If the maximum value of y =-x²+ax+b is 8 when x = 3, find the values of a and b​

Answers

Answer 1

Answer:

a = 6 and b = -1.

Step-by-step explanation:

To find the maximum value of y = -x²+ ax + b we differentiate it with respect to x to find the value of x at which it is maximum.

So dy/dx = d(-x²+ ax + b)/dx = -2x + a

we equate it to zero.

-2x + a = 0

-2x = -a

a = 2x

Now, given that x = 3 at the maximum value,

a = 2x = 2(3) = 6

Also, substituting y = 8 and x = 3 into y, we have

y = -x²+ ax + b

8 = -(3)²+ a(3) + b

8 = -9 + 3a + b

3a + b = 8 + 9

3a + b = 17

So, b = 17 - 3a

substituting a = 6, we have

b = 17 - 3(6)

b = 17 - 18

b = -1

So, a = 6 and b = -1.


Related Questions

⚠️HELP⚠️MY HW IS DUE IN 10 MINS
A water tank is being filled with water. Before water is pumped in, the water level in the tank is 11 inches high. After 20 minutes, the water level is 56 inches high.

If "t" represents the time in minutes, and "h" represents the water level, which of the following equations can be used to model this situation?

A. h=2.25t + 11
B. h=2.25t - 11
C. h=11t + 2.25
D. h=45 + 11t​

Answers

Answer:

Step-by-step explanation:

so coz there was already 11 inches but after 20min the tank is 56inch so wht u do is this

45+11t if im right

Find the slope of the line that passes through the two points below.
(3,6) and (10,4)

Answers

Answer:

Slope: -2/7

Step-by-step explanation:

Slope is change in y over change in x.

(4-6)/(10-3)

= -2/7

Solve The Equation
1/7 (63n - 77) = -11 + 9n
A. No Solution
B. n = 0
C. Infinite Solutions
D. n = 11/9
E. n = -11/9

Answers

Answer:

C. Infinite Solutions

Step-by-step explanation:

In order to solve this we fist have to simplify the equation so we do the following:

[tex]\frac{1}{7}(63n -77) = -11 + 9n\\\\(\frac{1}{7})(7)(63n - 77) = (7)(-11 + 9n) \\\\63n - 77 = -77 + 63n\\63n - 77 = 63n - 77[/tex]

From here we know that any value of n is the solution of this equation so the answer is option C.

For the expression StartFraction 15 x cubed + 25 x squared + 5 x + 2 Over (5 x squared + 1) squared EndFraction, which sum represents the correct form of the partial fraction decomposition?

Answers

Answer:

StartFraction 15 x cubed + 25 x squared + 5 x + 2 Over (5 x squared + 1) squared EndFraction, can be written in mathematical form as

Let y = [tex]\frac{15 x^3 + 25x^2 +5x+2}{({5x^2+1})^2}[/tex]

on  expanding [tex]{({5x^2+1})^2 = 25x^4 +1 + 10x^2[/tex]

⇒ y = [tex]\frac{15 x^3 + 25x^2 +5x+2}{25x^4 +1 + 10x^2}[/tex]  

there correct form of partial fraction is [tex]\frac{15 x^3 + 25x^2 +5x+2}{25x^4 +1 + 10x^2}[/tex]  

Answer:

Option-B

Step-by-step explanation:

edge

(4 + 2/9) =(6 + 1/3)b

Answers

Step-by-step explanation:

(4 + [tex]\frac{2}{9}[/tex] ) = (6 + [tex]\frac{1}{3}[/tex] ) b       Original equation

4 + [tex]\frac{2}{9}[/tex] = 6b + [tex]\frac{1}{3}[/tex]b            Distributive property

4 [tex]\frac{2}{9}[/tex] = 6[tex]\frac{1}{3}[/tex] b                     Simplification

[tex]\frac{38}{9}[/tex] = [tex]\frac{19}{3}[/tex]b                        Extra simplification

[tex]\frac{38}{9}[/tex] × [tex]\frac{3}{19}[/tex] = [tex]\frac{19}{3}[/tex]b × [tex]\frac{3}{19}[/tex]          Isolating the variable

[tex]\frac{2}{3}[/tex] = b                            Your answer

I hope this helps!!!

( do not answer if you do not know, I need urgent, I will report if answer is wrong and I will give brainiest )


How much vanilla extract will be needed to make 2 frozen cookies? Show your work.


If you only want to make 9 cookies ( 0.75 of a dozen ) how much quick cooking oats do you need?


How many cups of flour would you need to make 3 dozen cookies?

Answers

Answer:

2 teaspoons for the two frozen cookies

3/4 a cup for the cooking oats

2 cups for the flour

Step-by-step explanation:

First Question

The recipe makes 18 cookies. Divide the cookies by 9, half of the batch, to get 2. Now all you have to do is devide the amount of vanilla extract by 9, it will give you two teaspoons.

Second Question

1 and 1/2 devided by two since you're devidng the recpie by two to get 9 cookies. A cup is four so 3/4 plus 3/4 equals 6/4. Simplified it'd be 1 and 1/2 or 1 and 2/4.

Third Question

The recipe already calls for 1 and 1/2 a dozen. All you're doing is multiplying the recipe b two to get 3 dozen cookies. Now focusing our attention to the flour, there is 1 cup for 1 and 1/2. Multiply 1 by 2 since there is already half of the recipe here. 1 and 1/2 + 1 and 1/2 is 3 so there'd be 2 cups. Basically just double the recipe.

Answer:

3/4 but if its in decimal form then 0.75

Step-by-step explanation:


Aldrine is buying coffee for his coworkers. He orders small and large coffees. Small coffees
cost $3 and large coffees cost $5. He spent $30 and ordered eight cups of coffee in total.
Write a system of equations that represents the situation
How many of each coffee did he buy? How do you know?

Answers

Let small cups = S

Large cups = L

They bought a total of 8 cups, so S + L = 8

Rewrite as S = 8-L (1st equation)

Then you also have

$3S + $5L = $30 (2nd equation)

Replace the S in the second equation with the first equation:

$3(8-L) + $5L = $30

Simplify:

24 - 3L + 5L = 30

Combine like terms:

24+2L = 30

Subtract 24 from both sides:

2L = 6

Divide both sides by 2:

L = 3

They bought 3 large cups

Since they bought a total of 8 cups, that means they bought 5 small cups ( 8-3=5)

Large = 3 cups, Small = 5 cups

If point A(4, -10) is translated to A'(2 ,-4), what was the translation? Please represent algebraically

Answers

Answer:

b

Step-by-step explanation:

Answer:

A translation by 2 units to the left and 6 units up.

Step-by-step explanation:

HELP WILL MARK BRAINLIEST PLEASE ANSWER ALL THREE

Answers

Step-by-step explanation:

8. ∠COB and ∠AOD are vertical angles or C

9. Vertical angles are equivalent to each other so 4x-16 = 112°

4x - 16 = 112°

4x - 16 + 16 = 112 + 16

4x = 128

4x/4 = 128/4

x= 32° or D

10. ∠AOC is vertical to ∠DOB therefore the 2 angles are congruent

You can do 360 - (112 + 112) = 2AOC

360 - 224 = 2AOC

136 = 2AOC

AOC = 68°or A

OR

You could just do 180 -112

Since ∠AOD and ∠AOC are supplementary angles, they both add up to 180°

We already know the measure of ∠AOD, it's 112°

So all you would need to do is subtract 112 from 180

And you get 68° or A

I REALLY hope this helps!!!

-4=2/3x solve the equation for the value of the variable show all work please please solve this problem and thanks:)

Answers

Step-by-step explanation:

-4=2/3x

-4/1=2/3x

cross multipy,

-4 × 3x = 2 × 1

-12x = 2

x=-2/12

x=-1/6

At a grocery store you can purchase loose lemons at 2 for $0.99. You can also buy a bag of 6 lemons for $2.50. Which is the better buy? Be sure to show the unit cost for each

Answers

Answer:

Bag of lemon

Step-by-step explanation:

Given that:

Cost of loose lemon = $0.99 for 2

Cost of bag of lemon = $2.50 for 6

Calculating the cost per 1 for loose and bag of lemon (unit cost) ;

Loose lemon :

$0.99 /2 = $0.495

Bagged lemon :

$2.50 / 6 = $0.4167

Hence, since the unit cost of bagged lemon is lesser than loose lemon, then purchasing a bag of lemon is better

ASAP Analyze the Error: What is the error in the way the calculation of the slope of the two points is set up and/or solved? Please be specific.

Answers

Answer/Step-by-step explanation:

Given two points on a line, (-4, 10) and (0, 2), the slope of the line is calculated as follows:

[tex] slope (m) = \frac{y_2 - y_1}{x_2 - x_1} [/tex]

Let,

[tex] (-4, 10) = (x_1, y_1) [/tex]

[tex] (0, 2) = (x_2, y_2) [/tex]

Plug in the values

[tex] slope (m) = \frac{2 - 10}{0 - (-4)} [/tex]

[tex] slope (m) = \frac{-8}{4} = -2 [/tex]

Slope = -2

The wrong formula was used. Slope is supposed to be change in y over change in x. Rather the difference of each coordinates was solved and divided by each other, which makes the whole calculation wrong.

Object A has 50 kg while Object B has 75 kg. They were pushed with the same amount of force. Which will have greater acceleration

Answers

Answer:

Object A will have greater acceleration.

Step-by-step explanation:

Given that,

The mass of object A = 50 kg

The mass of object B = 75 kg

They were pushed with the same amount of force.

We know that, the force acting on an object is given by :

F = ma

Here F is same for both mass

[tex]m_1a_1=m_2a_2[/tex]

Mass and acceleration have inverse relation. It means the object whose mass is less will have greater acceleration. Hence, the acceleration is greater for object A.

Help me quickly just give the answer

Answers

Answer: your answer might be 2

HOPE THIS HELPS IF NOT THEN SORRY

BRAINLIEST IF U ANSWER!!! BTW I WILL BE CHECKING IF THE ANSWER IS CORRECT ONLY IF ITS CORRECT BRIANLIEST ANSWER WITHIN 30 MINS!!! The value of a baseball​ player's rookie card began to increase once the player retired. When he retired in 2000 his card was worth ​$4.23 The value has increased by ​$2.92 each year since then. Express the relationship relating the value of the card y in dollars and the number of years x the player has been in retirement with an equation. Is the relationship between x and y​ proportional? What was the value of the card in 2010 ​?

Answers

Answer:

Relationship: [tex]y =2.92x+4.23[/tex]

They are not proportional

The value is $33.43

Step-by-step explanation:

Given:

[tex]x = years[/tex]

[tex]y = amount[/tex]

When he retired, the expression is:

[tex](x_1,y_1) = (0,4.23)[/tex]

and the rate (m) is:

[tex]m = 2.92[/tex]

Solving (a): The relationship between y and x

This can be solved using the following point-slope formula:

[tex]y - y_1=m(x-x_1)[/tex]

Substitute values for x1, y1 and m

[tex]y - 4.23=2.92(x-0)[/tex]

[tex]y - 4.23=2.92(x)[/tex]

Make y the subject

[tex]y =2.92(x)+4.23[/tex]

[tex]y =2.92x+4.23[/tex]

Solving (b): Are they proportional?

No, they are not

A proportional relationship is expressed as:

[tex]y = mx[/tex]

By comparing this to [tex]y =2.92x+4.23[/tex]; they have different format

Solving (c): Value in 2010?

First, we determine the value of x in 2010

2000; x = 0

2001; x = 1

---

--

-

2010; x = 10

Substitute 10 for x in [tex]y =2.92x+4.23[/tex]

[tex]y = 2.92*10+4.23[/tex]

[tex]y = 29.2+4.23[/tex]

[tex]y = 33.43[/tex]

STOP PUTTING WRONG ANSWERS

Answers

Answer:

why did you put this as a question?  you seriously could have just saved some points and commented it on a question you know

Step-by-step explanation:

Kierra drew a line that is 3 times four-sevenths inches long. Which fraction represents the same length?

Four-sevenths inches
Seven-sevenths inches
Twelve-sevenths inches
StartFraction 25 over 7 EndFraction inches

Answers

Answer: [tex]\frac{12}{7}[/tex] inches

Step-by-step explanation:

3 × [tex]\frac{4}{7}[/tex]

= [tex]\frac{3 x 4}{1 x 7}[/tex]

= [tex]\frac{12}{7}[/tex]

= 1[tex]\frac{5}{7}[/tex]

Will give brainliest!!! The MTC Theater holds 250 people, and last night’s performance sold out! Students under the age of 16 paid $2.50 per ticket, while everyone else paid $4.00 per ticket. Last night’s show brought in $910.
Write a system to represent the given equations.

How many adult tickets were sold?

How many under the age of 16 tickets sold

Answers

Answer:

Student's tickets: 60

Adult's tickets: 190

I think this is right

Step-by-step explanation:

"Let x represent the number of tickets sold to students under the age of 16. Let y represent those over the age of 16.

Equation 1, number of tickets sold:

The total number of tickets sold to students under the age of 16 plus the number of tickets sold to students over 16 must equal 250 (since the theater was sold out). The equation becomes:

x + y = 250

Equation 2, revenue from tickets sold.

The total revenue was $910. The cost of tickets under 16 is $2.50 and the cost of tickets over 16 is $4.00. The equation becomes:

2.50 * x + 4.00 * y = 910.00

The system of equations to solve is:

         x  +  y = 250

2.50 * x +  4.00 * y = 910.00 "

How much is 1232323 divided by 232 x 3
This sounds crazy but its on my test..
Ly.
100 poins

Answers

ANSWER -

1232323 ÷ 232 x 3 = 15935.2112069

It is cray cray lol.

Plz give brainliest I would rlly appreciate it :)

1232323 / (232 x 3)

1232323 / 696

= 1770.57902 times

Or is approx 1771 times

Evaluate this expression if r = 2, t = -7, and u = -5
3(r+u)

Answers

Answer:

the answer is -9

Step-by-step explanation:

3(2 - 5)

6 - 15

-9

Answer:[tex]\boxed{-9}[/tex]Solution Steps:

______________________________

1.) Fill in the given variables into a new equation: [tex]r=2[/tex][tex]t=-7[/tex][tex]u=-5[/tex][tex]3(2+(-5))[/tex]

 - We do this since it gives us the missing variables, which makes it so we can solve it like any regular equation.

Equation at the end of Step 1:

[tex]3(2+(-5))[/tex]2.) Subtract 5 from 2:[tex]2-5=-3[/tex]

 - We do this because we need 1 number, not 2 at the end.

Equation at the end of Step 2:

[tex]3(-3)[/tex]3.) Multiply 3 and −3:[tex]3[/tex] × [tex]-3=-9[/tex]

______________________________

Simplify 2y-6x+5+4y
What is the answer?

Answers

Answer:

Answer = −6x+6y+5

help plissssssssssssssssssssss​

Answers

Answer:

......can u tranlate it?

What’s the translation??

1,5,25,61.....
What's following number? ​

Answers

Given:

1,5,25,61.....

To find:

The following number.

Solution:

We can see a pattern in the given sequence.

[tex](-1)^2+(0)^2=1+0=1[/tex]

[tex](1)^2+(2)^2=1+4=5[/tex]

[tex](3)^2+(4)^2=9+16=25[/tex]

[tex](5)^2+(6)^2=25+36=61[/tex]

Using this pattern the next term is the sum of squares of 7 and 8.

[tex](7)^2+(8)^2=49+64=113[/tex]

Therefore, the next number is 113.

Are y=-9 and y=-9x parallel perpendicular or neither? Explain your answer in one sentence.

Answers

Answer:

y=−3

Step-by-step explanation:

The radius of a circle is 3 millimeters. What is the circle's area? Use 3.14 for ​.

Answers

Answer:

Area =9π

Step-by-step explanation:

A=π times r^2

Substitite 3 in for r and get 3^2=9 then multiply by π to get 9π as your answer

Can someone help me please?? You buy 3 pairs of jeans for $35.95 each and get a fourth pair for free. What is your cost per pair of jeans?

Answers

Answer:

3x35.96= $107.88

If you get a 4th one for free

107.88/4 = $26.97 each

Step-by-step explanation:

Sarah took the advertising department from her company on a round trip to meet with a potential client. Including Sarah, a total of 10 people took the trip. She was able to purchase coach tickets for ​$320 and first-class tickets for ​$960. She used her total budget for airfare for the​ trip, which was ​$4480. How many first-class tickets did she​ buy? How many coach tickets did she​ buy?

Answers

Answer:

she bought 8 coach, 2 first-class

Step-by-step explanation:

let x = number of coach tickets

equation I used:  320x + 960(10 - x) = 4480

                            320x + 9600 - 960x = 4480

                            -640x = -5120

                             x = 8

here’s the answer in the photo down below

Solve the compound inequality: n+1<=-3 or -4n<-8

Answers

Answer:

-4n<-8 the answer for this is (n>2)

n+1<=-3 the answer for this is (n<=-4)

The value of n is less than equal to negative 4 and greater than 2. n ≤ –4 and n > 2.

What is inequality?

Inequality is defined as an equation that does not contain an equal sign. Inequality is a term that describes a statement's relative size and can be used to compare these two claims.

The inequalities are given below.

n + 1 ≤ –3  …1

–4n < –8   …2

On solving equation 1, we have

n + 1 ≤ –3

     n ≤ –4

On solving equation 2, we have

–4n < –8

    n > 2

More about the inequality link is given below.

https://brainly.com/question/19491153

#SPJ2

15 = 5/ 3(x + 12) solve for x in simplest form

Answers

Answer:

x= -10 1/5 or -10.2

Step-by-step explanation:

11. Find the sum of all prime numbers between 50
and 60.
A. 109
B. 110 -0. 112 D. 122​

Answers

Answer:

[tex]C.112[/tex]

Step-by-step explanation:

[tex]First,\\Lets\ list\ out\ all\ the\ primes\ between\ 50\ and\ 60:\\53,59\\Hence,\\By\ adding\ them\ we\ get:\\53+59\\=112[/tex]

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