Answers
Answer:
Function maximum of 7 at x = - 3Function minimum of - 1 at x = 5The function is increasing on the intervals:- ∞ < x ≤ -3 and 5 ≤ x < ∞
The function is decreasing on the intervals:
-3 ≤ x ≤ 5The domain of the function is - ∞ < x < ∞
The range of the function is also - ∞ < f(x)< ∞
Step-by-step explanation:
Function maximum
Related Questions
Tommy had a bag of 100 balloons. He took out 2 red balloons and 1 blue baloon for each party favor. He created 12 party favors. How many balloons did Tommy have left?
Answers
3x12=36
100-36=64
Ans.= 64balloons
need help with this what is it asking exactly? wouldnt the square root of x^2 be x
Answers
I suppose you're given [tex]f(x) = x^2 + 2[/tex], which would mean [tex]f^{-1}(x) = \sqrt{x-2}[/tex]. Then
[tex]f^{-1}(f(x)) = f^{-1}(x^2 + 2)[/tex]
and
[tex]f^{-1}(x) = \sqrt{x - 2} \implies f^{-1}(x^2+2) = \sqrt{(x^2+2) - 2}[/tex].
You should have [tex]x^2+2[/tex] where you wrote [tex]x+2[/tex]. This then simplifies to [tex]\sqrt{x^2} = x[/tex] (as long as [tex]x\ge0[/tex]).
Determine the most convenient method to graph the following line.
3x+2y=12
Answers
The most convenient method to graph the line is to plot the equation y = -3/2x + 6 to represent the equation 3x + 2y = 12
What are linear equations?Linear equations are equations that have constant average rates of change.
Note that the constant average rates of change can also be regarded as the slope or the gradient
How to determine the method of plotting the graph?The equation is given as
3x + 2y = 12
The above equation is a linear equation
All forms of equation can be conveniently plotted by a graphing utility
However, the best way is to start by simplifying the equation
So, we have
3x + 2y = 12
Divide through the equation by 2
So, we have
3/2x + y = 6
Make y the subject of the equation
So, we have
y = -3/2x + 6
This means that we plot the equation y = -3/2x + 6 to represent the equation 3x + 2y = 12
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Which property of addition is shown?
3 + (2 + 5) = (3 + 2) + 5
Answers
Step by step
When we add three or more numbers, the sum is the same regardless of the grouping of the numbers. It also means that when we add three different numbers, the result is not affected by the addition pattern such as:
A +( B+C) = (A + B)+C
A motorboat can maintain a constant speed of 48 miles per hour relative to the water. The boat makes a trip upstream to a certain point in 19 minutes; the return trip takes 13 minutes. What is the speed of the current?
Answers
The speed of the current will be 8.89 miles per hour.
Given that,
The constant speed of motorboat = x = 48 miles per hour
And,
The Time taken by boat to make the upstream trip = 19/60 hour
And,
The Time taken by boat to make the return trip = 13/60 hour
Now,
According to the question,
Let,
The speed of the current = y miles per hour
And,
The total distance covered = z miles
And,
We know that,
Speed = Distance/Time
So,
For the upstream trip,
x - y = z/(19/60),
So,
z = (x-y) * (19/60) .....(i)
And,
For downstream trip
x + y = z/(13/60)
So,
z = (x + y) * (13/60) .....(ii)
From equations (i) and (ii),
We get,
(x - y) * (19/60) = (x + y) * (13/60)
i.e.
(48 - y) * (0.32) = (48 + y) * (0.22)
On solving we get,
15.36 - 0.32y = 10.56 + 0.22y
We get,
0.54y = 4.8
y = 4.8/0.54 = 8.89 miles per hour
So,
The speed of current = 8.89 miles per hour
Hence we can say that the speed of the current will be 8.89 miles per hour.
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Express the set-4≤ x ≤0 using interval notation.
Answers
Answer:
[-4, 0]
Step-by-step explanation:
You want the set -4 ≤ x ≤ 0 expressed using interval notation.
Interval notationIn interval notation, an interval is expressed as an ordered pair, with the first number of the pair being the lower end of the interval, and the second number being the upper end.
When the inequality symbol used to describe the interval is "less than" (<), the bracket used is a round bracket (parenthesis). When the symbol is "less than or equal to" (≤), a square bracket is used. The brackets need not be of the same kind.
When one end of the interval is an infinity (positive or negative), a round bracket is used.
ApplicationThe interval
-4 ≤ x ≤ 0
is written using the ordered pair ...
[-4, 0]
The number sequence x satisfying-4< x <0 is an interval containing -4,0 as well as all numbers between -4 and 0.
[-4, 0]
What is Interval Notation on a Graph?A graph for interval notation is created when we describe the solution set of an interval on even a number line.
How do you write interval notation?Intervals are represented in rectangular brackets as well as parentheses, and two numbers are separated by a comma. The two numbers are referred to as the interval's endpoints. The number on the left represents the smallest element or lower bound.
Briefing:Interval notation is a technique for representing any subset of the real number line. To write interval notation, we utilize different symbols depending on the type of interval.. For instance, the set of numbers x satisfying 1 x 6 is an interval containing 1, 6, and all values between 1 and 6.
According to the information provided:The ordered pair is used to write the interval -4 x 0.
[-4, 0].
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A profit of $86,250 was shared by the two partners of a business. If one partner received $13,000 more than the other, how much did each of them receive?
Answers
The amount of profit each of them received $49625 and $36625 respectively
How to find how much of profit each partner received?To solve the problem, we need to write a system of equations.
Let
x = amount of profit first partner received and y = amount of profit second partner received.Given that a profit of $86,250 was shared by the two partners of a business, we have that
x + y = 86,250 (1)
Also, since one partner received $13,000 more than the other, we have that
x - y = 13,000 (2)
We now solve for x and y in the system of equations
x + y = 86,250 (1)
x - y = 13,000 (2)
Adding equations (1) and (2), we have
x + y = 86,250 (1)
+
x - y = 13,000 (2)
2x = 99250
x = 99250/2
x = $49625
From equation (2) y = x - 13000
Substituting x into the equation, we have
y = x - 13000
= 49625 - 13000
= $36625
Since x = $49625 and y = $36625,
So, the amount of profit each of them received $49625 and $36625 respectively
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what is -1/3+1/14 then simplified
Answers
Answer:
-1/12
Step-by-step explanation:
-⅓ + ¼
= (-4 + 3)/12
= -1/12
please help quick!!!!!
Answers
The total cost for 4 tickets, 2 popcorns, and 1 bottled water is $46.25
How to find an equation to find the cost?
Here we know that:
Each ticket costs $9.75Popcorn costs $6.25Bottled water costs $4.75Then the cost of 4 tickets, 2 popcorns, and 1 bottled water is given by the expression:
4*$9.75 + 2*$6.25 + 1*$4.75
Solving this expression we will get that the total cost is:
C = 4*$9.75 + 2*$6.25 + 1*$4.75 = $46.25
We can conclude that the total cost for 4 tickets, 2 popcorns, and 1 bottled water is $46.25.
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At a toy store, there are 53 toy trucks on display. There are also 4 large boxes of trucks stored in back. Each of those boxes has 24 trucks inside.
Answers
Simply and then evaluate the equation when x=-1 and y=3 -2x+3(y-5x)-x
Answers
Answer:
27
Step-by-step explanation:
-2x+3(y-5x)-x --- distribute the parenthesis
-2x+3y-15x-x --- evaluate by combining similar terms
3y-18x --- plug in -1 for x and 3 for y
3(3)-18(-1) --- evaluate
9+18 --- evaluate
27
Answer:
27
Step-by-step explanation:
-2(-1)+3{3-5(-1)}-1(-1)
2+3(3+5)+1
2+3(8)+1
2+24+1
=27
Polygon mnopq is dilated by a scale factor of 5.4 with point M as the center of dilation to form the image m’n’o’p’q compare no and n’o
Answers
N'O' does not pass through point M.
NO and N'O' both have the same slopes.
A closed polygonal chain made up of a finite number of straight line segments defines a polygon as a planar figure. A polygon is a region that is bounded by a bounding circuit, a bounding plane, or both. A polygonal circuit's segments are referred to as its edges or sides.
Every point will be 5.4 times farther away from point M after dilation by a factor of 5.4 around that point. (The only point that stays put is point M.) If a line didn't cross point M before the dilation, it won't cross point M after the dilation.
Point M is not traversed by segment N'O'.
Only the distances from the dilation center are altered by dilation. Angles or orientation are unaffected.
NO and N'O' both have the same slopes.
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After taking a dose of medication, the amount of medicine remaining in a person's bloodstream, in milligrams, after xx hours can be modeled by the function f(x)=110(0.91)^{x}.f(x)=110(0.91)
x
. Find and interpret the given function values and determine an appropriate domain for the function.
Answers
The Domain is [0, ∞) and range is (0, ∞)
What is exponential function?An exponential function is a mathematical function of the following form: f ( x ) = [tex]a^{x}[/tex]. where x is a variable, and a is a constant called the base of the function.
Given:
After taking a dose of medication, the amount of medicine remaining in a person's bloodstream, in milligrams, after x hours can be modeled by the function
f(x)=110[tex](0.91)^{x}[/tex]
as, the general form of exponential function is
f(x)= [tex](ab)^{x}[/tex]
where a is the initial value, 0<b<1 is decay factor and b>1 is growth factor.
Now comparing with main function we have 110 is the initial value and 0.91 is the decay factor.
As, exponential function is defined for all real values of x but the time cannot be negative.
so, Domain: [0, ∞)
and, [tex](0.91)^{x}[/tex]>0
so, 110[tex](0.91)^{x}[/tex]>0
Then the range is (0, ∞)
Hence, the Domain: [0, ∞) and range is (0, ∞)
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The vehicle's fuel efficiency is no less than 35 miles per gallon
Answers
Based on the fact that the vehicle's fuel efficiency is not less than 35 miles per gallon, using f to represent the vehicle's fuel efficiency gives f ≥ 35.
How to represent information as inequality?The fuel efficiency of the vehicle is no less than 35 miles per gallon. This means that the fuel efficiency is either 35 miles per gallon, or greater than 35 miles per gallon.
Assuming f is meant to represent this fuel efficiency of a vehicle, this means that f can be shown as being either greater than, or equal to 35 miles per gallon.
A representation of this would be:
f ≥ 35
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(4.1 x 10^5) + (5.6 x 10^6)
Answers
The simplified answer is 6.01* 10^6.
What is standard form?Any number that we can write as a decimal number, between 1.0 and 10.0, multiplied by a power of 10, is said to be in standard form.
Given:
(4.1 x 10^5) + (5.6 x 10^6)
Solving further
4.1 * 10^5 + 5.6 * 10^6
4.1* 10^5 + 5.6*10*10^5
4.1* 10^5 + 56*10^5
(4.1 + 56 ) * 10^5
60.1* 10^5
6.01* 10^6
Hence, the simplified answer is 6.01* 10^6
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5x=8x-75
Solve for X
Answers
Answer:
75=8x-5x
75=3x
75/3=x
x=25 answer
-3x=-75
x= 25
A city has a population of 350000 the population has decreased by 30% in the past ten years what was the population Of the city ten years ago. Show solving steps
Answers
Answer:
30% x 350000 + 105000
Step-by-step explanation:
30
100
(350000)
=(
30
100
)(
350000
1
)
=(
3
10
)(
350000
1
)
=
(3)(350000)
(10)(1)
=
1050000
10
=105000
Which explains why the graph is not a function?
Answers
The explanation for the reason why the graph is not a function is: It is not a function because the graph has two different y-values for a single x-value.
What makes a Graph a Function?A graph is a function when there are exactly one y-value for every x-value that is plotted on the graph.
This implies that, no single x-value can have two different y-values in a graph that represents a function. If there are two different y-values for a single x-value, then the graph is not a function.
In the graph given below, the x-value, 4, has two different y-values, -2 and 4. This makes the graph not a function.
Therefore, the explanation for the reason why the graph is not a function is: It is not a function because the graph has two different y-values for a single x-value.
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Answer:
Step-by-step explanation:
It is not a function because there are two different y-values for a single x-value.
The product of all positive real values of x satisfying the equation [tex] \sf {x}^{(16( log_{5} {x})^{3} - 68 log_{5}x) } = {5}^{ - 16} [/tex] is
Answers
Take the base-5 logarithm on both sides and simplify.
