Consider continuous functions f, g, and k. Then complete the statements.
The function that has the least minimum value is function
_____.
The function that has the greatest minimum value is function _____.
Answers
The function that has the least minimum value is function is h and The function that has the greatest minimum value is function is k .
What is quadratic function ?we define a quadratic function as an function of degree 2, meaning that the highest exponent of this function is 2. The standard form of a quadratic is y = ax² + bx + c, where a, b, and c are numbers and a cannot be 0.
According to the question
f(x) = x² - 2x - 6
as per graph
its minimum value at (1,-7)
h(x) = 2(x-1)²
h(x) = 2 (x² + 1 -2x )
h(x) = 2x² - 4x + 2
By plotting the graph
we can observe the
minimum value at (1,0)
k(x) = [tex]x^{4} + 2x^{2} + 8x -4[/tex]
By plotting the graph
we can observe the
minimum value at (-1,-9)
For g(x)
Standard form of quadratic equation :
y = ax² + bx + c
or
g(x) = ax² + bx + c
at x = 0
g(x) = -4
-4 = a* 0 + b* 0 + c
c = -4
at x = 1
g(x) = -5
-5 = a + b - 4
a + b = -1 --------------------(1)
at x = -1
g(x) = -11
-11 = a*(-1)²+ b* (-1) + -4
-7 = a - b --------------------(2)
Adding equation (1) and (2)
a = -4
b = 3
g(x) = -4x² + 3x -4
as x² is negative parabola will be downward
therefore it will have max value
i.e
at (0.375,-3.438)
Now, The function that has the least minimum value is function is h with x = 1 and h(x) = 0
The function that has the greatest minimum value is function is k with x = -1 and k(x) = -9
Hence, The function that has the least minimum value is function is h and The function that has the greatest minimum value is function is k .
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Related Questions
Solve for x.
Enter the number that belongs in the green box
Answers
Answer:
x = 45
Step-by-step explanation:
Because these are two congruent triangles inside of each other we can set up an equivalency ratio.
25/35 = x/65
Multiply both sides by 65 to get x alone
65 * 25/35 = x/65 * 65
(65 * 25)/35 = x1
1576/35 = x
x = 45
Hope this helps,
Four less than twice a number is fifty
Answers
Answer:
28
Step-by-step explanation:
50+4= 54
54/2=28
Answer:
2a - 4 = 50
Step-by-step explanation:
Less than means that you subtract 4.
Twice a number just means that you multiply a number by 2.
And we know that all of that equals 50.
If you want to solve it..
2a - 4 = 50
+4 +4
-----------------
2a = 54
Divide both sides by 2. 54/2 = 27
a = 27
Jack works after school. Each day he is paid a set amount, plus an hourly wage. Hours 1 1.5 2 2.5 3 Pay 18 23 28 33 38 Assume Jack works from 2:30 P.M. to 7:00 P.M. Using the function f(x) = 10x + 8, how much would he earn? A. $33 B. $35.50 C. $45 D. $53
Answers
Answer: C
Step-by-step explanation:
Answer:
Step-by-step explanation:
Which equation is quadratic in form?
2(x + 5)2 + 8x + 5 + 6 = 0
x6 + 6x4 + 8 = 0
7x6 + 36x3 + 5 = 0
4x9 + 20x3 + 25 = 0
Answers
Answer:
I think it's the first one... but I'm not pretty sure.
Answer:
C
Step-by-step explanation:
edge 2020
A new hard drive costs $225, plus $40 per hour for labor. The linear equation y = 40x + 225 gives the cost y in dollars for x hours of labor. If Jane has $385 to spend on computer repairs, using plug and chug strategy for x hours of labor, what is the maximum number of hours the computer technician can work?
Answers
Answer:
Step-by-step explanation:
225+40h=y
225 + 40x = 385
-225 -225
------- -------
40x = 160
x= 4
Find the z-score separating the lowest 9% of scores from the highest score of 91%
Answers
Answer:
I'm not sure of my answer but try this:
7n + 5 =68.... how to solve this problem and show my work
Answers
Answer:
n=9
Step-by-step explanation:
7n+5=68 Subtract 5 on both sides.
-5 -5
7n=63 Divide both sides by 7.
/7 /7
n=9
Hope this helps! Have a nice day ^^
Answer:
n = 9
Step-by-step explanation:
1) Move similar terms to one side. Here we are moving the 5 over to the side with 68 by subtracting it. We also have to subtract 5 from the other side too (what you do to one side you must do to the other)
7n + 5 = 68
- 5 -5
7n = 63
2) Isolate the variable. We do this by dividing the 7 from 7n. We also have to divide 7 from other other side too.
7n = 63
/7 /7
n =9
what is 2+2 my brain has been in circles about this
Answers
Answer:
hey welcome to Brainly, and 2 + 2 = 4
Step-by-step explanation:
2+2=4
3+3=6
4+4=8
5+5=10
and so on just keep adding 2
please help! finding coordinates of a point :)
Answers
Answer:
Step-by-step explanation:
Follow the numbers.
Which two numbers below have a least common multiple of 48?
Answers
Answer:
its 3 and 16 just trust me
The least common multiple is divisible by both a and b. The two numbers below have a least common multiple of 48 is 3 and 16.
What is LCM?The least common multiple that is divisible by both a and b is the smallest positive integer, lowest common multiple, or smallest common multiple of two numbers a and b, generally indicated by LCM.
The two numbers below have a least common multiple of 48 are,
3 and 16 ⇒ 3×16=48
Hence, the two numbers below have a least common multiple of 48 is 3 and 16.
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Cedrick earns $9.75 for each day he pet-sits; is the relationship between the money he earns and the days he works proportional?
Answers
Answer:
Marianne is 15 years old and her brother is 5 years old; is the relationship between their ages proportional?
Step-by-step explanation:
i just did it !!
System of Equations in Three Variables Word Problem
Answers
Answer:
i think the answer is a number or multiple number and maybe a decimal.
Step-by-step explanation:
go to Tiger Algebra Solver
Twenty percent of all telephones of a certain type are submitted for service while under warranty. Of these, 70% can be repaired, whereas the other 30% must be replaced with new units. If a company purchases ten of these telephones, what is the probability that exactly two will end up being replaced under warranty?
Answers
Answer:
The required probability is 0.09875
Step-by-step explanation:
From the given information;
the probability of repairing the telephones = 0.70
the probability of the replaced = 0.30
Suppose we consider Mto denotes the telephone that is submitted for service while under warranty and must be replaced.
Then;
p = P(S) = P(replaced | submitted) P(submitted)
= 0.30 × 0.20
= 0.06
Now, the probability that exactly two will end up being replaced under warranty given that it assumes a binomial distribution where n = 10 and p = 0.06
[tex]P(X=2)=\bigg (^{10}_{2}\bigg) 0.06^2(1-0.06)^{10-2}[/tex]
[tex]P(X=2)=\dfrac{10!}{2!(10-2)!}\times 0.06^2\times (0.94)^{8}[/tex]
[tex]\mathbf{P(X=2)=0.09875}[/tex]
Determine if the lines are parallel, perpendicular, or neither. y + 3 = 7/4x and -4/7x + y = 9. Do I still have to solve y + 3 = 7/4x?
Answers
Answer:
No you dont have to solve it. And I believe it is perpendicular.
Step-by-step explanation:
Answer:
Perpendicular
Step-by-step explanation:
you have to solve both. If you make the lines in a graph it will turn out to be perpendicular because they are going to intersect.
13x456+345 divided by 45x265-256=?
Answers
Answer:
7703.66666667
Step-by-step explanation:
in ABC, D∈AB so that AD;DB=1 : 3. If ACDB = 12ft2 Find AACD and AABC
Answers
Answer:
Area of [tex]\triangle[/tex]ACD = 4 [tex]ft^2[/tex]
Area of [tex]\triangle[/tex]ABC = 16 [tex]ft^2[/tex]
Step-by-step explanation:
Given that:
D is a point on AB.
and ABC is a triangle.
AD:DB = 1 : 3
Area of [tex]\triangle[/tex]CDB = 12 [tex]ft^2[/tex]
Kindly refer to the attached image as per the given dimensions and values.
To find:
Area of [tex]\triangle[/tex]ACD and Area of [tex]\triangle[/tex]ABC = ?
Solution:
Formula for area of a triangle = [tex]\frac{1}{2}\times Base \times Height[/tex]
The altitudes of triangles [tex]\triangle[/tex]CDB and [tex]\triangle[/tex]ACD are equal in dimensions.
Therefore the area of triangles [tex]\triangle[/tex]CDB and [tex]\triangle[/tex]ACD will be equal to the ratio of their bases.
Area of [tex]\triangle[/tex]ACD : Area of [tex]\triangle[/tex]CDB = AD: DB = 1 : 3
[tex]\Rightarrow[/tex] Area of [tex]\triangle[/tex]ACD = [tex]\frac{12}{3} = \bold{4 ft^2}[/tex]
Area of [tex]\triangle[/tex]ABC = Area of [tex]\triangle[/tex]ACD + Area of [tex]\triangle[/tex]CDB = 12 + 4 = 16 [tex]ft^2[/tex]
Therefore, the answer is:
Area of [tex]\triangle[/tex]ACD = 4 [tex]ft^2[/tex]
Area of [tex]\triangle[/tex]ABC = 16 [tex]ft^2[/tex]
IF UR GOOD AT PRECALC PLEASE HELP
Answers
Answer:
Answer is C, u can find this just by looking at domain
The difference of three times a number and two is twelve more than the number. Find the number. pls help
Answers
I may be wrong but I got x³- 2 + 12.
How many distinct ways are there to arrange 2 orange marbles, 2 clear marbles, and 3 yellow marbles in a row? Give your
answer as an integer.
Provide your answer below:
Answers
Answer:
144
Step-by-step explanation:
3x2x2
the sum is 12, and after that you do 12^2
the final answer is 144
The number of distinct ways to arrange 2 orange marbles, 2 clear marbles, and 3 yellow marbles in a row will be 144.
What is a permutation?A permutation is an act of arranging items or elements in the correct order.
There are 2 orange marbles, 2 clear marbles, and 3 yellow marbles.
Then the number of distinct ways to arrange 2 orange marbles, 2 clear marbles, and 3 yellow marbles in a row will be
⇒ (3 x 2 x 2)²
⇒ 12²
⇒ 144
More about the permutation link is given below.
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you paid $3.36 for a 16 minute phone call to your family what is a unit rate
Answers
Answer:
0.21
Step-by-step explanation:
3.36/16=0.21
Answer:
$0.21
Step-by-step explanation:
How to find the value of x
Answers
One card is drawn at random from a deck of 52 cards. The first card is not replaced, and a second card is drawn. (Enter your probabilities as fractions.)
Required:
a. Find the probability that both cards are clubs.
b. Find the probability that the first card is a spade and the second is a club.
Answers
Answer:
We have a 52 card deck:
a. Find the probability that both cards are clubs.
The probability of drawing a club will be equal to the quotient between the number of clubs in the deck divided by the total number of cards in the deck.
We initially have 13 clubs and 52 cards, then the probability of drawing a club in the first draw is:
p1 = 13/52.
Now the probability of drawing a club in the second draw will be:
p2 = 12/51
Where each number is decreased by one because we already drew a card, and that card was a club.
Then the probability of both events happening will be equal to the product of the individual probabilities:
P = p1*p2 = (13/52)*( 12/51) = 0.059
b. Find the probability that the first card is a spade and the second is a club.
Same as before, the probability of first drawing a spade is:
p1 = 13/52
And the probability of drawing a club in the second draw will be:
p2 = 13/51
This case differs from the prior one because for the second draw we have 13 clubs in the deck, and as we already drew one card (that was not a club) the total number of cards in the deck is 51.
Now the joint probability will be:
P = p1*p2 = (13/52)*(13/51) = 0.064
The length of a rectangle is four times its width. The length is 4 2/3 feet. What is the area of the rectangle?
Answers
Answer:
4.687225
Step-by-step explanation:
Find the indicated probability by using the complementation rule. A percentage distribution is given below for the size of families in one U.S. city. Size Percentage 2 39.9 3 24.4 4 20.1 5 10.8 6 3.3 7 1.5 A family is selected at random. Find the probability that the size of the family is 4 or more. Round results to three decimal places.
a. 0.156
b. 0.844
c. 0.357
d. 0.201
Answers
Answer:
The correct option is c.
Step-by-step explanation:
The percentage probability distribution is:
Size (X) Percentage
2 39.9
3 24.4
4 20.1
5 10.8
6 3.3
7 1.5
Total 100.0
Compute the probability that the size of the family is 4 or more as follows:
P (X ≥ 4) = P (X = 4) + P (X = 5) + P (X = 6) + P (X = 7)
= 0.201 + 0.108 + 0.033 + 0.015
= 0.357
Thus, the probability that the size of the family is 4 or more is 0.357.
The correct option is c.
a corn vendor at a farmers market was selling a bag of 8 ears of corn for $2.56 anithert vendor was selling a bad of 12 for 4.32. which bag is the better deal?
Answers
2.56/8 = 0.32
4.32/12 = 0.36
8 ears of corn is thebetter deal
can u find all angles
Answers
Answer:
I think it's 118°73°49° not really sure
sorry
What is the answer here
Answers
Answer is B. 6a/b^7
If correct make brainliest?
Please help me it’s very important please answer it correctly
Thank you
Answers
Answer:
a. m<CBA = m<DBA because of the definition of an angle bisector (angle bisector cuts the angle in half) We are also told that segment BD and Segment BC are congruent.
We don't know if segment AC and AD are congruent so we can't say those angles (the other two) are congruent.
b. point A and B will stay fixed because they are colinear to segment AB (on the same line)
c. Those two are needed because If those are true we can prove that they are congruent by SAS (Side Angle Side)
d. the reflection an prove that the lines and angles are congruent.
find the original price of a pair of shoes if the sale price is $40 after a 60% discount
Answers
Answer:
Thus, the original price of the pair of shoes was $100.
Step-by-step explanation:
Percentages
After a 60% discount, the sale price is now valued at 100-60=40% of its original price.
If the sale price is $40, then the original price is calculated as
$40 / 40 * 100 = $100
Thus, the original price of the pair of shoes was $100.
Verify applying 60% discount:
$100 - 60*$100/100 = $40
Valery and Manuel ride their bikes 40 miles every Saturday. Valery rides at an Average speed of 9.6 miles per hour (mph)
exactly how many hours does it take Valery to ride her bike 40 miles?
Answers
Answer:Around 10 hours
Step-by-step explanation:
