? thank you!

Answers

Answer: You are correct. AB is longer than DC.

============================================

Explanation:

OM and ON are not equal in length, so the chords AB and CD are not the same length. The chords would need to be equally distant from the center for the chords to be equal.

The further a chord gets from the center, the smaller the chord gets. This is because the diameter is the largest chord possible and its distance from the center is 0 units. Increase that distance and the chord will shrink until it reaches 0 units in length.

You are correct in stating that AB is longer than DC because AB is closer to the center (or that OM is smaller than ON).

I need you to answer ASAP
Line R: 2x + 2y = 18
Line M: x + y = 9
Which statement is true about the solution to the set of equatic
It is (189)
It is (9, 18)
There are infinitely many solutions
There is no solution

Answers

Answer:

infinitely many solutions

Step-by-step explanation:

2x + 2y = 18

 x +   y = 9

multiply Line M equation by -2 to eliminate at least one variable:

2x + 2y = 18

-2x - 2y = -18

use elimination:

2x + 2y = 18

-2x - 2y = -18

__________

0 + 0 = 0

since this statement is true, there are infinitely many solutions.

help me please, explanation not necessary but would be appreciated

Answers

Answer:

55°

Step-by-step explanation:

The following data were obtained from the diagram given above:

Adjacent = 4

Hypothenus = 7

Angle A =?

The value of angle A can be obtained as follow:

Cos A = Adjacent / Hypothenus

Cos A = 4/7

Take the inverse of Cos.

A = Cos¯¹(4/7)

A = 55.1° ≈ 55°

Therefore, the value of angle A is approximately 55°.

can someone help me fill out this chart

Answers

Answer:

is there a y part of this equation?

Step-by-step explanation:

Any fake answers will get reported but if u do good u get brainliest:) ----------------------------------- Fred's coffee shop sells two blends of beans at the following prices. a) House Blend ($3.50/lb) b) Exotic Blend ($4.00/lb). House blend is 1/2 Costa Rican beans and 1/2 Ethiopian beans. Exotic blend is 1/4 Costa Rican beans and 3/4 Ethiopian beans. Every day Fred receives 200 lbs of Costa Rican Beans and 330 lbs of Ethiopian beans. What are the common sense constraints? ------ ---------------------------------- x or = 530 ---- x > or = 0, and y > or = 0

Answers

Since he needs beans to sell. The common sense constraints would be that both x and y need to be equal to or greater than 0, otherwise he wouldn’t have anything to sell.

The answer is the last choice

Answer:

x>=0, and

y>=0

Step-by-step explanation:

Let

x = pounds of house blend he sells/makes every day

y = pounds of exoted blend he makes/sells every day

constraint for costa rican beans

x/2 + y/4 <= 200 ...............(1)

constraint for Ethiopian beans

x/2 + 3y/4 <=330..................(2)

Total weight per day

x+y <= 200+330 = 530............(3)

common sense constraints, cannot have negative weight for coffee

x>=0, and

y>=0

which geometric solid is formed by rotating the rectangle about line m?

Answers

Answer:

rectangular prism

Step-by-step explanation:

check by rotating the shape in images

I need the answers to B and C please and thank you! :)

Answers

Answer:

2/9 and 4/9

Step-by-step explanation:

There are 3 * 3 = 9 possible outcomes of spinning the spinners. Out of those, there are only 2 ways to achieve a product of 6 (2 and 3 or 6 and 1) so the answer to B is 2/9. For C, there are 4 ways for the total to be greater than 10 (12, 18, 20, 30) so the answer is 4/9.

Answer:

b=2/9

c=4/9

Step-by-step explanation:

b: 2/3(there are two options you can land on that have a pair that multiplies to six)*1/3(each only has one pair)= 2/9

c: 2/3(6 or 4)*2/3(3 or 5) =4/9

What is the y-intercept of the function, represented by the table of values
below?
x
у
-2
16
1
4.
2
0
4
-8
7
-20

Answers

Answer:

8

Step-by-step explanation:

The y-intercept (b) of the function is the point at which the line of the graph of the given values of the table above crosses the y-axis, for which x = 0.

To find the y-intercept of the function represented by the tables, recall the equation of a straight line which is given as:

y = mx + b

Where, m is the slope = (y2 - y1)/(x2 - x1)

b = the y-intercept we are to find

y and x could be any values of a point on the graph which is represented in the table of values.

First, let's find the slope (m):

Let's use any 2 given pairs of the values in the table above.

Using,

(1, 4), (2, 0),

y1 = 4,

y2 = 0

x1 = 1

x2 = 2

m = (0 - 4)/(2 - 1)

m = -4/1 = -4

=>Using, y = mx + b, let's find the y-intercept (b), taking any of the coordinate pairs from the table of values given.

Let's use, (1, 4) as our x and y values.

Thus,

4 = -4(1) + b

4 = -4 + b

Add 4 to both sides to solve for b

4 + 4 = -4 + b + 4

8 = b

y-intercept of the function represented by the table of values = 8

30 POINTS!! Given triangle ABC shown below, which graph shows the transformation (x-2, y+4)?

Answers

Answer:

Its C

Step-by-step explanation:

Answer:

C

Step-by-step explanation:

Take point A at ( 4,-1)

We are shifting down 2 and to the right 4

(4-2, -1+4) becomes ( 2,3)

Choice C has A' at ( 2,3)

At the toy store, you could get 4 board games for $25.84. Online, the price for 5 board games is $32.15. Which place has the highest price for a board game?

Answers

Answer:

The board game store

Step-by-step explanation:

Just divide the store price by 4 and online by 5

Answer:

Toy store

Step-by-step explanation:

Let's find the unit rates for the toy store and the online store. To find the unit rate, divide the price by the number of board games.

price/board games

Toy Store

price/board games

The toy store sells 4 board games for $25.84

$25.84 / 4 board games

25.84/5

6.46

Online Store

price/ board games

The online store sells 5 board games for $32.15

$32.15 / 5 board games

32.15/5

6.43

At the toy store, a board game costs $6.46. Online, it costs $6.43.

6.46 is greater than 5.43, therefore, the toy store has the higher price for a board game.

Type the correct answer in each box. If necessary, use / for the fraction bar. Complete the statements about series A and B. Series A: 10+4+8/5+16/25+32/125+⋯ Series B: 15+3/5+9/5+27/5+81/5+⋯ Series__ has an r value of___where 0<|r|<1. So, we can find the sum of the series. The sum of the series is___ need help guys please :/

Answers

Answer:

Series A has an r value of 2/5 and series A has an r value of 3. The sum of the series A is 50/3

Step-by-step explanation:

A geometric sequence is in the form a, ar, ar², ar³, .  .   .

Where a is the first term and r is the common ratio = [tex]\frac{a_{n+1}}{a_n}[/tex]

For series A:  10+4+8/5+16/25+32/125+⋯   The common ratio r is given as:

[tex]r=\frac{a_{n+1}}{a_n}=\frac{4}{10} =\frac{2}{5}[/tex]

For series B: 1/5+3/5+9/5+27/5+81/5+⋯   The common ratio r is given as:

[tex]r=\frac{a_{n+1}}{a_n}=\frac{3/5}{1/5} =3[/tex]

For series A a = 10, r = 2/5, which mean 0 < r < 1, the sum of the series is given as:

[tex]S_{\infty}=\frac{a}{1-r}=\frac{10}{1-\frac{2}{5} } =\frac{50}{3}[/tex]

what are the like terms??? 5x2+3x-10+7x2-8x+11 PLEASE HELP!!!! ASAP!!!!

Answers

Answer:

5x² and 7x² are like terms because they contain x².

3x and 8x are like terms because they contain x.

10 and 11 are like terms because they are constants.

Step-by-step explanation:

Let's recall that the definition of like terms is that they are terms that contain the same variables raised to the same power and only like terms can be combined.

Upon saying that, we have:

5x² and 7x² are like terms because they contain x²

3x and 8x are like terms because they contain x

10 and 11 are like terms because they are constants.

Simplify the expression.

–6.5(–4.9)

Answers

Answer:

31.85

Step-by-step explanation:

Hey there!

Well to simplify the given expression we do,

-6.5 * -4.9

= 31.85

Hope this helps :)

HELPPPPPPPPPPPPPPPPPPPPPPP

Answers

Answer:

1) A'(8, -10)

B'(10, -8)

C'(2, -4)

2) A''(8, -4)

B''(10, -6)

C''(10, -10)

Step-by-step explanation:

1) For reflection across the line y = -1, given that the lowest point is of ABC which is point C with coordinates (2, 2), we have;

The vertical distance from the point C to the line y = -1 is 3 units down, therefore, the coordinate of the reflection of C will be 3 units below the line y = -1 at C'(2, -4)

The coordinates of the point A(8, 8) will be A'(8, -10)

The coordinate of the point B(10, 6) will be B'(10, -8)

2) Given that we have A'(8, -10), B'(10, -8), and C'(2, -4), we have reflection over y = -7, we have;

The coordinates of the point A'(8, -10) will be A''(8, -4)

The coordinate of the point B'(10, -8) will be B''(10, -6)

The coordinate of the point C'(2, -4)will be C''(10, -10)

Which gives, a total translation of -12 units down as follows;

A''(8, -4) - A(8, 8) = (0, -12)

B(10, 6) - B''(10, -6) = (0, -12)

C(2, 2) - C''(10, -10) = (0, -12).

Plzzzz help me

Consider the function below.
Х
-1
0
1
2
(x)
3
oo
13
N
Which of the following functions could be the inverse of function ?

Answers

Answer:

i think its option b but im not sure

Please help. I will give out brainliest

Answers

Answer:

the table is correct

the graph will look like:

If a cone is 5 meters tall and has a radius of 3 meters, What is its volume? 15π m3 60π m3 45π m3 30π m3

Answers

Answer:

V = 15 pi m^3

Step-by-step explanation:

The volume of a cone is

V = 1/3 pi r^2 h

The radius is 3 and the height is 5

V = 1/3 pi ( 3)^2 *5

V = 15 pi m^3

Answer:

15 pi m3

Step-by-step explanation:

2. Hessa was playing a computer game. She scored 43 points in Round 1 and 26 points in Round 2. Which sum could she use to add the points together? a. 40 + 20 + 3 + 6 b. 4 + 3 + 2 + 6 c. 40 + 30 + 20 + 60 d. 30 + 4 + 60 + 2

Answers

Answer:

a. 40 + 20 + 3 + 6

Step-by-step explanation:

Points scored by Hessa is as shown below;

Round 1 = 43 points

Round 2 = 26 points

Total points for both rounds = 43 + 26 = 69 points

To determine the sum she could use to add the points together, we must select the sum that will give us the same total of points for both rounds i.e 69 points.

The Round 1 score (43 pt)can also be expressed as (40+3) points

The Round 2 score (26 pt)can also be expressed as (20+6) points

The sum she could use to add the points together will be  (40+3)+(20+6)

which is also equal to  40 + 20 + 3 + 6  = 69points

Hence, option a is correct

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