On which interval(s) is the function f(x) = x3+3x^2−4x−12 increasing?
The intervals over which the function is increasing are -
x ∈ (- ∞, - 2.5) and x ∈ (0.5, ∞). We can write it as one single set (S) as -
S = (- ∞, - 2.5) ∪ (0.5, ∞).
What is increasing or decreasing interval of a function?The interval in which the y - coordinate of the points gets larger, or the graph gets higher as it moves from left to right over the interval is called increasing interval. Similarly, the interval in which the y - coordinate of the points gets smaller or the graph gets lower as it moves from left to right over the interval is called decreasing interval.
Given is the following function f(x) -
f(x) = x³ + 3x² - 4x - 12
First, we will plot the graph of this function. The graph is attached with the answer. On the graph, there are two black dots. From the definition of increasing functions, we know that the interval along which the y - coordinate gets larger is called increasing interval of the function. The first interval over which the function is increasing is- x ∈ (- ∞, - 2.5). The second interval over which the function is increasing is- x ∈ (0.5, ∞).
Therefore, the intervals over which the function is increasing are -
x ∈ (- ∞, - 2.5) and x ∈ (0.5, ∞). We can write it as one single set (S) as -
S = (- ∞, - 2.5) ∪ (0.5, ∞).
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6-2d=42
What is D please help me find what it is
Answer: -18
Step-by-step explanation:
if 6-2d=42
just subtract 6 from both sides
-2d=42-6
-2d=36 now divide by 2
-d=18
multiply by -1
d=-18
Answer: d=-18
Step-by-step explanation:
6-2d=42
First subtract 6 from both sides
-2d=36
Now divide both sides by -2 to get d alone
d=-18
Sam does 11 jumping jacks in 8 seconds. If he does the jumping jacks at a constant rate, how many jumping jacks can he do in 20 seconds?
Answer:
baila como juana la cubana
Step-by-step explanation:
. What is the mode of the data set below? 5, 4, 0, 1, 1, 0, 2, 2, 3, 1, 0, 4, 1, 1, 5, 2, 4 (1 point) 0 1 2 3
The mode of the given data set is 1.
The given data set is 5, 4, 0, 1, 1, 0, 2, 2, 3, 1, 0, 4, 1, 1, 5, 2, 4, 0, 1, 2, 3.
We need to find the mode of the given data set.
What is the mode?The mode is the value that appears most frequently in a data set. A set of data may have one mode, more than one mode, or no mode at all.
The order of the given data set is
0, 0, 0, 0, 1, 1, 1, 1, 1, 1, 2, 2, 2, 2, 3, 3, 4, 4, 4, 5, and 5.
Here, mode=1 (appear 6 times)
Therefore, the mode of the given data set is 1.
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4x+3=8x-9 what does x equal
Answer:
x=75/4
Step-by-step explanation:
4x+3=8x-9
4x+3= -72
4x= -72-3
4x= -75
x=75/4
Choose True or False for each equation for x = 6.
6x = 12
5 + x = 11
x ÷ 2 = 3
17 – x = 11
Answer:
false true true true
Step-by-step explanation:
The equation for x = 6 is true and would be equal to 6x = 12. and the rest are false.
What does it mean to solve an equation?An equation represents the equality of two or more mathematical expressions. When someone asks you to solve an equation, then they usually mean to find the values of the unknowns for which that equation would be true (the equality between expressions should hold for those values). Solutions to an equation are those values of the variables involved in that equation for which the equation is true.
The given equations are;
6x = 12
Substitute x = 6 to check whether the solution satisfies the equation;
6(6) = 36
Thus, it is False.
5 + x = 11
Substitute x = 6 to check whether the solution satisfies the equation;
5 + x = 11
5+ 6 = 11
Thus, it is True.
x ÷ 2 = 3
Substitute x = 6 to check whether the solution satisfies the equation;
6/2 = 3
Thus, it is True.
17 – x = 11
Substitute x = 6 to check whether the solution satisfies the equation;
17 - 6 = 11
Thus, it is True.
Hence, the equation for x = 6 is true and would be equal to 6x = 12. and the rest are false.
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find the point of inflexion for the function f(x)=x^4-6x^2
The points of inflection for the function [f(x) = (x⁴ - 6x²)] are (1, -5) and
(-1, -5).
As per the question statement, we are provided with a function
[f(x) = (x⁴ - 6x²)].
We are required to determine the points of inflection for the above mentioned function.
To solve this question, we will have to calculate the second derivative of the given function. Then, we will have to equate the derivative to zero and solve for x. The obtained values for "x" will be our abscissa, and substituting these values of "x" in f(x), we will obtain our respective ordinates [Since, {y = f(x)}].
[tex]f(x)=(x^{4} -6x^{2})\\or,\frac{d[f(x)}{dx} = \frac{d(x^{4} -6x^{2}) }{dx}\\ or, f'(x)=\frac{dx^{4}}{dx}-\frac{d(6x^{2})}{dx}\\ or, f'(x)=\frac{dx^{4}}{dx}-6\frac{d(x^{2})}{dx}\\or, f'(x)=4x^{(4-1)}-(6*2)[x^{(2-1)}]\\ or,f'(x)=4x^{3}-12x\\[/tex]
Therefore, the second derivative of f(x) = [tex]\frac{d^{2}f(x)}{dx^{2} }[/tex]
[tex]or,f"(x)=\frac{d[f'(x)]}{dx}\\or,f"(x)=\frac{d(4x^{3} -12x)}{dx}\\or, f"(x)=\frac{d(4x^{3}) }{dx}-\frac{d(12x)}{dx}\\ or, f"(x)=4\frac{d(x^{3}) }{dx}-12\frac{d(x)}{dx}\\or,f"(x)=(4*3)[x^{(3-1)}]-(12*1)[x^{(1-1)}]\\ or, f"(x)=12x^{2} -12[/tex]
Now, equating (12x² - 12) to Zero, we get,
[tex](12x^{2} -12)=0\\or,12x^{2} =12\\or,x^{2} =1\\or,x=(1, -1)[/tex]
Now, substituting (x = 1) in f(x), we get,
[tex]y=f(1)=[(1)^{4}-6(1)^{2}]\\ or,y=[1-(6*1)]\\or,y=(1-6)\\or,y=(-5)[/tex]
Hence, one point of inflection for the function [f(x) = (x⁴ - 6x²)] is (1, -5).
Again, substituting [x = (-1)] in f(x), we get,
[tex]y=f(-1)=[(-1)^{4}-6(-1)^{2}]\\ or,y=[1-(6*1)]\\or,y=(1-6)\\or,y=(-5)[/tex]
That is, another point of inflection for the function
[f(x) = (x⁴ - 6x²)] is (-1, -5).
Inflection Point (Of a Function): In differential calculus and differential geometry, an inflection point, point of inflection or flex, is that point on a smooth plane curve at which the curvature changes its concavity i.e. from being "concave up" to being "concave down" or vice versa, or if stated in simpler terms, that point where the curve changes its sign.To learn more about Points of Inflection, click on the link below.
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Kathy bought a pair of jeans on sale for 30% off of the regular price. If the jeans regularly cost $75.00, how much did she pay?
Answer:
$22.50
Step-by-step explanation:
15 POINTS
write an equation un point slope form for the line through the gives point with the given slope.
(-3,4);m=2/3
a. y+3=2/3(x-50
b. y+5=(2/3)(x+3)
c. y-5=2/3(x-3)
d. y-5=2/3(x+3)
To find the answer, all we need to do is plug in the slope and point they gave us into the Point Slope Formula!
The point slope formula is ...
[tex]y - y_{1} = m ( x - x_{1} )[/tex]
So lets put them in!
y - 4 = 2/3 (x - (-3))
Tip: remember when you subtract a negative number, it turns into adding !
So our final answer is probably D (I think you may have put a typo)
[tex]y - 4 = \frac{2}{3} (x + 3)[/tex]
The stemplot displays 26 students’ scores on a 90-point statistics test.
A stemplot titled Test scores has values 43, 45, 46, 51, 52, 53, 55, 57, 60, 63, 63, 65, 66, 67, 67, 69, 69, 71, 71, 72, 74, 76, 77, 79, 84, 85.
Which of the following best describes the center and variability of the distribution?
The scores on the test are centered around 63 and vary from 45 to 85.
The scores on the test are centered around 66 and vary from 43 to 85.
The scores on the test are centered around 66 and vary from 40 to 80.
The scores on the test are centered around 69 and vary from 45 to 85.
The scores on the test are centered around 66 and vary from 43 to 85.
What is the center and variability of the dataset?A stemplot is a type of table where figures are divided into a stem and a leaf. The stem is the first number in the digit while the leaf is the last number. For example in the number 31, 3 would be the stem and 1 would be the leaf.
The range is used to measure variation. The range is the difference between the highest number and the smallest number. The largest number is 85 and the smallest number is 43.
The data would be centered around the median. The median is the number at the center of a dataset. The median is a measure of central tendency.
Median = (sum of numbers + 1) / 2
(26 + 1) / 2
= 27 / 2 = 13.5th number
(66 + 67) / 2 = 66.5
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Min saved 334 pennies. Rami saved 6 times as many pennies as Min.
How many pennies did Rami save?
Answer: Rami saved 2004 pennies
Step-by-step explanation:
PLZ HELP ME WITH THIS I BEG OF YOU PLZ?!?!
Expand and simplify , 4(x+3)^2-3(x+4)(x-4)
Answer:
x² + 24x + 84
Step-by-step explanation:
4 * (x+3)(x+3) - 3 * (x+4)(x-4)
4(x²+6x+9) - 3(x²-16)
4x² + 24x + 36 - 3x² + 48
x² + 24x - 84
1/4 plus 1/5 plus 11/12
Answer:
41/30
Step-by-step explanation:
5(2x-10)-3(2x-10)=4 what is x????? helpppp
Answer:
x = 6
Step-by-step explanation: (See picture)
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Hope this helps!
Have a great day and God bless! :)
Mrs. Jones wants to make cookies.
She can make chocolate, vanilla, butter, or oatmeal cookies.
She will add either chocolate chips, nuts, or raisins.
How many different types of cookies can Mrs. Jones make?
Answer:
16
Step-by-step explanation:
A school carnival sold tickets to ride on a Ferris wheel. The charge was $3.00 for adults and $2.00 for students. If 54 tickets were sold for a total of $141.00, how many adult tickets were sold?
Answer:
33 adult tickets and 21 student tickets
Step-by-step explanation:
We will create a system of equations.
Let x = the number of adult tickets sold and let y = the number of student tickets sold
x + y = 54
3x + 2y = 141
We can cancel out the y by multiplying the first equation by -2.
-2x - 2y = -108
3x + 2y = 141
Adding these equations together we get:
x = 33
Plugging this into the equation, we have:
38 + y = 54
y = 21
There were 33 adult tickets and 21 student tickets
If f(x)=2x and g(x)=x−3, then find f(x)·g(x).
Question 19 options:
2x2−6x
2x2−6
2x2−3
3x−3
Answer:
f(x)g(x) = 2x² - 6x
General Formulas and Concepts:
Algebra I
Expand by FOIL-ing (First, Outside, Inside, Last)Step-by-step explanation:
Step 1: Define
f(x) = 2x
g(x) = x - 3
Step 2: Find f(x)g(x)
Substitute: f(x)g(x) = 2x(x - 3)Distribute 2x: f(x)g(x) = 2x² - 6xI need help PLEASE
I’m confused, is 1/52 and 52/1 the same?
Answer: No
Step-by-step explanation:
Because 52/1 is just plain 52
But 1/52 is one thing out of 52 of them.
So 52/1 is just the number 52 versus 1/52 is one of fifty-two.
Answer:
Yes, 1/52 is the same as 52/1 because 52/1 is the inversed fraction of 1/52. Inversed fractions is a fraction with the denominator and numerator swapped.
Step-by-step explanation:
Hope this helped and please tell me if I'm incorrect :)
I WILL GIVE BRAIN THING
Use algebra tiles to model the expression and combine like terms. Complete the statements. x + x + x + x + 4 – 1 Combine the x tiles to get . Combine the integer tiles to get . The equivalent expression is . You can use to verify the expressions are equivalent.
Answer:
1) Combine the x tiles to get: [tex]\mathbf{4x}[/tex]
2) Combine integer tiles to get: 3
3) The equivalent function is: [tex]\mathbf{4x+3}[/tex]
4) If we Substitute any value of x both expressions will be equivalent
Step-by-step explanation:
We are given expression: [tex]x+x+x+x++4-1\\[/tex]
We need to complete following statements.
1) Combine the x tiles to get:
[tex]x+x+x+x\\=4x[/tex]
Combine the x tiles to get: [tex]\mathbf{4x}[/tex]
2) Combine integer tiles to get:
[tex]+4-1\\=3[/tex]
Combine integer tiles to get: 3
3) The equivalent function is:
[tex]x+x+x+x++4-1\\\\4x+3[/tex]
The equivalent function is: [tex]\mathbf{4x+3}[/tex]
4) If we Substitute any value of x both expressions will be equivalent
Verifying:
[tex]x+x+x+x+4-1=4x+3\\Let\: x = 1\\1+1+1+1+4-1=4(1)+3\\4+4-1=4+3\\7=7[/tex]
So, Both expressions are equivalent.
The answer is "4x" for the first box
"3" for the second box
"4x + 3" for the third box
And "Substitution" for the last box
You're Welcome!
PS: I want to thank the first person for answering, you are amazing,
thanks!
Which of the following can be used as "reasons" in a two-column proof?
given
inductive reasoning
definitions
algebraic properties
Answer:
Algebraic properties can be used as "reasons" in a two-column proof.
Step-by-step explanation:
Algebraic properties can be used as "reasons" in a two-column proof.Let's take an example:
Given: F = 9/5C + 32
Prove: C = 5/9(F-32)
Statements Reasons
1) F = 9/5C + 32 1) Given
2) F-32 = 9/5C 2) subtraction
3) 5/9(F-32) = C 3) multiplication
4) C = 5/9(F-32) 4) symmetric property
Therefore, we conclude that Algebraic properties can be used as "reasons" in a two-column proof.
15
A researcher wants to determine if the behavior of children is alle
video games that have violent content. He asks the parents of 100 children in a
day care center how often each child plays video games and whether the video
games they play have violent content. The children are then allowed to play in
a controlled environment, such as the day care center's playground. Any violent
behaviors are then noted.
What type of study is the researcher conducting?
A. census
B. experiment
C. observational study
D. sample survey
Answer:
hey ok
Step-by-step explanation:
a
2(7m−5)+(−8+9m)=?
Does anybody know what the answer to this question is?
If you know, please tell me. I'm really in a hurry.
Answer:
23m-18
Step-by-step explanation:
2(7m−5)+(−8+9m)
Remove parenthesis
2(7m-5)-8+9m
expand
14m-10
14m-10-8+9
simplify
23m-18
Ask me for more questions brainliest please.
Solve by graphing
y+5 = 2x
3y + 6x = -3
Answer:
(1, -3)
Step-by-step explanation:
Use Desmos! It's really useful.
some two step equations can be written in the form ax+b=c where a b and c are constants and x is the varible A. write the equation ax+b=c in terms of x B use the formula to solve 3x+7=19 and 1/2x - =5
A. The equation for x is c - b/a
B. x = 4
x = 10
How to determine the equationGiven the equation;
ax + b = c
Let's make 'x' the subject of formula by expressing it in terms of other variables
We have;
ax = c - b
Divide both sides by the coefficient of 'x'
ax/a = c - b/ a
x = c - b/a
B. 3x + 7 = 19
Let's solve for x
3x = 19 - 7
3x = 12
Make 'x' the subject
x = 12/ 3
x = 4
1/2x = 5
cross multiply
x = 5 × 2
x = 10
Thus, the equation for x is c - b/a
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Davita jogs 2000 feet in four minutes. At this rate, how many feet can she jog in eight minutes?
Answer:
In 8 minutes, she can jog 4000 feet.
Step-by-step explanation:
Davita jogs 2000 feet in 4 minutes.
Her rate is 2000/4 or 500 feet per minute.
500*8 = 4000
A wall is 412 feet long and has an area of 1534 square feet. What is its height in feet?
Answer:
3.72 ft
Step-by-step explanation:
Height of the wall will be equal to the width of the wall because we are considering over surface area of the wall
Therefore,
Area of the wall = length * height
1534 = 412 * height
Height = 1534/412
Height = 3.72 ft
Find the value of a?
A) 3
B) 4
C) 6
D) 9
Answer:
3
Step-by-step explanation:
Every Sunday, Chase and his friends get together to play their favorite board game, The Gems of Rawumba. Whoever collects the most gems wins! Players can earn gems by building mines.
There is a proportional relationship between the number of mines Chase builds, x, and the number of gems he earns, y.
x (mines) y (gems)
1 4
4 16
8 32
9 36
What is the constant of proportionality? Write your answer as a whole number or decimal.
The constant of proportionality is 4, while the equation is given as y = 4x.
What is an equation?An equation is an expression that shows the relationship between two or more numbers and variables.
A variable can either be dependent or independent. A dependent variable depend on other variable while an independent variable does not depend on other variables.
Let x represent number of mines and y represent the number of gems. Since this is a proportional relationship, hence:
y = kx; where k is the constant of proportionality
From the table when y = 4, x = 1, hence:
4 = k(1)
k = 4
y = 4x
The constant of proportionality is 4, while the equation is given as y = 4x.
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