We want the maximun or minimum of [tex]g(x)=-4x^2+4x-2[/tex]
Firstly, notice that we have a leading coefficient of -4, wich means our parabola is concave down. Thus, our function will have a maximum.
To find what is the maximum, let's firstly find on wich value of x it happens. We'll start by taking the first derivative of the function:
[tex]g'(x)=-8x+4[/tex]
To find the extremes of the function, we just need to find where the derivative equals zero. Setting g'(x)=0 we have
[tex]0 = -8x+4\\8x=4\\x=\frac{1}{2}[/tex]
So we found that the x coordinate of the maximum is x=1/2. To find the y coordinate we just need to substitute the value of x into the original function.
[tex]g(1/2)=-4(1/2)^2+4(1/2)-2\\g(1/2)=-1+2-2\\g(1/2) = -1[/tex]
Therefore, the maximum point [tex]M[/tex] of the function is
[tex]\boxed{M=(0.5,-1)}[/tex]
Glad to help! Wish you great studies.
If you found this helpful consider giving this answer brainliest ;)
Help Hurry!!! Timed!!!!!
What is 1.452 rounded to the nearest hundredth
Answer:
1.450
Step-by-step explanation:
what grade ar4e you in I'm guessing 4th or 5th
Jeremy wants to give a 20% gratuity to his cab driver. His fare is $35.50. What is the total amount he will pay the driver?
Answer:
$42.60.
Step-by-step explanation:
You multiply 35.50 by .20 (that's decimal version of 20%) which equals 7.10. Then you add 35.50+7.10=42.60
Question 1
Convert the mixed number to an improper fraction.
Step-by-step explanation:
to convert a mixed number to an improper fraction: take the big whole new on the right and multiply it by the denominators or number on the bottom of the fraction. then add thay amount to the numerator, or number on top and leave the denominator as it was before
example: 2 3/5 = 13/5
you can dissect the example to figure out the formula (formula is the way to solve an equation)
Answer:
Since you didn’t give us a mixed number is to turn into an improper fraction, I’ll show you how to do it.
Step-by-step Explanation:
First, you need to multiply the denominator by the whole number. Then, add the numerator to it. Lastly, you need to put the same denominator in that was from the mixed number to get an improper fraction. I’ll give you an example:
Look at the diagram below ↓
You can see that you need to multiply the denominator 4 and the whole number 2, which gives you 8. Then you add the numerator 3 to 8, which gives you 11. Lastly, you need to use the same denominator from the mixed, which was 4, and put it with the 11 to get the improper fraction [tex]\frac{11}{4}[/tex].
I hope you understand and that this helps with your question :)
A train travels 240 miles in 5 hours. At this rate, how far could the train go in 13 hours? What is the rate of speed of the train
Which expression represents 5/8
8 divided by 3
8 divided by 5
5 divided by 8
3 divided by 8
Answer:
5 divided by 8
Step-by-step explanation:
/ is another symbol for ÷
Answer:
5 divided by 8
Step-by-step explanation:
Write the decimal equivalent
Two hundred and thirty-four hundredths
PLEASE PLEASE PLEASE HELP!!!!!!!! I GIVE 100 POINTS!!!!!!!!!!!!!
Answer:
P = 11x + 14
Step-by-step explanation:
6x - 1 + 5x + 6 + 9
Move them around
6x + 5x - 1 + 6 + 9
Combine like terms
11x + 5 + 9
Add
11x + 14
Answer:
[tex]P=11x+14[/tex]
How is Triangle ABC similar to DBE?
Answer:
Triangle ABC is similar to triangle DBE: ∆ABC~∆DBE. ... Therefore, in conformity with first sign of the similarity of triangles, if two angles of one triangle are equal to two angles of another triangle, they are similar to each other. ∠BDE=∠BAC,∠BED=∠BCA ⇒ ∆ABC~∆DBE
Please Help Me. I am so mad at this freaking problem
need help asap
Google maps determines that a destination is 50 miles away and that the average speed of a car in this area is 23.2 miles/hour. How long should Google maps predict it will take you to drive to your destination?
Answer:
2 hours, 9 minutes (and 19 seconds if u wanna be exact)
Step-by-step explanation:
There are 3 directors, 4 management executives, 2 statisticians and 1 administrator. A committee of 4 members among them is to be formed. Find the probability that the committee consists of i) one of each kind III) one administrator and the other three III) at least one director
I need this answer Help me?
Answer:
1) 4/35
2) 11/14
3) 5/6
Step-by-step explanation:
First find the number of selections possible.
[tex]\frac{10!}{(10-4)!4!} = 210[/tex]
There are 210 possible selections. Now we can determine the possibility for each group. For the first probability, since we only want one member from each committee, you would create a fraction by (group members in total / group member being extracted). For this instance, since its only one, we will do whole numbers. Multiply each other.
[tex]4*3*2*1=24[/tex]
The probability for each member to get selected from each kind is : [tex]24/210[/tex] or can be simplified to [tex]4/35[/tex].
The probability of (I assume) at least one administrator is slightly different. Separate our two selections, the other three and the administrator. Find the number of selections possible for the other three... 4+3+2 = 9 others.
Find the probability for both a administrator included and three others.
[tex]\frac{11}{3} * \frac{1}{1} \\\frac{11!}{(11-3)!3!} \\\\165[/tex]
[tex]\frac{165}{210} = \frac{11}{14}[/tex]
The probability for an administrator and the other three is 165/210 or 11/14.
For the last one, you will figure out what the probability is for no director and use that % to substract from 100.
4+2+1 = 7
Get selections possible.
[tex]\frac{7!}{(7-4)!4!} = 35[/tex]
Get probability of no director.
[tex]\frac{35}{210} = \frac{1}{6}[/tex]
Substract 1/6 from 100%
1 - 1/6 = 5/6
The probability of having at least one director is 5/6.
An adult elephant drinks about 225 liters of water each day
Are the two following expressions equivalent? ( yes or no ) 24x + 6y and 6(4x + y
Answer:
yes because on the second one you have to use the distribution property (multiply the term outside the parenthesis by the terms inside them)
Step-by-step explanation:
Answer:
Yes.
Step-by-step explanation:
Distribute 6 to (4x+y), and you will get the same expression of 24x+6y.
4x times 6 = 24x
6 x y = 6y
24x+6y
What number can you divide both 4 and 2 by?
Answer:
Well, an infinite amount of numbers. . .
Step-by-step explanation:
1 and 2 would work
I would be so happy if you helped me with this question:3
Answer:
650
Step-by-step explanation:
18,000-3,000
13,000
13,000 x 5%
$650
Answer:
$900.
Step-by-step explanation:
What is 106 divided by 1/2?
106 divided by 1/2 in simplified form will be written as 212 .
Given, 106 divided by 1/2 .
Division property:
The rules for division are:
(1) positive ÷ positive = positive
(2) positive ÷ negative = negative
(3) negative or ÷ negative = positive
Solve the division:
[tex]106 /\frac{1}{2}[/tex]
= 106 × 2
= 212
Know more about division,
https://brainly.com/question/29775887
#SPJ6
please help me, it’s asking what the constant rate of change, if it’s possible.
If
Answer: If you were born in April you a amiable, and always ready to help others and a faithful lover.
Step-by-step explanation:
What is the area of a square with side a = 3m?
Answer:
12
Step-by-step explanation:
Answer:
9 Square Meters
Step-by-step explanation:
3x3=9
Help ASAP!!!!!!!!!!!!!!
Which expression represents the difference when (x^3+3x^2+5x-7) is subtracted from (2x^2-x+1)
Answer choices
1.) -x^3-x^2-6x+8
2.) -x^3-x^2-4x-8
3.) x^3-x^2-6x-8
4.) x^3-x^2-6x+8
Answer:A
Step-by-step explanation:
Identify all the functions that have a greater rate of change and the function represented in the graph
A y= 2x+7
B y=1.5x+ 1
C y=0.5x-5
D y=2.5x-20
E y=3x+12
F y=x +7
The equation with the greater rate of change is y = 3x + 12, which has a rate of change of 3.
A linear equation is in the form:
y = mx + b
where y, x are variables, m is the rate of change and b is the y intercept.
Given the equations, the equation with the greater rate of change is y = 3x + 12, which has a rate of change of 3.
Find out more on linear equation at: https://brainly.com/question/14323743
A bag has 5 yellow marbles 3 red marbles and 2 blue marbles. How many times would quinn expect to pick a blue marble if he picks a marble 200 times
Answer: 20% of the time.
Step-by-step explanation: 5+3+2 = 10 There are 2 blue so 2/10=1/5=20%
slope = 2; y-intercept = -1
Answer:
line equation: y= 2x-1
Slope intercept formula
y=mx+b
m is also the slope
b is the y-intercept
y=2x+(-1)
+ positive sign and -negative sign= - negative sign
y=2x-1
Answer :
y=2x-1
Choose the one alternative that best completes the statement or answers the question
Answer:
B) 60
Step-by-step explanation:
5*2*3*2=60 types by multiplying all the categories together.
Evaluate x−y when x=23 and y=−13
Answer:
36
Step-by-step explanation:
The equation would turn out as 23--13
But when there are two negatives, it turns into a positive, creating the equation of 23+13
Then you add to equal 36.
Hii! Can someone please answer these quickly? I'm giving BRAINLIEST! ❤️
Answer:
1. 3
2. -45
3. -25
4. 220
5. 57
6. -100
7. -209
Answer:
1.) -7 + 10 = 3 (Different signs, so you subtract and keep the sign of the bigger number).
2.) -30 - 15 = -45 (same sign, so you just add and keep the same sign)
3.) 65 - 90 = -25 (Different signs, so you subtract and keep the sign of the bigger number).
4.) 100 + 120 = 220 (both positive,you add and keep the same sign, which is +)
5.) -32 + 89 = 57 (Different signs, so you subtract and keep the sign of the bigger number).
6.) 100 - 200 = -100 (Different signs, so you subtract and keep the sign of the bigger number).
2.) -75 - 12 = -87 (same sign, so you just add and keep the same sign)
5TH GRADE LEVEL QUESTION: look at photo and answer.
Answer 11/20
Step-by-step explanation:
Answer:
11/20
Step-by-step explanation:
3/4 - 1/5
Write all numerators above the least common denominator
15-4/20
Subtract numbers
11/20
Question 1
1 pts
Given the sequence:
25, 21, 17, 13,...
Write the explicit equation that models the sequence.
A. an
4n + 29
B. an
25 +(-4)(n-1)
C. an = -25 +(-4)(n-1)
D. an
= 4 + 25
Edit
View
Insert
Format
Tools
Table
Answer:
The correct answer is: Option B: [tex]a_n = 25+(-4)(n-1)[/tex]
Step-by-step explanation:
Given sequence is:
25, 21, 17, 13,...
Here
a1 = 25
a2 = 21
a3 = 17
First of all we have to determine the common difference. Common difference is the difference between consecutive terms of an arithmetic sequence.
So,
[tex]d = a_2 - a_1 = 21-25 = -4\\d =a_3-a_2 = 17-21 = -4[/tex]
The explicit formula is given by:
[tex]a_n = a_1 + (n-1)d[/tex]
Putting the value of a1 and d
[tex]a_n = 25 + (n-1)(-4)\\a_n = 25-4n+4\\a_n = 29-4n[/tex]
Hence,
The correct answer is: Option B: [tex]a_n = 25+(-4)(n-1)[/tex]
Laura has 160 pounds of green beans at her vegetable stand. If she sells 10 pounds of green beans every hour, what is the percent decrease in green beans after 3 hours?
A
18.75%
B
81.25%
C
23.07%
D
16%
Given:
Laura has 160 pounds of green beans at her vegetable stand.
She sells 10 pounds of green beans every hour.
To find:
The percent decrease in green beans after 3 hours.
Solution:
We have,
Beans sold in 1 hour = 10 pounds
So, Beans sold in 3 hours = 30 pounds
Decrease in green beans after 3 hours is 30 pounds.
Now,
[tex]\%\text{Decrease}=\dfrac{\text{Decrease in green beans after 3 hours }}{\text{Initial amount of green beans}}\times 100[/tex]
[tex]\%\text{Decrease in green beans after 3 hours}=\dfrac{30}{160}\times 100[/tex]
[tex]\%\text{Decrease in green beans after 3 hours}=\dfrac{300}{16}[/tex]
[tex]\%\text{Decrease in green beans after 3 hours}=18.75\%[/tex]
Therefore, the correct option is A.