[tex]x^{16 \log^3_5(x) - 68 \log_5(x)} = 5^{-16}[/tex]
[tex]\left(16 \log^3_5(x) - 68 \log_5(x)\right) \log_5(x) = -16[/tex]
[tex]16 \log^4_5(x) - 68 \log^2_5(x) + 16 = 0[/tex]
[tex]4 \log^4_5(x) - 17 \log^2_5(x) + 4 = 0[/tex]
Factorize the left side.
[tex]\left(4 \log^2_5(x) - 1\right) \left(\log^2_5(x) - 4\right) = 0[/tex]
Then
[tex]4 \log^2_5(x) - 1 = 0 \implies \log^2_5(x) = \dfrac14 \\\\ ~~~~~~~~ \implies \log_5(x) = \pm \dfrac12 \\\\ ~~~~~~~~ \implies x = \dfrac1{\sqrt5} \text{ or } x = \sqrt5[/tex]
or
[tex]\log^2_5(x) - 4 = 0 \implies \log^2_5(x) = 4 \\\\ ~~~~~~~~ \implies \log_5(x) = \pm 2 \\\\ ~~~~~~~~ \implies x = \dfrac1{25} \text{ or } x = 25[/tex]
and the product of these solutions is of course 1.
16. The greatest distance between the Sun and
Jupiter is about 8.166 × 10^8 kilometers. The
greatest distance between the Sun and Saturn
is about 1.515 X 10^9 kilometers. What is the
difference of these two distances?
Answers
Answer:
6.984×10^8 km
Step-by-step explanation:
Your calculator can tell you the answer to this.
15.15×10^8 -8.166×10^8 = 6.984×10^8
The difference between the distances is about 6.984×10^8 km.
_____
Additional comment
If you're paying attention to significant figures, you must round this to 6.98×10^8 km. The precision of the Saturn distance does not allow any better precision in the difference.
4 Select the correct answer. If the function 5x + y = 1 has the domain {-2, 1, 6), then what is the corresponding range? {-9, 6, 31) (9, -6, -31) {-11, 4, 29) O D. (11,-4, -29} A. B. C. tum. All rights reserved. Reset Next
Answers
The range of the function is (11, -4, 29}.
What is the range of a function?
The set of all a function's outputs is its range. In the function, f : A→B, A is the domain and B is the co-domain. The range is then created by this function's output. "Set of even natural numbers" defines the range. The mapped elements of the co-domain are referred to as the images, while domain elements are referred to as pre-images. The set of all images representing the domain's elements, or the set of all its outputs, defines the range of the function f in this case.
The range in this case is (11, -4, 29}.
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Find the inverse of the following function.
f(x) = 2x³
Answers
Answer:
Step-by-step explanation:
A basketball team sells tickets that cost $10, $20, or, for VIP seats, $30. The team has sold 3227 tickets overall. It has sold 158 more $20 tickets than $10 tickets. The total sales are $62.410. How many
tickets of each kind have been sold?
How many $10 tickets were sold?
Answers
A basketball team sells tickets that cost $10 $20 or VIP seats, $30.
The no. of three types of tickets = x, y, z
;
The team has sold 492 tickets over all.
x + y + z = 492
:
It has sold 177 more $20 tickets than $10 tickets.
y = x + 177
:
The total sales are $8580.
10x + 20y + 30z = 8580
:
How Many tickets of each kind have been sold?
:
Replace (x+177) for y in the 1st and 3rd equations
x + (177+x) + z = 492
2x + z = 492 - 177
2x + z = 315
and
10x + 20(x+177) + 30z = 8580
10x + 20x + 3540 + 30z = 8580
30x + 30z = 8580 - 3540
30x + 30z = 5040
Simplify, divide equation by 30
x + z = 168
:
Using these two equations for elimination
2x + z = 315
x + z = 168
---------------subtracting eliminates z
x = 147 ea $10 tickets sold
:
y = 147 + 177
y = 324 ea $20 tickets sold
;
Find z using the 1st equation
147 + 324 + z = 492
471 + z = 492
z = 492 - 471
z = 21 ea $30 tickets sold:
Check solution in the $$ equation
10(147) + 20(324) + 30(21) =
1470 + 6480 + 630 = 8580; confirms our solutions
The number of $10 tickets sold is 1094.
What is an equation?An equation is a mathematical statement that is made up of two expressions connected by an equal sign.
We have,
Number of $10 tickets = x
Number of $20 tickets = x + 158
Number of $30 tickets = y
Total tickets = 3227
Total sales = $62410
We can make two equations.
x + (x + 158) + y = 3227
2x + y = 3227 - 158
2x + y = 3069 ____(1)
10x + 20(x + 158) + 30y = 62410
10x + 20x + 3160 + 30y = 62410
30x + 30y = 62410 - 3160
30x + 30y = 59250
30 (x + y) = 59240
x + y = 1975 ____(2)
From (1) and (2).
2x + y = 3069
x + y = 1975
(-) (-) (-)
x = 3069 - 1975
x = 1094
And,
Substituting x = 1094 in (2)
x + y = 1975
y = 1975 - x
y = 1975 - 1094
y = 881
The number of $10 tickets.
= x
=1094
Thus,
The number of $10 tickets is 1094.
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if anyone could help me with this question I really thank you
Answers
Answer:
it would be C
Step-by-step explanation:
because youd multiply the weeks by the total money made per day and subtract it by the amount the bike costs to see if you made enough
Ruby has 20 oranges. If she eats 3/5 of them, how many does she have left.
Answers
Answer:
She has 12 oranges left
Step-by-step explanation:
convert 3/5 to a decimal
3÷5=0.6
then multiply that by 20
0.6*20=12
42. Ishmael claims that the square root of a number is always less than the number under the radical
symbol. Laurie claims there are lots of numbers whose square root is larger than the number und
the radical. What type of numbers is Laurie talking about? Convince Ishmael with at least two
examples.
Answers
Laurie is talking about numbers which are lesser than 1 as their square root is the perfect example.
We are given that:
Ishmael claims:
the square root of a number is always less than the number under the radical symbol.
Laurie claims:
there are lots of numbers whose square root is larger than the number and the radical.
Laurie can convince Ishmael by giving examples like 1/4 whose square root is 1/2 which is greater than 1/2.
Another number is 1/9 whose square root is 1/3.
Therefore, Laurie is talking about numbers which are lesser than 1 as their square root is the perfect example.
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What is an
equation of the line that passes through the points (1, -5) and (4,4)?
Answers
For the given coordinates, The equation of line is x - 3y + 8 =0
How do you determine a line's equation?to get the equation of a line given a point and its slope.Recognize the slope.Decide on the point.In the point-slope form, y - y 1 = m (x - x 1), substitute the values. y − y 1 = m (x − x 1) .Slope-intercept form should be used to write the equation.The equation of line is given by -
y − y 1 = m ( x − x 1 )
here x1,y1 = (1,-5)
m = x2 - x1/ y2 - y1
m = 4-1/4+5
m = 3/9
m = 1/3
y - 1 = 1/3 (x +5)
3y - 3 = x + 5
x - 3y = -8
x - 3y + 8 =0
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Solve the systems by graphing x+y=3
Y=3x-1
Answers
The solution of the system of equation by graphing is (1,2)
According to the question we have been given two equation which are :
x + y = 3 and y = 3x - 1
We need solve this system of equation by graphing that is we have to find the value of x and y from the graph.
For the solution of the system of equation from graph we need to find the intersecting point.
First we will plot the graph of both the equation
For , x+y = 3
the coordinates are (0,3) and (1,2)
For, y = 3x-1
the coordinates are (0,-1) and (1,2)
Hence the below image is the graph of both the equation
From the graph we will see the point where both the lines are intersecting.
Thus the point where they intersect is (1,2).
Hence the solution is (1,2)
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There are 64 people coming to your party and each person will need one cup. How many packages of cups should you buy if one package contains 23 cups?
Answers
Answer:
3 packages
Step-by-step explanation:
64/23 = 2 18/23, so 3 packages will be needed.
Alternately, 23 + 23 = 46, and 64 - 46 = 18.
So 2 packages will not be enough; 3 packages will do.
If sin(x)=-1/2, what is cos(x) and tan(-x)?
Answers
Answer:
the value of cos(x) is ±√3/2 and tan(x) is ±1/√3.
Step-by-step explanation: