Answers
Answer:
Step-by-step explanation:
Given function is,
f(x) = [tex]x\sqrt{x}[/tex]
We can rewrite this function as,
f(x) = [tex]x^{\frac{3}{2}}[/tex]
a). Domain of the function is [0, ∞)
Derivative of the function in this domain,
f'(x) = [tex]\frac{3}{2}x^{(\frac{3}{2}-1)}[/tex]
= [tex]\frac{3}{2}x^{\frac{1}{2}}[/tex]
Since, f'(x) > 0 in the interval [0, ∞)
Function is increasing in the interval [0, ∞)
b). For local maxima and local minima,
Second derivative of the function,
f"(x) = [tex]\frac{3}{2}(\frac{1}{2})x^{\frac{1}{2}-1}[/tex]
= [tex]\frac{3}{4}x^{-\frac{1}{2}}[/tex] > 0
So the function should have a local minima.
But the function is continuous in the interval x ≥ 0,
There is no local minima (only absolute minima).
c). Since, second derivative is undefined at x = 0,
There are no inflection points.
d). Since, f"(x) > 0 in the interval [0, ∞)
Concavity of the curve is UPWARDS.
Related Questions
-3x+5y=2x+3y−3x+5y=2x+3y Which ordered pair is a solution of the equation?
Answers
Answer:
the answer is neither
Step-by-step explanation:
Hey ill give brainlist
Answers
Answer:
[tex]2.\:\frac{41}{9}[/tex]
Step-by-step explanation:
Recall that [tex]\frac{x}{9}=\lfloor \frac{x}{9} \rfloor + 0.\overline{[x\:\mod9]}[/tex].
Therefore, [tex]4.\bar{5}=\frac{4\cdot 9 + 5}{9}=\fbox{$2)\:\frac{41}{9}$}[/tex].
Answer:
B is correct answer.................
6=xy does this show direct variation Explain your reasoning. 6=xy does this show direct variation Explain your reasoning. 6=xy does this show direct variation Explain your reasoning.6=xy does this show direct variation Explain your reasoning.
Answers
9514 1404 393
Answer:
no; the variation is inverse
Step-by-step explanation:
Solving for y, the equation becomes ...
y = 6/x
The variation is as the inverse of x. It is not direct variation.
can some one help me please
Answers
Answer:
With what?
Step-by-step explanation:
Given 1 inch = 2.54 centimeters, enter the value that will complete this expression for converting 3.5 feet to centimeters. (What value goes where the ♣ is?)
[tex](\frac{3.5 feet}{1} )(\frac{♣inches}{1 foot})(\frac{2.54}{1 inch})\\[/tex]
Answers
Answer: the answer is 12
Step-by-step explanation: the answer is 12 because there are 12 inches in a foot.
Gretchen computed the geometric mean of two numbers. One of the
numbers was 7 and the geometric mean turned out to be 7 as well. The other number
would be ?
Answers
9514 1404 393
Answer:
7
Step-by-step explanation:
When the mean of two numbers is the same as one of the numbers, then the other number also has that same value. This is true for any kind of mean:
arithmetic, geometric, harmonic.
The other number would be 7.
__
The geometric mean (m) of a and b is ...
m = √(ab)
We have ...
7 = √(7b)
49 = 7b . . . . . square both sides
7 = b . . . . . . . .divide by 7
a = b = m = 7 in this case.
the equation of a circle whose center is (-5, 3) and whose radius is 6?
Answers
Answer:
Center:(-5,3)
The center of a circle is a point from which all points on a circle are the same distance.
Radius:6
The radius of a circle is the length of a line segment from its center to its perimeter.
The radius is typically denoted as "r" or "R".
Diameter:12
The diameter of a circle is any straight line segment that passes through the center of the circle and whose endpoints lie on the circle. It can also be defined as the longest chord of the circle.
Circumference or (or Permieter) = 2*π*R = 2*3.14*6 = 37.6991118430775
The circumference of a circle is the distance around it.
Area:113.097335529233
Area of a Circle is the amount of space occupied by the circle.The area of a circle is p times the radius squared, which is written: A = π*R2.
The length of a rectangle is 2 meters less than 3 times the width. The perimeter is 44
meters. Find the width
Answers
Answer:
Width of rectangle = 6 meters
Step-by-step explanation:
Let
Width of rectangle = x
Length of rectangle = 3x-2
Perimeter of rectangle = 44 meters
We need to find:
The Width of rectangle.
The formula used is:
[tex]Perimeter\:of\:rectangle=2(Length\times Width)[/tex]
Putting values and finding value of x
[tex]Perimeter\:of\:rectangle=2(Length\times Width)\\44=2(3x-2+x)\\44=2(4x-2)\\44=8x-4\\8x=44+4\\8x=48\\x=\frac{48}{8}\\x=6[/tex]
So, we get the value of x = 6.
We know that Width of rectangle = x = 6
So, Width of rectangle = 6 meters
Which statement about 4(x-3) is true?
O A. 4(x-3) has three terms.
OB. 4(x-3) is a sum.
O C. 4(x - 3) is a product.
O D. 4(x-3) has two variables.
Answers
4(x-3) cannot be a product or a sum as it is not simplified or finished, it is still missing a number. It cannot be D as it has three variables.
I deeply apologize if that is wrong but to my understanding your answer is A.
can someone help me please im struggling and can’t figure these 2 problems out :(
Answers
9514 1404 393
Answer:
2. G 10.72 units
3. B 3.6, 6, 4.8
Step-by-step explanation:
2. The Pythagorean theorem tells you the square of the hypotenuse is the sum of the squares of the sides.
14^2 = 9^2 + CB^2
196 = 81 + CB^2 . . . . find the square values
115 = CB^2 . . . . . . . . subtract 81
√115 = CB ≈ 10.72 . . . . . matches G
__
3. You know that lengths 3, 4, 5 form a right triangle. This is a special triple for several reasons. One of them is that it is the smallest integer Pythagorean triple. Another is that it is the only Pythagorean triple that is an arithmetic sequence (has constant differences between lengths).
You can use this as a reference to look at the choices offered.
A. The lengths 3.2, 4.1 and 5.0 have constant differences of 0.9. The shortest length is not 3 times this value, so this is not a right triangle.
B. The lengths 3.6, 4.8, 6 have constant differences of 1.2. These numbers are 3, 4, and 5 times that difference, so these segments will form a right triangle.
C, D. The longest length is an integer. The sums of the squares of the decimal values will not be integers, so these are not right triangles.
4.5^2 +6.7^2 = 65.14 not 8^2
5.2^2 +8.5^2 = 99.29 not 10^2
find the value of x in the following parallelogram:
6x-15=5x+10=x+15
Answers
Answer:
x=6
Step-by-step explanation:
Using your knowledge of inverse operations, the inverse operation for the equation 4,560/120 = 38 is ______?
38/120 = 4,560
38 * 120 = 4,560
4,560/38 = 120
4,560 * 38 = 120
Answers
Given:
The equation is
[tex]\dfrac{4560}{120}=38[/tex]
To find:
The inverse operation for the equation using the knowledge of inverse operations.
Solution:
We have,
[tex]\dfrac{4560}{120}=38[/tex]
Here, 4560 is divided by 120. So, in this equation the operation is division.
We know that inverse operation of division is multiplication. So, multiply both sides by 120.
[tex]\dfrac{4560}{120}\times 120=38\times 120[/tex]
[tex]4560=38\times 120[/tex]
It can be written as
[tex]38\times 120=4560[/tex]
The inverse operation for the equation is [tex]38\times 120=4560[/tex].
Therefore, the correct option is B.
Which point is the reflection of point E across the y-axis ? What’s are it’s coordinates?
Answers
Answer:
The reflection of point E across the y-axis is J(-2, 0).
Step-by-step explanation:
PLATO
PLEASE ANSWER ASASP FOR BRAINLEST!!!!!!!!!!!!!!!!!!!!!!!!
Answers
Add six on both sides
-5m >= 30
Divide by negative five on both sides
m >= -6
the following figures are similar, find the value of x
Answers
Answer:
x=143
Step-by-step explanation:
scale factor (if that is the correct term) is 13. you find that by matching sides to side. this means that 91/7=13, therefore you know that 4*13 is 52 and 11*13 is 143
If MN is a midsegment of ∆ABC, find the values of x and y.
Answers
Answer:
Step-by-step explanation:h
Answer:
d
Step-by-step explanation:
The sum of two numbers is 25 one number is five less than the other number find the larger number
Answers
*NOT MY WORK ITS FROM SOMEONE ELSE WHO ASKED THE SAME PROBLEM*
Answer: x=15, y= 10
Step-by-step explanation:
Answer: x=15, y=10
*Note: x and y are only variables used to solve this problem, but know that the two numbers are 15 and 10.
Step-by-step explanation:
For this problem, we can use system of equations. Let's use x for one number and y for the other.
First Equation:
x+y=25
We get this equation because it states that the sum of the two numbers is 25.
Second Equation:
y=x-5
We get this equation because it says one number (y) is 5 less than the other (x).
Since we have two equations, we can use substitution method to solve.
[distribute 1 to (x-5)]
[combine like terms]
[add both sides by 5]
[divide both sides by 2]
Now that we have x, we can plug it into any of the equations to find y.
[plug in x=15]
[subtract both sides by 15]
Finally, we have our answer, x=15 and y=10.
2x-5= 25
2x=30
X=15
So the larger number is 15 , it’s easy to figure it out but you could get mark for workingnout
The graphs of x=2(y-4) and x=5(y-4) are shown below.
How does the graph of x=2(y-4) compare with the graph of x=5(y-4)
A. The graph of x=2(y-4) crosses the y-axis lower than the graph of x=5(y-4)
B. The graph of x=2(y-4) has greater slope than the graph of x=5(y-4)
C. The graph of x=5(y-4) has greater slope than the graph of x=2(y-4)
D. The graph of x=2(y-4) crosses the y-axis higher than the graph of x=5(y-4)
Answers
Answer:
B is the correct answer
Step-by-step explanation:
because x=2y-8 is same as y=1/2 x+4 x=5y-20 is the same as y=1/5 x+4 slope of the first is 1/2 slope of the second is 1/5 so 1/2>1/5there y intercept are the same which is 4
The graph of x=2(y-4) has greater slope than the graph of x=5(y-4), the correct option is B.
What is the standard equation of a line?The standard equation of a line is given by
y = mx+c
Here m is the slope and c is the y intercept
The slope can be determined by
m = (y₂ -y₁)/(x₂ -x₁)
The equation of the line is
x=2(y-4)
x=5(y-4)
y = (1/2)x +4
y = (1/5)x +4
The slope is (1/2) and (1/5),
(1/2) > (1/5)
To known more about standard equation of a line
https://brainly.com/question/12452575
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Line m has a slope of 10. Another line n is parallel to line m. What is the slope of line n ?
Answers
Answer:
We conclude that the slope of line 'n' is: m₂ = 10
Step-by-step explanation:
Given
The slope of line m is: m₁ = 10
It is stated that another line is parallel to line m.Let m₂ be the slope of the 'n' line.
We know that when two lines are parallel, they have equal slopes.
i.e. m₁ = m₂
as
The slope of line m is: m₁ = 10
and
The lines are parallel
so
The slope of line 'n' is: m₂ = 10
Therefore, we conclude that the slope of line 'n' is: m₂ = 10
Which sentence best contrasts Greg’s father and Lemon Brown, in "The Treasure of Lemon Brown”? Lemon Brown has shown a deep concern for his son, while Greg’s father shows only a nagging concern for Greg. Lemon Brown has lived a more exciting life of a musician, while Greg’s father lives a more stable existence as a postal worker. Lemon Brown lives a tragic life, while Greg’s father does not take the risks that can lead to tragedy. Lemon Brown shows regret for his son’s loss, while Greg’s father does not show remorse for his mistreatment of Greg.
Answers
Answer:
the correct answer will be B i took the test and got a 100%
Step-by-step explanation:
B. Lemon Brown has lived a more exciting life of a musician, while Greg’s father lives a more stable existence as a postal worker.
There are 2 boys for every 3 girls in Sappy Sunshine Childcare center. If there are a total of 171 girls at the center, how many boys are there? (do not include units in your answer, just the number)
Answers
Answer:
114 boys
Step-by-step explanation:
This question can be solved using a rule of three.
For each 2 boys, there are 3 girls on the center. So, how many boys will be there when there are 171 girls?
2 boys - 3 girls
x boys - 171 girls
[tex]3x = 2*171[/tex]
Simplifying both sides by 3
[tex]x = 2*57 = 114[/tex]
There are 114 boys there
PLS HELP I WILL GIVE BRAINLEST
1. Patrick is saving money to buy a video game that costs $68.
Part A. Patrick receives $6 every week for doing chores at home. Patrick spends $2.00 every week and saves the rest.
How many full weeks will it take Patrick to save enough money to purchase the video game? Show your work and justify your answer.
Part B. Patrick can earn extra money by cutting grass. His neighbors will pay him $4.00 for each lawn that takes him 30 minutes. What is the amount of time, in extra HOURS, that Patrick would have to spend cutting grass to be able to buy a second $68 video game for his friend? Show your work to justify your answer.
Answers
Answer:
Part A - 17 full weeks
Part B - 8 hours and 30 minutes
Step-by-step explanation:
Key skills needed: Rate of change, Equation Creating & Solving
PART A
1) We need to make an equation for the amount of money Patrick saves each week. He earns $6.00 and then spends $2.00
Since he saves the rest, the amount of money he saves each week is
---> $6.00 - $2.00 = $6 - $2 = $4
2) Since Patrick saves $4 a week, let's say that the number of weeks is "[tex]w[/tex]"
Since the game costs $68 we can make the equation
--> [tex]4w = 68[/tex]
4 is the money he saves each week.
w is the number of weeks he saves
68 is the cost of the game
3) Divide by 4 on both sides and you will get --> [tex]w = 17[/tex]
(68 divided by 4 is equal to 17)
Therefore 17 full weeks is your answer.
Part B
1) Patrick earns 4 dollars for each lawn mowed. Each lawn takes 30 minutes to mow.
30 minutes is half an hour ---> This means that for each hour he would be making $8 (since $4 x 2 = $8)
2) So if we say the number of hours is "[tex]h[/tex]", the equation we can make is
---> [tex]8h = 68[/tex]
8 is the money he makes per hour
h is the number of hours he mows the lawns
68 is the cost of the game he wants to buy for his friend
3) Divide both sides by 8 and you will get
--> [tex]h = 8.5[/tex]
(68 divided by 8 is 8.5 (8 and a half))
This means that he needs to mow lawns for 8.5 hours in order to buy the video game for his friend.
8.5 hours is the same as 8 hours and 30 minutes, which is the answer.
Hope you understand and have a nice day!! :D
A line passes through the points (6,-6) and (9,-5). What is it’s equation in point slope form?
Answers
Answer:
[tex]y=\frac{1}{3}x-8[/tex]
Step-by-step explanation:
Slope-intercept form of an equation is written as [tex]y=mx+b[/tex], where [tex]m[/tex] is the slope and [tex]b[/tex] is the y-intercept.
The slope of a line that passes through the points [tex](x_1,\: y_1)[/tex] and [tex](x_2, \: y_2)[/tex] is [tex]m=\frac{\Delta y}{\Delta x}=\frac{y_2-y_1}{x_2-x_1}[/tex]. Using the coordinates [tex](6,-6)[/tex] and [tex](9,-5)[/tex] as given in the problem, we have slope of this line to be:
[tex]m=\frac{-5-(-6)}{9-6}=\frac{1}{3}[/tex].
Now using this slope we've found and any point the line passes through, we can find the y-intercept of this equation:
[tex]-6=\frac{1}{3}(6)+b, \\ b=-8[/tex]
Therefore, the equation of this line in slope-intercept form is [tex]\fbox{$y=\frac{1}{3}x-8$}[/tex].
I will give brainlist. its math 2 honor
Answers
Answer:
option 2
Step-by-step explanation:
I did this already
please look at the question, I uploaded it!
Answers
Answer:
angle JKL is 21
Step-by-step explanation:
the angle of the two triangles are the same, so (2x + 1) = (3x - 9)
You would then find the x, which equals to 10.
Then replace x with ten with the equation.
Gareth 30 students in a class and the ratio of boys to girls in the class is 2:3 calculate the number of goals
Answers
Answer:
There are 12 boys and 18 girls
Step-by-step explanation:
Equations
There are 30 students in a class. Let's call:
x = number of boys
Since the sum of boys and girls is 30:
30 - x = number of girls
The ratio of boys to girls is 2:3, thus:
[tex]\displaystyle \frac{x}{30-x}=\frac{2}{3}[/tex]
Crossing denominators:
3x = 2(30 - x)
Operating the parentheses:
3x = 60 - 2x
Adding 2x:
5x = 60
Dividing by 5:
x = 60/5 = 12
x = 12
There are 12 boys and 30-12=18 girls
Think about all the ways in which a line and a parabola can intersect select all the numbers of ways in which a line in a parabola can intersect 01234 infinitely many
Answers
Answer:
0, 1, 2
Step-by-step explanation:
There is a way for them to intersect at 0 points, for example y=x^2 and y = -1
The way to intersect at 1 point is for the linear function to be tangent to the parabola, like y = x^2 and y = 0
The way to intersect 2 points is just for the linear function to be a secant to the parabola, like y = x^2 and y = 1
Find the area of each triangle?
Answers
Area of triangle A = 1/2bh
= 1/2 x 6 x 4
= 3 x 4
= 12 units
Area of triangle B = 1/2bh
= 1/2 x 4 x 3
= 2 x 3
= 6 units
I will give brainiest to whoever answers correctly !!
Answers
Answer:
What is the question????
whats the opposite intger of 6.72
Answers
Answer:
-6.72 plzz mark me as Brainly
Step-by-step explanation: