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.
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.
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:
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?
Answer:
what grade is this
Step-by-step explanation:
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.
__________________________________________________
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)
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
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
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
[tex]2[/tex][tex]1/8[/tex] ÷ [tex]34= 0.0625=1/16[/tex]
B.
[tex]Goesy[/tex]
Every person has a unique tongue print like finger prints
Answer:
is this a question? but yes that is most likely true.
Step-by-step explanation:
explanation? uh my brain? :'>
please help me i need two answers
Answer:
-7 3/4x-7(3)
7(-3/4x)-7(3)
Step-by-step explanation:
PLS HELP NEEDED TODAY
What is the multiplicative rate of change of the function?
1/3
2/3
2
9
Answer:
it is 2/3.
Step-by-step explanation:
please mark as brainliest .
A bicyclist goes 43.54 miles in 3.5 hours. What is her speed??
PLEASE EXPLAIN WHY!!!!!
(03.04 MC) EXPLAIN!!!
Solve for x:
(-3/2)x - 9 = -27
Select one:
a. −24
b. −12
c. 11
d. 12
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
I need help with this ASAP!!!
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
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
ANSWER ASAP PLZZ!!!!
What type of roots would you expect plants to have in the desert?
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 ^-^
an 8 1/2 ounce bottle costs $0.99. Calculate the cost per ounce
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
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.
Answer:
38.4 minutes
Hope this helps!!!
"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
answer plzzzzzzzzzzzzzzzz
Answer:
which one, or all of them?
Step-by-step explanation:
HELPPPPPPPP TYYY <333
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:
Create a simple equation that has infinite solutions, and a simple equation that has no solutions
Answer:
-9m - 4 = -9m - 4 and one that doesn't have any solution is -4 + 2b = 2b - 9
Step-by-step explanation:
X + 3(12 X 3y)-35+59Z
base= 1.5 area=2 but what does height equal
I think the answer is 3
Answer:
i think its 1.33 repeating
Step-by-step explanation:
When two factors have opposite signs, is the product negative or positive??
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 :)
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
Answer:
the answer is A, y = 3/2x + 1
Step-by-step explanation:
PLEASE HELPPPPPPPPPPPPPPPPPPP
Answer:the answer is D
Step-by-step explanation:
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.
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:
can you guys do this and show work so i can copy it? ill give you brainliest and point :
HELPPPPPPPPPPPPPPPPPPPPPPPPPPPPPPPPPPPPPPPPPPPPPPPPPPPPPPPPPPPPPPPP PLEASE
Answer:
use formula
area = 1/2 *Height *(side 1 + side 2)
Answer:
use the equation of area of parallelogram = height ×base
there are 200 freshmen in a high school. 30% of them take history. how many freshmen are enrolled in Spanish?
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.