f(x) = x^2. What is g(x)?

The equation of the parabola is y = -x² - 2x + 5

What is a Parabola?

A Parabola, open curve, a conic section produced by the intersection of a right circular cone and a plane parallel to an element of the cone. A parabola is a plane curve generated by a point moving so that its distance from a fixed point is equal to its distance from a fixed line

The equation of the parabola is given by

( x - h )² = 4p ( y - k )

where ( h , k ) is the vertex and ( h , k + p ) is the focus

y is the directrix and y = k - p

The equation of the parabola is also given by the equation

y = ax² + bx + c

where a , b , and c are the three coefficients and the parabola is uniquely identified

Given data ,

The equation of the parabola with the points

A ( -5 , -10 ) , B ( -3 , 2 ) and C ( 2 , -3 )

So , from the equation of parabola ,we get

y = ax² + bx + c

Substituting the values of x and y , in the equation of point A , we get

-10 = a ( -5 )² - 5b + c

-10 = 25a - 5b + c   be equation (1)

Substituting the values of x and y , in the equation of point B , we get

2 = a ( -3 )² - 3b + c

2 = 9a - 3b + c   be equation (2)

Substituting the values of x and y , in the equation of point C , we get

-3 = a ( 2 )² + 2b + c

-3 = 4a + 2b + c   be equation (3)

By the method of brute force , we can solve the equations and derive the equation for the parabola

So , the equation for the parabola will be

y = -x² - 2x + 5

Now , substituting the values of x and y from the points , we get

For point A ( -5, -10 )

-10 = - 25 + 10 + 5

-10 = -10

Therefore , the equation is TRUE

Now , substituting the values of x and y from the points , we get

For point B ( -3, 2 )

2 = -9 + 6 + 5

2 = 2

Therefore , the equation is TRUE

Now , substituting the values of x and y from the points , we get

For point C ( 2 , -3 )

-3 = -4 - 4 + 5

-3 = -3

Therefore , the equation is TRUE

Hence , the equation of the parabola is y = -x² - 2x + 5

To learn more about equation of parabola click :

https://brainly.com/question/24042022

#SPJ1

Answer:

  $7

Step-by-step explanation:

You want to know the cost of each friend's meal if 5 friends spend $41 on their food, which includes a $6 delivery charge.

For 'a' friends spending 'x' on each meal, the total cost is ...

  6 + ax = 41

Solving for x, we have ...

  ax = 41 -6 = 35

  x = 35/a

When the number of friends is a = 5, the cost of a meal is ...

  x = 35/5 = 7

The cost of each friend's mean when the number of friends is 5 is $7.

<95141404393>

The probability percentage the year will have an annual rainfall less than 43 inches is 61.41%.

How to calculate the probability?

Given

μ = 41.4

σ = 5.5

First, we need to find the z score when the rainfall 43 inches. So:

z = (x - μ) / σ

z = (43 - 41.4) / 5.5

z = 0.2909

Then, to find out the probability we need to find P(z < 0.2909) in the z score table. So, we get 0.6141 or in percentage is 61.41%.

Thus, the probability percentage the year will have an annual rainfall less than 43 inches is 61.41%.

Learn more about probability here:

brainly.com/question/29057124

#SPJ4

Answer:

Step-by-step explanation: 0.2

Answer: x=0  y=4

Step-by-step explanation:

6x - 3(2x + 4) = 12

6x - 6x - 12 = 12

0 = 0

therefore, x = 0

substitute x=0 into y = 2x + 4

y = 2(0) + 4 = 4

The G.P. of a term is 256/243.

To find out the G.P. for the 3rd term:

Let us consider the 1st term to be 'a'.

So, [tex]ar^{2}=18[/tex] ....... Equation (1)

Also [tex]ar^{6} = \frac{32}{9}[/tex] .....  Equation (2)

Dividing (2) by (1), we get,

[tex]\frac{ar^{6}}{ar^{2}} = \frac{32}{162}[/tex]

[tex]r^{4}[/tex] = 16/81.

r = 2/3.

Putting r in equation (1) than we will get

a = 81/2.

So, 10th term = [tex]ar^{9}[/tex]

= (81/2) ×(512/19683)

= 256/243.

Hence the answer is the G.P. of a term is 256/243.

To learn more about Probability click here https://brainly.com/question/24756209

#SPJ9

Answer:20

Step-by-step explanation: my man

Answer:

20

Step-by-step explanation:

1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 = 10

+ 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 = 10

= 20

The linear function or equation represents the height of the bamboo h with respect to time t is y = 3x + 12 and the time taken to reach 66 inches is 3 months.

A straight line on the coordinate plane is represented by a linear function.

A linear function always has the same and constant slope.

A linear function is a function that varies linearly with respect to the changing variable.

4.1)

The linear equation is given as y = mx + c

Here, m is the slope while c is the y-intercept.

Given line has a y-intercept of 12.

Slope m = (12 - 24)/(0 - 4) = 3

Thus, h = 3t + 12

4.2)

Time is taken to bamboo to 66 inches tall,

66 = 3t + 12

3t = 54

t = 3 months.

Hence "The linear function or equation represents the height of the bamboo h with respect to time t is y = 3x + 12 and the time taken to reach 66 inches is 3 months".

For more about the linear function,

brainly.com/question/21107621

#SPJ1

(a) Hamburgers sells faster than Wraps ,

(b) The graph of the equations that represents the Hamburgers and Wraps sold are shown below .

In the question ,

it is given that

the rate at which the hamburgers are selling = 160 hamburgers per hour ,

we need to find the rate at which the wraps are selling

From the table ,

we can see that the wraps are sold in an Arithmetic Progression ,

So , at 60 minutes the wraps sold = 2.5 + (n-1)d

= 2.5 + 59×2.5

= 2.5 + 147.5

= 150

So , after one hour , number of wraps sold is 150 and the number of hamburgers sold is 160 .

Similarly , after 2 hours , the number of wraps sold will be 300 and number of hamburgers sold will be 320 .

So, the hamburgers sells faster than wraps .

the slope(steepness)  of the hamburgers = (number of hamburgers sold)/60

= 160/60

= 2.667

the slope(steepness) of the wraps = (number of wraps sold)/60

= 150/60

= 2.5

from the above data , we can see that the steepness of hamburgers is more ,

which means that the hamburgers sells faster than wraps .

the equation that denotes the number of hamburgers sold is y = 2.667x

the equation that denotes the number of wraps sold is y = 2.5x

where x is time in minutes .

The graph that represents the growth rate of hamburger and wraps is shown below .

Therefore , (a) Hamburgers sells faster than Wraps ,

(b) The graph of the equations that represents the Hamburgers and Wraps sold are shown below .

Learn more about Equations here

https://brainly.com/question/15685060

#SPJ1

The formula used in the situation of sending the emails is distributive property of multiplication and simple addition formula

information gotten from the question

you send e-mails to tell your four friends about the school fair

Then those people send e-mails to four more people

From the first statement the number of emails sent is 4

The second statement says that the 4 persons sent to 4 more people hence each person sent one email

The total number of email sent is solved by

= 4 emails sent by you + 1 email sent by each friend * 4 (distributive property)

= 4 emails sent by you + 4  emails sent by friends

= 8 emails

Learn more about equations containing addition:

https://brainly.com/question/29321903

#SPJ1

Answer:

$325

Step-by-step explanation:

t +b = 582

t = b - 68

b - 68 + b = 582

2b = 582 + 68

2b = 650

2/2 b = 650 / 2

b = 325

Answer: 745.31 cm²

Total area of the figure can be obtained by adding area of the semi circle and rectangle.

The radius of the semi circle is given as 12.5cm and it's area is equal to (πr²)/2

I hope you understand It's simple!

The larger bottle will be able to hold a volume of 1372ml

If two solids are similar, then the ratio of their volumes is equal to the cube of the ratio of their corresponding linear measures.

This shows that the ratio of the cube of length of the bottle is equal to the the ratio of their volumes

the length of the smaller bottle = 15, the cube of the length= 15^3= 3375

the length of the larger volume = 21, the cube of the length is 21^3=9261

therefore 3375/9261= 500/x

x is the volume of the larger bottle

therefore x= 500×9261/3375

x= 1372ml.

therefore the volume of the larger bottle is 1372ml

learn more about volume of similar shapes from

https://brainly.com/question/16246860

#SPJ1

Ther right option is that there is not enough evidence to conclude that there is enough association between vaccine location and severe reaction.

Given that,

Children who received the vaccine in the thigh received the first random sample. Children who received the immunization in the arm provided the second random sample.

The chi-square test yields a chi square is 2.0609 with a P value of 0.1511 meaning, the chi square test is not statistically significant.

A,B is therefore out.

C is not also right.

D is what we get when we cannot reject null hypothesis.

Therefore, We cannot conclude that there is dependence.

Learn more about null hypothesis :

brainly.com/question/28920252

#SPJ4

Answer:

Step-by-step explanation:

reciprocal of 51/3 is 3/16

Hi you need to change 5 1/3 from mixed number to improper fraction 51/3=(5x3)+1  /3 =16/3

The  reciprocal   of 16/3 is 3/16

The solution for the intersection point of a triangle is given below.

A triangle is a geometric figure with three edges, three angles and three vertices. It is a basic figure in geometry.

The sum of angle of a triangle is always 180°

Perpendicular bisectors of the sides is circum center.

The bisector of angles of a triangle is in center.

Intersection point of medians is centroid

The intersection point of altitudes is ortho center.

To know more about Triangle on :

https://brainly.com/question/2773823

#SPJ1

Answer:

B. 700+200

Step-by-step explanation:

691+208=899

A. 600+200=700

B.700+200=900

C.700+300=1000

D.900+200=1100

B is closest to 899

Answer:

700+200

Step-by-step explanation:

we round these numbers to the closest hundreds by looking at the tenth place

5 or more we round up

4 or less we let it rest and round down

691 since it is 9 in the tenths place we round up to 700

208 since the tenths place is 0 we round down to get 200

700+200 is the answer hopes this helps please mark brainliest

The particle will move to the right for t > a .

In the question ,

it is given that ,

a particle moves along the x axis , such that at any time t ≥ 0 ,

its position is given by the equation

x(t) = 12(a−t)²  ,

where a is = positive constant

to find value of the particle moves right ,

we differentiate x(t) , with respect to "x" .

x'(t) = 12×2(a - t)×(-1)

v(t) = -24(a-t)        ..... because x'(t) = v(t)

for particle to move right , v(t) > 0 .

-24(a-t) > 0

dividing both sides by "-24" , we get

a - t < 0

a < t

t > a .

Therefore , The particle will move to the right for t > a .

The given question is incomplete , the complete question is

A particle moves along the x-axis so that at any time t ≥ 0 its position is given by x(t)=12(a−t)² , where a is a positive constant. For what values of t is the particle moving to the right ?  

Learn more about Derivative here

https://brainly.com/question/18800858

#SPJ4

Answer:B= 7/9 C=10/9 A=0.62

Step-by-step explanation:

i know this because i multiplyed by 1/3 by 3 to get 3/9 6/9 9/9 for the number line

Answer:

a) x=5

b) x=4

Step-by-step explanation:

4x-3=2x+7

-2x.  -2x

2x-3=7

   +3. +3

2x=10

x=5

2x+6=7x-14

-2x.   -2x

6=5x-14

+14. +14

20=5x

/5. /5

4=x

Hopes this helps please mark brainliest

Answer: x = -2/3 , 1

Step-by-step explanation:

step 1 (hardest step!) factor by grouping:

(3x + 2)(x-1) = 0

the rest is easy:

3x + 2 = 0  or (x-1) = 0

Solve each for x:

3x + 2 = 0

x = -2/3

x-1 = 0

x = 1

So your 2 solutions for x are -2/3 and 1

a. The value of 9.9² × 1.79 is 175.44.

b. The value of ✓97.5 + 1.96 is 11.83

An exponent is the number of times that a number is multiplied by itself. It should be noted that the power is an expression which shows the multiplication for the same number. For example, in 6⁴ , 4 is the exponent and 6⁴ is called 6 raise to the power of 4.

In this case, the value of 9.9² × 1.79 will be:

= 9.9² × 1.79

= 98.01 × 1.79

= 175.44

The value of ✓97.5 + 1.96 will be:

= ✓97.5 + 1.96

= 9.87 + 1.96

= 11.83

Learn more about exponents on:

brainly.com/question/13669161

#SPJ1

sin y =12/13 but can't find cos x as sin x can't exceed from 1.

It can be solved by using identities of trigonometry.

What are the  trigonometric identities?

These are the equivalent ways to define trigonometric functions.

Basic identities are:

sin²x + cos²x = 1

1 + tan²x = sec²x

1 + cot²x = cosec²x

For cos x:
cos²x = 1 - sin²x

          = 1 - (5/3)²

          = 1- (25/9)

          = -16/9

i.e. not possible

For sin y:

sin²y = 1 - cos²y

         = 1 - (5/13)²

         = 1 - 25/169

         = 144/169

So, sin y = ±(12/13)

but as mentioned x and y are in 1st quadrant ,

so, sin y = 12/13.

Learn more about trigonometric identities from the given link:

https://brainly.com/question/24496175

#SPJ1

The equation  that can be used to find the number of hotdogs

and sodas sold at the swim meet.

a)x+0.50y=150

b)  y=-2x+300

c)Number of soda sold y =220 if hot dog is 40.

d)  x intercept=150. It is related to the total earnings of soda and hot dogs sold.

f) y intercept = 300 . It is related to the 2 times of the total earnings of soda and hot dogs sold.

What is x-intercept and y-intercept?

An equation's or a function's graph that contacts the x axis is said to have a "X intercept." This is comparable to a point having a value of zero. Given that it is located on the horizontal axis, this is sometimes referred to as the horizontal intercept. The y value at the point where the line meets the y axis is known as the y intercept. By examining the graph and identifying the point that crosses the y axis, we may determine the y intercept. This point's x coordinate will always be 0. It will be recorded as (0,y). Given that it is on the vertical axis, this is also referred to as a vertical intercept.

Let us take number of hot dogs sold as x and number of soda sold as y.

Cost of one hot dog = $1.00

Cost of one soda = $0.50

Then , cost of x number of hot dogs sold = 1x

cost of y number of soda sold = 0.50y

Then, . At the end of the day you made $150.

=> 1x+0.50y= 150

a) standard form of the equation is ,

=> x+0.50y=150 ------->1

b) x+0.50y=150

=> x+[tex]\frac{1}{2}[/tex]y=150

=>2x+y=150*2

=>2x+y=300

Then slope intercept form is  y=-2x+300------->2

c) Number of hot dogs sold x=40 and put into 2 ,

then ,  y=-2(40)+300

=> y=-80+300

=>y=220

Number of soda sold y =220

d) To find x intercept put y=0 into 1 , then

=> x+0=150

=>x=150

Here x intercept=150. It is related to the total earnings of soda and hot dogs sold.

e)To find y intercept put x=0 into 1,

=> 0+0.50y=150

=> y = 150/0.50

=> y =300

Here y intercept = 300 . It is related to the 2 times of the total earnings of soda and hot dogs sold.

To learn more about x-intercept and y-intercept refer the below link

https://brainly.com/question/18176433

#SPJ1

Answer: -2

Step-by-step explanation:

since g(x) is a function, x needs to be 0 in order to find the y-intercept. so we plug in 0 to the function. -|0+6|+4=-2 so the y-intercept is -2

The length of side x is 6cm

We need to find the scale factor of the shapes below are mathematically similar.

it can be found using the two bases given.

The base of the smaller triangle is 9  and that of large triangle is 12

9/12 = 3/4

The smaller triangle is 3/4 of the larger one.

Multiply the known side by 3/4

X = 8 x 3/4 = 6

X= 6

Therefore, the length of side x is 6cm

To learn more about scale factor refer here

https://brainly.com/question/15891755

#SPJ1

Answer:

12 ; 13 ; 14

Step-by-step explanation:

x = sister one

x+ 1 = sister two

x+2 = sister three

2x + 3(x+2) = 4(x+1) + 14

2x + 3x + 6 = 4x + 4 + 14

5x + 6 = 4x + 18

5x - 4x = 18 - 6

x = 12 (sister one)

12 + 1 = 13 (sister two)

12 + 2 = 14 (sister three)

The rates that are equivalent to the rate Rosario paid are $0.80 for 1 pound, $7.50 for 9 pounds, and $10.00 for 12 pounds​.

What are the rates?

A rate is a unique ratio where the two words are expressed in several units.

Rate formula

r = d/t

Here, we calculate different rates

a. Per pound price of apples = Total cost / total weights of apples

                                             = 0.80 / 1 = $0.80

Cost of 3 pounds of apples = 3 × 0.80 = $2.4

b. Per pound cost of apples = Total cost / total weights of apples

                                               = 14.50 / 5  = $2.9

Cost of 3 pounds of apples = 3 × 2.9 = $8.7

c. Per pound cost of apples = Total cost / total weights of apples

                                               = 7.50 / 9 = $0.833

Cost of 3 pounds of apples = 3 × 0.833 = $2.49

d. Per pound cost of apples = Total cost / total weights of apples

                                              = 9.60 / 11 = $0.872

Cost of 3 pounds of apples = 3 × 0.872 = $2.61

e. Per pound cost of apples = Total cost / total weights of apples

                                               = 10 / 12 = $0.833

Cost of 3 pounds of apples = 3 × 0.833 = $2.49

Hence, The rates that are equivalent to the rate Rosario paid are $0.80 for 1 pound, $7.50 for 9 pounds, and $10.00 for 12 pounds​.

To learn more about the rates from the given link

https://brainly.com/question/11209700

#SPJ1