On which interval(s) is the function f(x) = x3+3x^2−4x−12 increasing?
Answers
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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Related Questions
Angie and her family ordered a meal that cost $80. Angie paid 10% sales tax and left a 15% tip on $80. What was the total cost?
Answers
Answer:
100
Step-by-step explanation:
meal costs 80 dollars
ok
Angie paid 10%
ok
left 15% tip
ok
Ok so let's solve
80/100=0.8
now mutiply by 10
8
she paid 8$ sales tax
now get 0.8*15
12
she paid 12$ tip
total have to add now
12+8+80=100
Hope this helps
What is the perimeter of a triangle if two of its sides measure 6 in. and the other side
measures 7 in. ?
Answers
The perimeter of the triangle if its two sides measure 6 inches and the other side measures 7 inches will be 19 inches.
According to the given question.
The measure of the two sides of a triange is 6inches each.
And the measure of the other side is 7 inches.
As we know that,a perimeter is a closed path that encompasses, surrounds, or outlines either a two dimensional shape or a one-dimensional length or the perimeter of a shape is defined as the total length of its boundary.
Thereofre, the perimeter of the triangle if its two sides measure 6 inches and the other side measures 7 inches
= 6 inches + 6 inches + 7 inches
= 19 inches
Hence, the perimeter of the triangle if its two sides measure 6 inches and the other side measures 7 inches will be 19 inches.
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The weights of a certain dog breed are approximately normally distributed with a mean of = 49 pounds, and a standard deviation of = 6 pounds.
a. A dog of this breed weighs 54 pounds. What is the dog's z-score? Round your answer
to the nearest hundredth as needed.
b. A dog has a z-score of 0.94. What is the dog's weight? Round your answer to the
nearest tenth as needed.
c. A dog has a z-score of -0.94. What is the dog's weight? Round your answer to the
nearest tenth as needed
Answers
Answer:
A
Step-by-step explanation:
hoped it worked
If Frank builds a concrete rectangular walkway that is 4 feet wide by 1.5 feet deep, by 20 feet long from the house to the storage shed, what is the volume of concrete used to pave the walkway?
Feet Cubed
Answers
Answer:
120 ft
Step-by-step explanation:
Please review the full explanation below
Answer:
........................................................................................
Step-by-step explanation:
the lowest common denominator of 3/4, 4/5 and 2/3 is
Answers
Answer:
The Answer Is 60
Answer:
60
Step-by-step explanation:
4 8 12 16 20 24 28 32 36 40 44 48 52 56 60
5 10 15 20 25 30 35 40 45 50 55 60
3 6 9 12 15 18 21 24 27 30 33 36 39 42 45 48 51 54 57 60
The odds against Ishaq getting hired for a job are 17:18. Determine the probability
(a) Ishaq gets hired.
(b) Ishaq does not get hired.
Answers
Answer:
The odds against Ishaq getting hired are 17:18
This means that are 17 scenarios where Ishaq does not get hired, out of 18 total scenarios.
This means that the left scenario is when Ishaq gets hired, then the odds of Ishaq getting hired is equal to 1:18.
a) We want to find the probability that Ishaq gets hired.
This will be equal to the quotient between the number of scenarios where Ishaq gets hired (1) and the total number of scenarios (18).
Then this probability is
P = 1/18 = 0.056
b) We want to find the probability where Ishaq does not get hired, we can use the same reasoning as above, this time we will take the quotient between the number of scenarios where Ishaq does not get hired (17) and the total number of scenarios (18).
P = 17/18 = 0.944
1 triangle ABC was dilated by a scale factor of 2 centered at the origin of the result was as image of triangle A'B'C shown on the coordinate plane below the vertices of triangle A'b'c' are -4,4 -4,6 and 2,4 what are the coordinates of the vertices ABC
Answers
Answer:
The coordinates of ABC are respectively (-2,2), (-2,3), and (1,2).
Step-by-step explanation:
Dilation About the Origin
Given a point P(x,y), its dilation about the origin by a scale factor of k maps the point to a point P'(kx,ky).
If we are given the dilated point, then we can find the original point by dividing by the scale factor.
Triangle ABC was dilated by a scale factor of 2 about the origin mapping it to triangle A'B'C' with vertices A'(-4,4), B'(-4,6), and C(2,4).
The coordinates of triangle ABC are:
A=(-4/2,4/2) = (-2,2)
B=(-4/2,6/2) = (-2,3)
C=(2/2,4/2) = (1,2)
The coordinates of ABC are respectively (-2,2), (-2,3), and (1,2).
Answer:
The coordinates of ABC are (-2,2), (-2,3), and (1,2).
Step-by-step explanation:
four students set up a lemonade stand at the neighborhood park at the end of the summer their profit is $1752 how much money do they each have when the profit is split equally
Answers
Answer:
1752 ÷ 4 = 438
$438 is your answer
A parking lot has 27 empty spaces. If the ratio of empty spaces to taken spaces is 3:5, how many spaces are there total?
Answers
Answer:
There are 72 spaces
Step-by-step explanation:
You would first have to do 27/3, which shows what 1/5 is. This would get you 9, then multiply that by 5 to find the amount of taken spaces. Add 27 and 45 to get 72 spaces.
Answer:
72 spaces in total
Step-by-step explanation:
If there are 27 empty spaces in a 3:5 ratio, that means that for every 3 spaces that are empty, there are 5 that are taken. We notice that there are 9 times of 3 spaces that are empty, so we must multiply 9 by 5 to get 45 spaces that are taken. We then add these up to get the total amount of spaces 27 + 45 = 72 spaces
One side of a rectangle is 7 millimeters shorter than twice another side. Find the length of the longer side if we also know that the perimeter of the rectangle is 70 millimeters.
Answers
Answer:
What are the outstanding traditional Chinese culture? Calligraphy, Chinese knot, Peking Opera facial makeup, shadow play, martial arts, the Terra Cotta Warriors, jade carving, oracle, four treasures, flute, zither, pipa, longfeng pattern, painted pottery, traditional Chinese painting, modest, courteous and simple basic spirit of Chinese traditional culture" The basic spirit of Chinese traditional culture, in essence, is the national spirit of the Chinese nation.
A jeweler makes an ocean-inspired necklace using a total of 60 snails shells and shark teeth. The ratio of snail shells to shark teeth is 5:1. How many snail shells does he use?
Please help fast
Answers
Given that,
Total number of snails shells and shark teeth = 60
The ratio of snail shells to shark teeth is 5:1
To find,
Total no of snail shells used by the Jeweler.
Solution,
Let there are 5x snail shells and x shark shells.
According to question,
5x+x = 60
6x = 60
x = 10
Snail shell = 5x
= 5(10)
= 50
Hence, he uses 50 snail shells.
Use the given information to find the minimum sample size required to estimate an unknown population mean mu. How many students must be randomly selected to estimate the mean weekly earnings of students at one college? We want 95% confidence that the sample mean is within $2 of the population mean, and the population standard deviation is known to be $99.
A) 8296
B) 6630
C) 9413
D) 13,302
Answers
Answer:
9413
Step-by-step explanation:
Given that :
Error = $2 ; Standard deviation (σ) =99 ; α = 95% = 0.95
Zα/2 = Z0. 05/2 = 1.96 (Z probability calculator)...
n = sample size
Recall:
n = ((Zα/2 * σ) / Error)^2
Using the formular above, the sample size n can be obtained ;
n = ((1.96 * 99) / 2)^2
n = 97.02^2
n = 9412.8804
n = 9413
True or False
Reject the null hypothesis if the p-value is more than the significance level, a.
Answers
Answer:
true
Step-by-step explanation:
Reject the null hypothesis if the p-value is more than the significance level, a.
Determine whether the triangle with the given side lengths is acute, right, obtuse or not a triangle; 21, 28, 25
A. acute
B. right
C. obtuse
D. not a triangle
Answers
Answer:
a
Step-by-step explanation:
acute
find the value of x
a. 68
b. 44
c. 56
d. 22
Answers
Answer: x=68° because this triangle is a isoscele triangle which means that it haves 2 sides that are congruent and equivalent which means they have the same value and sides and are Congruent just means In geometry, two figures or objects are congruent if they have the same shape and size, or if one has the same shape and size as the mirror image of the other.
The value of angle [x] is equivalent to 44°.
What is Parallelogram? What is triangle? What is a expression? What is a mathematical equation?In Euclidean geometry, a parallelogram is a simple quadrilateral with two pairs of parallel sides. The opposite or facing sides of a parallelogram are of equal length and the opposite angles of a parallelogram are of equal measure.A triangle is a polygon with three edges and three vertices. The sum of all the angles of a triangle is 180 degrees. Mathematically - ∠x + ∠y + ∠z = 180°There are different types of triangles such as - equilateral triangle , scalene triangle , isosceles triangle etc.A mathematical expression is made up of terms (constants and variables) separated by mathematical operators. A mathematical equation is used to equate two expressions.We have a triangle as shown.
We know, the angles opposite to equal sides are equal.
So, we can write -
x + 68° + 68° = 180°
x = 180° - (136°)
x = 44°
Therefore, the value of angle [x] is equivalent to 44°.
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A small garden has an area of 25 square yards. How long is each side of the garden? *
Answers
Answer:
5
Step-by-step explanation:
which question can be answered by finding 3 1/2÷1/4?
Answers
Answer: 14
Step-by-step explanation:
3 1/2÷1/4=
3 1/2*4= ==> dividing by fractions is basically multiplying by the reciprocals of the fraction
(3+1/2)*4=
3*4+1/2 * 4=
12+2=14
Answer:
3 1/2÷1/4 = 14
Step-by-step explanation:
Divide 3 x 2 + 1 / 1 by 1 / 4 by multiplying 3 x 2 + 1 / 1 by the reciprocal of 1/4
Multiply 3 and 2 to get 6
Add 6 and 1 to get 7
Multiply 7 and 4 to get 28
Divide 28 by 2 to get 14
answer = 14
1. Explain how to determine the equation of the function with
the following zeros. Be sure to explain each step as you show
how to determine the equation.
-5 multiplicity 2
-2 multiplicity 1
Answers
Answer:
[tex]P(x)=x^3+12x^2+45x+50[/tex]
Step-by-step explanation:
Roots of a polynomial
If we know the roots of a polynomial, say x1,x2,x3,...,xn, we can construct the polynomial using the formula
[tex]P(x)=a(x-x_1)(x-x_2)(x-x_3)...(x-x_n)[/tex]
Where a is an arbitrary constant.
We are given the following roots:
-5 multiplicity 2 (-5 twice)
-2 multiplicity 1
Thus, the polynomial is:
[tex]P(x)=a(x-(-5))(x-(-5))(x-(-2))[/tex]
[tex]P(x)=a(x+5)(x+5)(x+2)[/tex]
We are not given any clue about the value of a, so we choose a=1. Multiplying:
[tex]P(x)=(x^2+5x+5x+25)(x+2)=(x^2+10x+25)(x+2)[/tex]
[tex]P(x)=x^3+2x^2+10x^2+20x+25x+50[/tex]
Simplifying:
[tex]\mathbf{P(x)=x^3+12x^2+45x+50}[/tex]
An experiment involving learning in animals requires placing white mice and rabbits
into separate, controlled environments, the environment I and environment II.
The maximum amount of time available in the environment I is 500 minutes, and the maximum
amount of time available in environment II is 600 minutes.
The white mice must spend 10 minutes in environment I and 25 minutes in environment II, and
the rabbits must spend 15 minutes in environment I and 15 minutes in environment II. Identify which set of constraints and objective function is correct? x=white mice and y=rabbits
Answers
Answer:
Kk Kkkkkkkkkkkkkkkkkkkkkkkkkkkkkkkkkkk
Following are the calculation to the given question:
Suppose x represents a number of white mice while y denotes the number of bunnies.10 minutes is the time needed by mice in habitat 1.15 minutes is indeed the time required by the rabbit in habitat 1.Overall time needed [tex]= 10x + 15y[/tex]In environment 1, the maximum allowed time is 500 minutes.[tex]\bold{10 x +15y \leq 500}[/tex]
Likewise,
Mice need 25 minutes in environment 2 to complete their tasks.15 minutes is indeed the time taken by a rabbit in environment 2.Overall time needed [tex]= 25x + 15y[/tex]In environment 2, the maximum amount of time accessible is 600 minutes.Hence, the answer is " [tex]\bold{25x +15y \leq 600}[/tex]".
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Five times the difference of a number and 7.
Answers
Answer:
Hello.
5(x-7)
5x-35
The equation is 5x-35.
Step-by-step explanation:
What is 3 and 4/5÷2/5 in the simplest form
Answers
Answer:
The answer is 19/2.
Step-by-step explanation:
Alternatives are 9 1/2 and 9.5.
Brainliest? Thanks!
Answer:
3 and 2/5
Step-by-step explanation:
because when it says divide it means take away and the denominator is the same so it stays the same
Divide the fractions: 20 divided by 15/16 =
Answers
Final Answer:
[tex]\frac{64}{3}[/tex]
Step-by-step explanation:
20 ÷ [tex]\frac{15}{16}[/tex]
[tex]\frac{20}{1}[/tex] ÷ [tex]\frac{15}{16}[/tex]
(reciprocal method):
[tex]\frac{20}{1}[/tex] ÷ [tex]\frac{16}{15}[/tex]
(change the operation to multiplication)
[tex]\frac{20}{1}[/tex] × [tex]\frac{16}{15}[/tex] = [tex]\frac{320}{15\\}[/tex] (multiply, then reduce)
64/3 ⇒ 64/3
The value of x in the expression 20 divided by 15/16 will be 21.33 .
Given , 20 divided by 15/16
Division property:
The rules for division are:
(1) positive ÷ positive = positive
(2) positive ÷ negative = negative
(3) negative or ÷ negative = positive
Here both the numbers are positive. Apply rule 1.
20 divided by 15/16
[tex]\frac{20}{\frac{15}{16} }[/tex]
= [tex]\frac{20 \times 16}{15}[/tex]
= 21.33
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Write an equation for each line (L,P ,N,M)
Answers
Answer:
LP = NM
Step-by-step explanation:
Answer:
Please post the graph with the line!
Original: $0.95, Markup: 60%
Answers
Answer:
$0.57
Step-by-step explanation:
.95 x .60 = .57
The store is selling lemons at $0.66 each. Each lemon yields about 2 tablespoons of juice. How much will it cost to buy enough lemons to make three 9-inch lemon pies, each requiring half a cup of lemon juice?
Answers
Answer:
$7.92
Step-by-step explanation:
Need help with 5 and 6 first one to answer gets brainliest
Answers
Answer:
5) 1
6) 131
Step-by-step explanation:
5)
f(1) = -1 - 8 = -9
-9 + 10 = 1
6)
g(-9) = [tex]9^{2}[/tex] + 8(9) - 15 = 138
138 - 7 = 131
Answer:
Step-by-step explanation:
5.
f(x) = -x -8
substitute x with 1 in the equation of f(x)
f(1) +10 = -1 -8 +10 = -9 +10 = 1
6.
g(x)= x²+8x -15
g(-9) -7 = (-9)²+8(-9) -15 -7 = 81 -72 -22 = 81 - 94 = -13
Abram and Fred leave opposite ends of a bike trail 12 miles apart and travel toward each other. Abram is traveling 8 mph faster than Fred. Find each of their speeds if they meet after 30 minutes.
Answers
Find the length x.
5
X
45
PLS THIS IS ERGENT
Answers
Answer:
X = 7.5
Step-by-step explanation:
First, divide 5 by 3 to find the scale factor:
5/3 = 1.667
Now, multiply 4.5 by 1.667 to find x:
x = (4.5)(1.667)
x = 7.5
Therefore, x is equal to 7.5.
I hope this helps!!
- Kay :)
I GIVE BRAINLILEST
Sidney's office recycled a total of 32 kilograms of paper over 4 weeks. After 12 weeks, how many kilograms of paper will Sidney's office have recycled? Assume the relationship is directly proportional.
Answers
Answer:
96 kilograms
Step-by-step explanation:
32x3=96 just trust me I don'T know how to explain
Dillon made $27 in interest by placing $300 in a savings account with simple interest for 1
year. What was the interest rate?
Use the formula 1 = prt, where I is the interest earned, p is the principal (starting amount),
is the interest rate expressed as a decimal, and t is the time in years,
%
Answers
Answer:
59% or 59
Step-by-step explanation: