Answer:
The domain of a function f(x) is the set of all values for which the function is defined, and the range of the function is the set of all values that f takes.
Step-by-step explanation:
given the function f(x)=-2x^4-16x^3-36x^2, determine all intervals on which f is both decreasing and concave down
Answer:
(0, ∞)
Step-by-step explanation:
The only maximum, local or otherwise, is at x=0. Since the leading coefficient is negative, the function is decreasing and concave down for x-values greater than 0.
0 < x < ∞ . . . . . decreasing and concave down
__
Since the leading coefficient of this even-degree function is negative, it will have a generally ∩ shape. It will be decreasing to the right of any local maximum.
The first derivative is negative only for x > 0, so that is the only region where the function is decreasing. Since that x=0 is a local maximum, the function must be concave downward in that neighborhood.
__
The attached graph shows the function and its first and second derivatives. The function is concave down where the second derivative is negative, to the right of the right-most point of inflection.
_____
Additional comment
A graphing calculator provides a quick answer to a question like this. You can find the same answer algebraically.
The first derivative is ...
f'(x) = -8x^3 -48x^2 -72x = -8x(x^2 +6x +9) = -8x(x+3)^2
This has a zero at x=-3 where the graph of it touches the x-axis, but does not change sign. That means f(x) has a flat spot at x=-3, but is not decreasing except to the right of x=0.
The second derivative is ...
f''(x) = -24x^2 -96x -72 = -24(x^2 +4x +3) = -24(x +1)(x +3)
The second derivative will be negative for x < -3 and x > -1, to the left and right of the points of inflection. This means f(x) is concave upward only for -3 < x < -1, and concave downward everywhere else.
The function is concave downward and decreasing for x > 0.
combine over common denominator 2/3a + 1/3 - 4/a
James is 5 ft. tall and casts a 6.5 ft. shadow. At the same time, a palm tree casts a 26 ft. shadow. How tall is the palm tree?
=====================================================
Work Shown:
(height)/(shadow length) = (height)/(shadow length)
(5 ft)/(6.5 ft) = (x ft)/(26 ft)
5/(6.5) = x/26
5*26 = 6.5*x
130 = 6.5x
6.5x = 130
x = 130/(6.5)
x = 20
The palm tree is 20 feet tall, which is the same height as a 2 story building (assuming each floor is 10 ft).
Jett leaves for the airport at 3:20 p.m. The airport is a 35-minute drive from his house. What time does he reach the airport?
Answer:
3:55
Step-by-step explanation:
add 35 to 20 then put the hour =
3:55
Which of the following are equivalent to the expression 9/4 ( 1.75 - 2 1/4)? Select all that apply.
A. -9/8
B. 1.6875
C. -2 1/4
D. 1 1/8
E. 7/4
F. -1.125
Answer:
9/4 (1.75 - 21/4)
=9/4 (1.75 - 5.25)
=2.25 -3.5
= -1.25
I think your f answer is wrong
there should be -1.25
Solve for y 8x - 7y = 23
[tex]8x - 7y = 23 \\ 8x - 23 = 7y \\y = \frac{8}{7} x - \frac{23}{7} [/tex]
The solution of the equation, when it is solved for y, has one variable term x with coefficient 8/7 and one constant term 23/7, 8/7x-23/7.
How to solve an equation for its variable?The solution of an equation is the value of the variable of the equation, for which the equation is satisfied.
To solve an equation for its variable, isolate the variable on one side of the equation using the mathematical operations.
The given expression is,
[tex]8x - 7y = 23[/tex]
The expression has two variables, x and y. To solve it for y, subtract 8x from both sides,
[tex]8x - 7y -8x= 23-8x\\-7y=23-8x[/tex]
Divide with number 7 both sides and change the sign of the equation,
[tex]y=-\left(\dfrac{23-8x}{7}\right)\\y=\dfrac{8x-23}{7}\\y=\dfrac{8}{7}x-\dfrac{23}{7}[/tex]
Thus, the solution of the equation, when it is solved for y, has one variable term x with coefficient 8/7 and one constant term 23/7, 8/7x-23/7.
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HELP what is the slope
Answer:
D
Step-by-step explanation:
The line starts at 10 so I think it's that
Answer:
Slope of a line
m = \frac{\text{rise}}{\text{run}} = \frac{y_2 - y_1}{x_2 - x_1}
m = slope
(x_1, y_1) = coordinates of first point in the line
(x_2, y_2) = coordinates of second point in the line
Step-by-step explanation:
Khan Academy
Slope review | Algebra (article) | Khan Academy
One gallon of gas costs $1.50. Three gallons of gas costs $4.50. How much will 9 gallons of gas cost?
Answer:
9 gallons will cost $13.50
Step-by-step explanation:
1 gallon = $1.50
1.50 x 9 = 13.50
or
3 gallons = $4.50
4.50 x 9 = 13.50
Answer:
13.5 dollars.
Step-by-step explanation:
4.50 times 3 is 13.5 dollars.
