The minimum/maximum value of the function y = a(x − 2)(x − 1) occurs at x = d, what is the value of d?

Answers

Answer 1

Answer:

[tex]d=\frac{3}{2}=1.5[/tex]

Step-by-step explanation:

We have the function:

[tex]y=a(x-2)(x-1)[/tex]

And we want to find x=d for which the minimum/maximum value will occur.

Notice that our function is a quadratic in factored form.

Remember that the minimum/maximum value always occurs at the vertex point.

And remember that the x-coordinate of the vertex is the axis of symmetry.

Since a quadratic is always symmetrical on both sides of its axis of symmetry, a quadratic’s axis of symmetry is the average of the two roots/zeros of the quadratic.

Therefore, the value x=d such that it produces the minimum/maximum value is the average of the two roots.

Our factors are (x-2) and (x-1).

Therefore, our roots/zeros are x=1, 2.

So, the average of them are:

[tex]d=\frac{1+2}{2}=3/2=1.5[/tex]

Therefore, regardless of the value of a, the minimum/maximum value will occur at x=d=1.5.

Alternative Method:

Of course, we can also expand to confirm our answer. So:

[tex]y=a(x^2-2x-x+2)\\y=a(x^2-3x+2)\\y=ax^2-3ax+2a[/tex]

The x-coordinate of the vertex is still going to be the place where the minimum/maximum is going to occur.

And the formula for the vertex is:

[tex]x=-\frac{b}{2a}[/tex]

So, we will substitute -3a for b and a for a. This yields:

[tex]x=-\frac{-3a}{2a}=\frac{3}{2}=1.5[/tex]

Confirming our answer.


Related Questions

Mei has 60 milliliters of a solution that is​ 35% nitric acid. How many milliliters of nitric acid does the solution​ contain?
(answer this and show your work please)
The solution contains _answer here_ milliliters of nitric acid.

Answers

Answer:

21ml

Step-by-step explanation:

60ml. 35% acid. What is 35% of 60 ml?

÷10 to find 10%

60÷10=6

6=10%

But this is no use

because you cannot multiply 10%to get 35%

(35% is not a multiple of 10)

So we try...

10%÷2=5%

So ÷2 to find 5%

6÷2=3

So 3=5%

5%x7=35%

So, we do

3x7=21

So 35%=21

Answer:

21ml

Step-by-step explanation:

It took 48 minutes to drive downtown. An app estimated it would be less than that. If the error was 20%, what was the app’s estimate? Give detailed steps and explanation.

Answers

Pretty sure that the answer is 57 minutes and 10 seconds.

Answer:

38.4 minutes

Hope this helps!!!

Which of the linear equations represents the graphed line?

A: y=3/2x+1


B: y=2/3x+1


C: y=-2/3x+1


D: y=-3/2x+1

Answers

B is the correct answer

Answer:

the answer is A, y = 3/2x + 1

Step-by-step explanation:

PLEASE HELP ME. THIS IS DUE TODAY
The table shows the relationship between X and Y.

X | Y

3 | 163.5

6 | 327

11 | 599.5


Which equation models this relationship?

A. y = 53x

B. y = 53.5x

C. y = 54x

D. y = 54.5x


PLEASE ANSWER I NEED THIS THE ANSWER NOW

Answers

Answer: C. y = 54x



Explanation:

Hope this helps you :)

An equation which models the relationship between X and Y is

y = 54.5x

The correct answer is option (D) y = 54.5x

What is equation?

"A mathematical statement which contains an equal symbol between two algebraic expressions that have the same value."

From given data we can observe that,

163.5/3 = 54.5                           ...................(1)

327/6 = 54.5                              ...................(2)

599.5/11 = 54.5                          ...................(3)

From (1), (2) and (3),

y/x = 54.5

y = (54.5)x

Therefore, an equation which models the relationship between X and Y is y = 54.5x

The correct answer is option (D).

Learn more about relationship between variables here:

https://brainly.com/question/17248931

#SPJ2

"Three times a number increased by eleven is seventeen" translates to which of the following equations?

11x + 3 = 17
11x - 3 = 17
3x + 11 = 17
3x - 11 = 17

Answers

3x + 11 = 17 i think
3x + 11 = 17 is the answer.

Which of the following equations is equivalent to 3(a + 4) – 5(a – 2) = 22?
-2a + 2 = 22
8a + 2 = 22
8a + 22 = 22
-2a + 22 = 22

Answers

-2a+2=22

3(a+4)-5(a-2)=22
3a+12-5a-10=22
-2a+12-10=22
-2a+2=22

Create a simple equation that has infinite solutions, and a simple equation that has no solutions

Answers

Answer:

-9m - 4 = -9m - 4 and one that doesn't have any solution is -4 + 2b = 2b - 9

Step-by-step explanation:

100 ÷ 33.33333333333333♾

ANSWER ASAP PLZZ!!!!

What type of roots would you expect plants to have in the desert?

Answers

Answer:

Phreatophytes, like the mesquite tree, have adapted to desert conditions by developing extremely long root systems to draw water from deep underground near the water table.

Step-by-step explanation:

The mesquite's roots are considered the longest of any desert plant and have been recorded as long as 80 feet.

Answer:

Long roots for desert plants look similar to other roots, only more lengthy. The roots spread out from the base of the plant deep into the earth. Typically, the roots are larger than regular thread roots so that they absorb more water.

Step-by-step explanation:

hope it helps ^-^

PLEASE ANSWER THIS FAST WILL MARK BRAINLIEST AND 15 POINTS

Barry simplified 5x – 3y – x + 6z, as shown.

5x – 3y – x + 6z

5x – x – 3y + 6z

5 + 3yz

Describe two mistakes Barry made, and find the correct solution.
__________________________________________________

Answers

Answer:

Step-by-step explanation:

we have that

5x – 3y – x + 6z

5x – x – 3y + 6z------> this step is correct

5 + 3yz------> is not correct

because

1) 5x-x=5---> is not correct

the correct is

5x-x=4x

2) -3y+6z=3yz-----> is not correct

the correct is

-3y+6z=3*(2z-y)

therefore ,

the correct solution is

4x+3*(2z-y)

HELPPPPPPPPPPPPPPPPPPPPPPPPPPPPPPPPPPPPPPPPPPPPPPPPPPPPPPPPPPPPPPPP PLEASE

Answers

Answer:

use formula

area = 1/2 *Height *(side 1 + side 2)

Answer:

use the equation of area of parallelogram = height ×base

A charity organization had to sell a few tickets to their fundraiser just to cover necessary production costs. After selling 101010 tickets, they were still at a net loss of \$800$800dollar sign, 800 (due to the production costs). They sold each ticket for \$70$70dollar sign, 70.

Answers

Answer:

Price of each ticket = $70

The revenue generated from sales of 10 tickets = 70 x 10 = $700

After selling the 10 tickets, organization was still at loss of $800. This means total product cost of tickets = $800 + $700 = $ 1500

Net Profit = Revenue - Cost

Revenue from n tickets will be = 70n

Cost = $1500

So, net profit as a function of number of tickets sold = P(n) = 70n - 1500

Step-by-step explanation:

X + 3(12 X 3y)-35+59Z

Answers

Answer x + 108y - 35 + 59z

A bicyclist goes 43.54 miles in 3.5 hours. What is her speed??
PLEASE EXPLAIN WHY!!!!!

Answers

So your answer would be 12.44 because to find speed you need to take her overall miles she traveled and divide it by 3.5 which was how long it took her and that would give you her speed. HOPE THAT HELP!
Divide 43.54 by 3.5
She was going 12.33 miles an hour

When two factors have opposite signs, is the product negative or positive??

Answers

Answer:

Negative

Step-by-step explanation:

If two signs differ the answer will always be negative. but if they are the same then the answer would be positive. Hope this helped!

Answer:

Negative

Hope this helped :)

Find the quotient. Your answer should be in simplest form.
2 and one eighth divided by 34



A. start fraction 51 over 32 end fraction

B. The fraction is 1 over 16.

C. two and one-third

D. two and five-sixths

Answers

[tex]2[/tex][tex]1/8[/tex] ÷ [tex]34= 0.0625=1/16[/tex]

B.

[tex]Goesy[/tex]

The answer is B. “The fraction is 1 over 16”

PLEASE HELPPPPPPPPPPPPPPPPPPP

Answers

Answer:the answer is D

Step-by-step explanation:

The answer is D
Your welcome

there are 200 freshmen in a high school. 30% of them take history. how many freshmen are enrolled in Spanish?

Answers

pretty sure it’s 140

Every person has a unique tongue print like finger prints

Answers

Answer:

is this a question? but yes that is most likely true.

Step-by-step explanation:

explanation? uh my brain? :'>

I need help with this ASAP!!!

Answers

Answer:

5.-2<x  

3.x-2 <0

2. 2<x

1.x<-2

4.x>2

Step-by-step explanation:

i think it could be sum else

Answer:

Step-by-step explanation:

-2x

answer plzzzzzzzzzzzzzzzz

Answers

Answer:

which one, or all of them?

Step-by-step explanation:

The ratio of the number of girls to the number of boys in choir is 4 to 5. There are 32 girls in the choir. How many boys are in the choir?

Answers

Answer:

what grade is this

Step-by-step explanation:

8. 32/4 is 8. 1/5 is boys, so no need to multiply. (answer is 8)

(03.04 MC) EXPLAIN!!!
Solve for x:
(-3/2)x - 9 = -27

Select one:
a. −24
b. −12
c. 11
d. 12

Answers

This is what the equation looks like: [tex]\frac{-3}{2}x - 9 = -27[/tex]

First, we transpose the terms to the other side. So after transposing [tex]-9[/tex], you get: [tex]\frac{-3}{2}x = -27 + 9[/tex]

Add them and you get: [tex]\frac{-3}{2}x = -18[/tex]

Next we transpose the coefficient of [tex]x[/tex] which is [tex]\frac{-3}{2}[/tex] to the other side, and while doing so the operation changes to a division. When dividing rational numbers, you take the reciprocal so you get: [tex]x = -18 * \frac{-2}{3}[/tex]

Multiply them and you get: [tex]x = 12[/tex]

Therefore, Option D is the correct answer :D

please help me i need two answers

Answers

its the first one and the last one

Answer:

-7 3/4x-7(3)

7(-3/4x)-7(3)

Step-by-step explanation:

can you guys do this and show work so i can copy it? ill give you brainliest and point :

Answers

Don’t mind the mistake I made. The answers are right and the work is correct.

PLS HELP NEEDED TODAY

Answers

A: 4 percent - 4% + 98 = 101.92

B:

Way One: 110 times 0.10 is 11. 110 - 11 = 99
Way Two: 110 times 0.90 is 99

C: yes, it would make sense to switch to company B because they have a lower price after discount.

What is the multiplicative rate of change of the function?

1/3
2/3
2
9

Answers

Answer:

it is 2/3.

Step-by-step explanation:

please mark as brainliest .

2/3

As x increases by 1
Y decreases by a rate of 2/3.
6x2/3=4
4x2/3=8/3
And so on
To find 2/3, all you need to do is find how y is changing.
First of all, we know that y is decreasing as x increases so the rate is less than 1.
Take y2/y1 to get m or the rate
Ex. 4/6=2/3 which is less than 1!

Hope this helps!!

an 8 1/2 ounce bottle costs $0.99. Calculate the cost per ounce

Answers

Answer:

Step-by-step explanation: Part 1) The units rates are

A)

B)

C)

D)

Part 2) The best buy is the size 48 1/4 we know that To find out the unit rate divide the total cost by the total volume

Part 1) Calculate the unit rate for each size

case A) we have 8 1/2 ounce bottle costs $0.99 Convert mixed number to an improper fraction

Find the unit rate

case B) we have

18 2/2 oz. bottle costs $1.49

Convert mixed number

Find the unit rate

case C) we have

48 1/4 oz. carton costs $2.49

Convert mixed number to an improper fraction

Find the unit rate

case D) we have

64 3/4 oz. carton costs $3.75

Convert mixed number to an improper fraction

Find the unit rate

Part 2) which size is the best buy

we know that

The best buy is the one with the smallest unit rate

so

The best buy is the size 48 1/4 oz

base= 1.5 area=2 but what does height equal

Answers

I think the answer is 3

Answer:

i think its 1.33 repeating

Step-by-step explanation:

Which situation represents a proportional relationship?

a
The cost of purchasing a basket of oranges for $1.30 per pound plus $5.00 for the basket.
b
The cost of purchasing grapefruit for $1.80 per pound with a coupon for $1.00 off the total cost.
c
The cost of purchasing apples for $1.75 per pound plus a shipping fee of $0.16 per pound.
d
The cost of purchasing peaches for $7.00 per box of peaches with a delivery charge of $3.00.

Answers

I’m pretty sure it is C? But I’m not 100% sure
I think its either c or d im not sure though but it might be c

‍HELPPPPPPPP TYYY <333

Answers

Answer:

D (0, -2), (1, 0), (3, 3), (4, -5)

Step-by-step explanation:

The first number in a coordinate pair (x, y) is the x, so the first number is how much left or right you go, where the second number is how far up or down you go. if the (x) is negative, you go left, if it's positive you go right, of the (y) is negative you go down, if it's positive you go up.

Answer:

D

Step-by-step explanation:

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