Have A Good Day!!! :)
Find values for a and b for which x = 4 is a solution of the equation shown.
ax + 4 = 5x + b
The values of a and be for which x = 4 is a solution of the equation shown.
ax + 4 = 5x + b are infinitely many
The given equation is:
ax + 4 = 5x + b
To find the values of a and b in the equation at x = 4, substitute x = 4 into the equation
4a + 4 = 5(4) + b
4a + 4 = 20 + b
Collect like terms
4a - b = 20 - 4
4a - b = 16
Since there are two unknowns in just a single equation, the equation has more than 1 solution.
The values of a and be for which x = 4 is a solution of the equation shown.
ax + 4 = 5x + b are infinitely many
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50 squared is rational
True
False
Answer:
false
Step-by-step explanation:
Answer:
A rational number can be written as a fraction. Try finding the square root of 50 and see if you can rewrite it in fraction form.
Step-by-step explanation:
[tex]\sqrt[n]{x} \\ x^{2} \sqrt[n]{x}[/tex]Ms. Sanchez is purchasing a car for $14,000. The tax rate in the state where she is buying the car is 7%. What is the total amount she will pay for the car including the tax?
Solve for x.
5.3>x+25
x>4910
x<5710
x<4910
x>5710
Answer:
x= < 4 9/10
Step-by-step explanation:
I hope this helps
Have a great and blessed day
Answer:
K12 Answer
Step-by-step explanation:
Tell whether the ordered pair is a solution to the equation please show how you solve it.
(3,2); x+6y = 13
Answer:
The ordered pair is not a solution as both sides of the equation do not equal each other.
Step-by-step explanation:
(3,2); x + 6y = 13
(3) + 6(2) = 13
3 + 12 = 13
15 = 13
sarah got a 80% on her pre algebra final exam. if there were 75 questions total how many did sarah get correc? How many did she get wrong? what percent did she get wrong?
HELP PLS
Answer: Sarah got 60 questions correct, 15 questions wrong, and she got 20% of the questions wrong.
Step-by-step explanation:
First, let's solve for how many questions Sarah got correct.
80% as a fraction can be simplified as [tex]\frac{8}{10}[/tex]. To find how many questions Sarah answered correctly, we can set up a proprtional relationship as follows:
[tex]\frac{8}{10}=\frac{?}{75}[/tex]
Next, after we cross multiply, 8 X 75 = 600, and 600 ÷ 10 = 60
So, Sarah got 60 out of 75 questions correct.
To find how many she missed, we can simply subtract 60 from 75 to get 15.
So, Sarah got 15 out of 75 questions wrong.
Finally, to find the percentage of the questions that Sarah got wrong, we can use the 15 out of 75 incorrect questions that we found earlier to create a percentage.
15 ÷ 75 = 0.2
0.2 X 100 = 20
So, Sarah got 20% of the questions wrong.
I need to know this give me answer
Answer:the answer is b 10/21
Step-by-step explanation:
Answer:
B) 10/21
Step-by-step explanation:
Keep, change, flip
keep 2/7, change to multiply, flip to 5/3
2/7 x 5/3 = 10/21
Hope this helps! Pls give brainliest!
Find the slope of the line.
Select the correct choice below and, if necessary, fill in the answer box to complete your choice.
O A. The slope of the line is
(Simplify your answer. Type an integer or a fraction.)
OB. The slope is undefined.
Answer:
sorry
for this answer
Labor unions arose in the nineteenth century as increasing numbers of Americans took jobs in factories, mines, and mills in the growing industrial economy.
The Knights of Labor, founded in 1869, was the first major labor organization in the United States. The Knights organized unskilled and skilled workers, campaigned for an eight hour workday, and aspired to form a cooperative society in which laborers owned the industries in which they worked.
The Knights’ membership collapsed following the 1886 Haymarket Square riot in Chicago. By 1886 the American Federation of Labor (AFL), an alliance of skilled workers’ trade unions, was growing.
a film start at 17:15 and finish at 1 hour and 45 minutes later. what time did it finish?
The total number of gallons of water in a tank, w, after t minutes is given in this table and the plot.
What is an equation showing the relationship between w and t?
Enter your answer by filling in the box to complete the equation.
w =
The equation showing the relationship between w and t is [tex]w = 4t[/tex]
From the table, we have the following points:
(0,0) and (1,4)
Start by calculating the slope (m)
[tex]m = \frac{y_2 -y_1}{x_2 -x_1}[/tex]
So, we have:
[tex]m = \frac{4 -0}{1 -0}[/tex]
Simplify the numerator and the denominator
[tex]m = \frac{4}{1}[/tex]
Divide 4 by 1
[tex]m = 4[/tex]
The equation is then calculated as:
[tex]w = m(t - t_1) + w_1[/tex]
This gives
[tex]w = 4(t - 0) + 0[/tex]
Simplify
[tex]w = 4t[/tex]
Hence, the equation is [tex]w = 4t[/tex]
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A line passes through (2, -1) and (4, 5).
-
Which answer is the equation of the line?
-3x+y=17
-3. + 5y = -13
-3x+y=-7
-3x+5y=13
Answer:
its c
Step-by-step explanation:
The sum of two numbers is 20. One number is 3 times the other number. Find the two numbers, show your work
Answer:
5 and 15
Step-by-step explanation:
20 = 3x+x
Answer: The smallest number is 20, and the largest number is 27. (27 - 20) + 1 = 8. Eight numbers make 4 pairs, and the sum of each pair is 47. 4 x 47 = 188. The sum of the numbers from 20 to 27 is 188.
The weight of a beaker is measured to be 78 grams, but the actual weight of the beaker is 82 grams. What is the approximate percent error in the measurement? A) 4% B) 5% C) 6% D) 7%
The approximate percentage error on the weight of the beaker is 5%
What is percentage error?Percent error is the difference between estimated value and the actual value in comparison to the actual value and is expressed as a percentage. In other words, the percent error is the relative error multiplied by 100.
Error = Actual value - estimated value =
Actual value = 82g, Estimated value = 78g
Error = 82 - 78 which is 4
percent error = error/estimated x 100%
percent error = 4/78 x 100 which is 5%
In conclusion the percent error is 5%
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Jackie likes coffee. She ________ about eight cups of coffee every day.
a-is drinking
b-drinks
c-is always drinking
d-drank
PLEASE HELP 60 POINTS
if l || m, find the value of x
Answer:
x = 15
Step-by-step explanation:
84 = 5x + 9
Subtract 9
75 = 5x
Divide by 5
x = 15
Answer:
x = 15
Step-by-step explanation:
5x + 9 and 84 are alternate angles and are congruent , so
5x + 9 = 84 ( subtract 9 from both sides )
5x = 75 ( divide both sides by 5 )
x = 15
HELP PLEASE ANYONE
Derrick has 3 times as many CDs as Joshua. Which equation compares the number of CDs that the two boys have? (Let d = number of Derrick's CDs and j = number of Joshua's CDs.) O A. 3d = j E ов O B. 3j = d c C. 3 + d = j OD. 3 + j = d
Answer:
b
Step-by-step explanation:
joshua times 3 is basically derrick's amount
so 3j = d
HELPPPPPP WIL GIVE BRANELISTTTT
Answer: i think the answer is B
Step-by-step explanation:
Write the equation of the line in fully simplified slope-intercept form
Answer:
y = -5/6x + 6
Step-by-step explanation:
Since we have 2 points, (6,0) and (6,1), we can calculate for the slope by using the formula
Slope = m = (y2 - y1)/(x2-x1) = (1-6)/(6-0) = -5/6
Then plug in m, x(from one of the point), and y(from one of the point) to the equation y = mx + b which get us 0 = -5/6*6+b if we use the point (6,0). Now we'll get b = 6. And then plug in -5/6 for m and 6 for b into the equation y = mx + b we'll get y = -5/6x + 6
I NEEEEED HELP AND QUICK T~T
Answer:
5. Alt ext, 6. Alt int, 7. Alt ext, 8, SS Int, 9. Corr
Step-by-step explanation:
5. Alternate exterior since they are on opposite sides of the transversal but both are exterior to parallel lines.
6. Alternate interior, opposite sides of transversal but both are inside the parallel lines.
7. Alternate exterior, same as #1
8. Same side interior since they are on the same side of the transversal and both are inside the parallel lines
9. Corresponding since they are at the same place on the 2 parallel lines.
For any number n>1, is
п
2 3
+ i
3
4
a. Greater than 1?
b. Less than 1?
C. Equal to 1?
A because the > symbol means greater so if n is on the open side that means its greater
~Shoto Todoroki here~
its option A
i figured this out by trial and error :/
have a good day!
Which is the best example of a down payment?
A. Margo leases an apartment and pays $500 cash as a security deposit when she moves in.
B. Robby pays 10 percent cash up front and gets a loan for the
remaining 90 percent of the cost of a condominium.
C. Billy orders a piano, pays half the cost up front, and has to pay the other half when the piano is delivered.
D. Jan signs a cell phone plan that includes a little of the cost of her new phone as part of her bill every month.
The best example of a down payment is given as follows:
C. Billy orders a piano, pays half the cost up front, and has to pay the other half when the piano is delivered.
What is the down payment of a purchase?The down payment of a purchase is when a part of the purchase is paid when the purchase is made, and the other part(subjected to interest or not), is paid later.
In this problem, the example of a down payment is given by option C.
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Answer:
B. Robby pays 10 percent cash up front and gets a loan for the remaining 90 percent of the cost of a condominium
Step-by-step explanation:
i just did it
In this diagram, lines AC and DE are parallel and line DC is perpendicular to each of them. What is a reasonable estimate for the length of side DE
The reasonable estimate for the length of side DE is 3 units
Find the diagram of the question attached. The given triangle ABC and BDE are similar triangles.
Using the similarity theorem of a triangle, this is expressed as:
AC = DE
Using the pythagoras theorem to get the length of AC:
AB^2 = AC^2 + BC^2
5^2 + AC^2 + 4^2
AC^2 = 25 - 16
AC^2 = 9
AC= 3
Since AC = DE, hence the reasonable estimate for the length of side DE is 3 units
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Answer:
5/3
Step-by-step explanation: