On what intervals is the function increasing?
Indicate intervals on the x-axis using the Ray tool for intervals that extend to infinity and the Segment tool for bounded intervals.
Graph a ray by selecting the endpoint followed by a point on the ray. Graph a segment by selecting an endpoint followed by the other endpoint.
Answers
Answer:
[-7, - 2] and [3, 7]--------------------------------------
The graph has two local maximums and two local minimums.
The intervals between those points are the increasing intervals.
Refer to the attached, where the intervals are marked.
The intervals are
x = [-7, - 2] and [3, 7]
Related Questions
Determine the center and radius of the circle with equation (x+3)² + (y − 2)² = 16
Answers
Answer: Center: (-3, 2). Radius: 4.
Step-by-step explanation:
The x-coordinate of the center of the circle is given by the constant within the parenthesis with variable x. Whatever number makes the equation x + 3 = 0 is the x-coordinate of the center of the circle, which in this case is -3.
The y-coordinate of the center of the circle is given by the constant within the parenthesis with variable y. Whatever number makes the equation y - 2 = 0 is the y-coordinate of the center of the circle, which in this case is -2.
The radius of the circle is the square root of the constant on the other side of the equation. So, r = [tex]\sqrt{16}[/tex] = 4.
The explanation is from the equation of a circle in a graph:
[tex](x-h)^2 + (y-k)^2 = r^2[/tex]
h and k in this equation stand for the coordinates of the center of the circle, with h being the x-coordinate and k being the y-coordinate. IN your equation, we have:
[tex](x+3)^2 + (y-2)^2 =16[/tex]
Which can also be written as
[tex](x-(-3))^2 + (y-(2))^2=16[/tex]
See the correlation of numbers -3 and 2 with h and k?
Notice also how the equation contains [tex]r^2[/tex], so to find the radius you do [tex]\sqrt{r^2}[/tex].
4. The distance needed to stop a car varies directly as the square of its speed. It
requires 120 m to stop a car at 70 km/h. What distance is required to stop a car
at 80 km/h?
Answers
Answer:
156.7 m (nearest tenth)
Step-by-step explanation:
Define the variables:
Let d = distance in meters.Let v = speed in kilometers per hour.If the distance needed to stop a car varies directly as the square of its speed:
[tex]\boxed{d \propto v^2 \implies d=kv^2}[/tex]
where k is the constant of proportionality.
Given:
d = 120 mv = 70 km/hTo find the constant of proportionality, k, substitute the given values into the equation:
[tex]\begin{aligned}\implies 120&=k(70)^2\\k&=\dfrac{120}{70^2}\\k&=\dfrac{6}{245}\end{aligned}[/tex]
Substitute the found value of k back into the formula to create an equation for the given relationship:
[tex]\implies d=\dfrac{6v^2}{245}[/tex]
To find the distance (in meters) required to stop a car at 80 km/h, substitute v = 80 into the equation:
[tex]\implies d=\dfrac{6(80)^2}{245}[/tex]
[tex]\implies d=\dfrac{6\cdot 6400}{245}[/tex]
[tex]\implies d=\dfrac{7680}{49}[/tex]
[tex]\implies d=156.73469...\; \sf m[/tex]
[tex]\implies d=156.7\; \sf m\; (nearest \;tenth)[/tex]
Therefore, the distance required to stop a car at 80 km/h is:
156.7 m (2 d.p.).GCF ( 160, 320, 480)
Answers
The greatest common factor of 160, 320 and 480 will be 160.
What is the Greatest Common Factor?The largest positive number that can be evenly divided into the supplied numbers is the most common factor. The largest number that evenly divides all the specified numbers is the greatest common factor.
In maths, the largest positive integer that divides each of the integers is known as the greatest common divisor of two or more integers that are not all equal to zero. The greatest common divisor of two numbers x and y is represented by the symbol GCD(x,y)
Assumed to be 160, 320 and 480. The numbers are factored to determine the largest common factor.
Factorize number 160
160 = 2×2×2×2×2×5
Factorize number 320
320 = 2×2×2×2×2×2×5
Factorize number 480
480 = 2×2×2×2×2×3×5
The common number between all three numbers is 2⁵×5. Therefore, the greatest common factor of 160, 320 and 480 will be 160.
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in each of the following lines, underline the smallest number and put a ring round the largest number
15/3, 12/6, 27/9, 8/2, 10/10
Answers
Answer:
this is how to do it. Now find the answer
Step-by-step explanation:
find the common factor for the denominators, which is 30.
then × the numerator by however much you ×tl the denominator by to get 30
Question 14 (2 points)
Complete the general form of the equation of a sinusoidal function having an
amplitude of 8, a period of 27, and a phase shift to the left 4 units.
Answers
The complete general form of the equation of the given sinusoidal function is y = 8sin[(27/2π)*(x - 4)] + c.
The general form of an equation for a sinusoidal function is presented below.
y = a×sin[b*(x - h)] + c
The variable "a" denotes the amplitude of the equation. The variable "T" represents the time period of the equation, and T = 2π/b. The variable "h" denotes the phase shift of the equation. The variable "c" denotes the vertical shift of the equation. The amplitude, period, and phase shift are 8, 27, and 4 units to the left, respectively. The general form of the equation of a sinusoidal function can be written as given below.
y = a×sin[b*(x - h)] + c
y = 8sin[(27/2π)*(x - 4)] + c
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What is/are the effects when you perform the following transformations on your figure?
a. Reflections –
b. Translations –
c. Rotations –
d. Dilations –
Answers
Answer:
A. REFLECTION
Please guys do some research i know you're not that stu p id-_-
CLASSIFYING A FUNCTION. Is the function represented by the ordered pairs linear or nonlinear? Explain your reasoning.
Answers
52 is 0.4% of what number? Use pencil and paper. Would you expect the answer to be a lot less than 52, slightly less than
52, slightly greater than 52, or a lot greater than 52? Explain.
Answers
Answer:
a lot less because 0.4 is not fully of 100%
Step-by-step explanation:
Answer:
52 is 0.4% of 130. You would expect the number to be a lot greater than 52
Step-by-step explanation:
If the number we are trying to find is x, we have to use the equation x*0.4=52 which can be rewritten as 52/0.4=x
If you solve that, you get 130.
The number is expected to be a lot greater than 52 because 0.4 is almost 0.5 and that would mean doubling 52 so the number would be almost double 52. That means it would be a lot greater.
Select all the equations that have {4} as its solution set.
Responses
79−3x=12x+19
7−x=12x
x2+3=10x−21
5 + 2x = 3x + 3
SELECT ALL, THIS IS MULTIPLE CHOICE.
Answers
Answers:
A. 79 − 3x = 12x + 19
B. 7 − x = 12/x
C. x^2 + 3 = 10x − 21
use f(x)=|x|
f(x) is shifted down 4 and right 3 to create h(x)
which answer shows the correct function for h(x)
Answers
Answer:
h(x)= |x-3|-4
Step-by-step explanation:
If f(x) = |x| is shifted down 4 and right 3 to create h(x), then h(x) = |x - 3| - 4
The function is given
f(x) = |x|
Translation of the shape mean the displacement of the shape from one place to another place. Some usually used displacements are shifted to right / left and shifted to up / down etc.
First f(x) is shifted down 4
Then the function will become
f(x) = |x| - 4
Then the function shifted right 3
Then the function will be
h(x) = |x - 3| - 4
Hence, if f(x) = |x| is shifted down 4 and right 3 to create h(x), then h(x) = |x - 3| - 4
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Find her mistake and it’s due today
Answers
Answer:
Step-by-step explanation:
A quadratic function y = f(x) is plotted on a graph and the vertex of the resulting
parabola is (-5, 3). What is the vertex of the function defined as g(x) = f(x) + 2?
Answer:
Submit Answer
Answers
Vertex of g(x) is: (-2, -4)
What is vertex?An element of a line is a line segment. A line segment that can be extended endlessly is known as a ray.An angle is created when two line segments or rays cross one another. A vertex is created by definition whenever two lines come together to produce an angle. Thus, we can state that a vertex is formed when two line segments or rays intersect.acc to our question:
Vertex form of a quadratic function:
f(x) = (x - h)² + k
We have (h, k) = (3, -4)
The function f(x) is:
f(x) = (x - 3)² - 4
The function g(x) is: g(x) = f(x + 5) =
(x + 5 - 3)² - 4 = (x + 2)² - 4Vertex of g(x) is:(-2, -4)
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Witch expression is equivalent to 10q + 5
Answers
Answer:
5q + 5q + 5 is equivalent to 10q + 5
Answer:
A.
Step-by-step explanation:
Find the ratio of 1.94 million to 2.16 million
Answers
Answer:
0.97m : 1.08m
Step-by-step explanation:
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Rohan bought some tiles for a kitchen floor. 3/5 of the tiles were white, 1/4 of the
remainder were yellow, and the rest were blue. There were 60 more white
tiles than blue tiles. Each tile cost $3. What was the total cost of the tiles?
Answers
The cost the tiles are = $182.55
what is unitary method?The unitary technique involves first determining the value of a single unit, followed by the value of the necessary number of units. What can be values and units.Let's say you go to the store to buy six apples. You are informed by the shopkeeper that he is offering 10 apples for Rs 100. In this instance, the value and the units are the price of the apples. Recognizing the units and values is crucial when using the unitary technique to a problem.Always write the items that need to be computed on the right side and the things that are known on the left side to simplify things. We are aware of the quantity of apples and the amount of money in the aforesaid problem.acc to our question-
white tiles =W = 1/4
3/5 = yellow
each tile costs= $3
= 0.25+ 0.6+ 60
= 60.85*3
$182.55
hence,The cost the tiles are = $182.55
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There are 7 new books and 5 used books on a shelf.
(a) What is the ratio of new books to all books on the shelf?
0
(b) What is the ratio of used books to all books on the shelf?
0
Answers
Answer:
7 * 5 =35 because if you say 5 10 15 20 25 30 35 then that's your answer
Answer:
a) 7:13 b) 5:13
Step-by-step explanation:
There are 7 new books (-> 7:--) theres 5 used books, add the 7 new books and 5 used books together. it said "The ratio for new books to all books?" it must be in that order. with leads you to 7:13
do the same thing for b) using the same steps.
Find the slope of the line using rise/run formula please help
Answers
Answer:
20/5 is the slope, or 4.
Step-by-step explanation:
It went up 20 units on the y axis, and over 5 units on the x-axis. So 20/5 is the slope.
-Hope this helped
Which symbol replaces the box to make the statement true? 18÷6+3□6+12÷3 Responses > greater than < less than =
Answers
The correct expression of the inequality expression is 18 ÷ 6 + 3 □ 6 + 12 ÷ 3
How to complete the inequality expression?From the question, the expression is given as
18 ÷ 6 + 3 □ 6 + 12 ÷ 3
We start by converting the above expression to the same form
So, we start by solving the quotients
This gives
3 + 3 □ 6 + 4
Next, we evaluate the sum
So, we have
6 □ 10
In the above expression, we have
6 and 10
By convention, the number 6 is less than the number 10
This is so because 6 has a smaller value and 10 has a higher value
When the above numbers are compared, we have
6 is less than 10
This means that we make use of the inequality symbol <
So, we have
18 ÷ 6 + 3 < 6 + 12 ÷ 3
Hence, the complete inequality is 18 ÷ 6 + 3 □ 6 + 12 ÷ 3
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please help me with these it is due tomm.
Answers
Answer:
1.) 10: 1, 2, 5, 10.
15: 1, 3, 5, 15,
Answer would be 5.
2.) 18: 1, 2, 3, 6, 9, 18
21: 1, 3, 7, 21
Answer would be 3.
3.) 12: 1, 2, 3, 4, 6, 12.
24: 1, 2, 3, 4, 6, 8, 12, 24.
Answer would be 12.
4.) 8: 1, 2, 4, 8.
20: 1, 2, 4, 5, 10, 20.
Answer would be 4.
5.) 14: 1, 2, 7, 14.
28: 1, 2, 4, 7, 14, 28.
Answer would be 14.
Step-by-step explanation:
Using the listing method, you would first list the common factors of each number, to which that number could be multiplied by. Then, you would search for the greatest common factor.
Please help me w this hehehehehh
Answers
Answer:
-25x-45y, because if we have got + and -, so we will write minus.
WILL GIVE BRAINLiST, RATE IT 5 STARS, AND HEART IT FOR CREATIVE WRITING HELP. PLEASE ANSWER BOTH QUESTIONS, IF ITS ONE QUESTION I CAN DO THAT TOO!
1. What are 5 observations you made about the setting of “Avatar” after watching the trailer? (Play the first avatar movie trailer)
2. Based on the trailer, what is one central theme of the movie? How does the setting contribute to this theme? (Play the first avatar movie trailer)
when answering, answer it like 1= and 2=
Answers
Answer: Read explanation
Step-by-step explanation: Observations of setting: Humanoid beings. Earth-like world. A human base to collect information. Forest like setting. Bird-like transportation creatures.
Theme ideas: Man a part of research group enters an avatar of beings to collect information on this world. Research group makes an invasion on these creatures home land.
Make any corrections if you want! Make it more comfortable to your style!
Add the 2 polynomials:
(-77x²¹ +
2
·x² + x
3
+[52*+
1
-
Answers
Answer:
Step-by-step explanation:
An amusement park has two types of season passes. Plan 1 charges a one-time fee of $145.00 for admission
plus $5.00 every trip for parking. Plan 2 charges a one-time fee of $40.00 for parking plus $12.00 every trip for
admission. For what number of trips is the cost of these plans the same?
Answers
The number of trips after the cost of the plan A and plan B is 16.
According to the question,
We have the following information:
Plan 1 charges a one-time fee of $145.00 for admission plus $5.00 every trip for parking. Plan 2 charges a one-time fee of $40.00 for parking plus $12.00 every trip for admission.
So, this will make an arithmetic progression.
The formula to find nth term of an A.P:
an = a+(n-1)d where a is the first term
Now, on left hand side, we have nth term for plan A and on the right hand side, we have the nth term for plan B because their nth term will be equal.
145+(n-1)5 = 40+(n-1)12
145+5n-5 = 40+12n-12
5n+140 = 12n+28
140-28 = 12n-5n
7n = 112
n = 112/7
n = 16
Hence, the number of trips after the cost of the plan A and plan B is 16.
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Use graphing to find the solutions to the system of equations.
- x² + y = 1
-x + y = 2
Answers
The solution to the equation using graph is x= -0.62 or x = 1.62.
What is equation?
A mathematical equation may be a formula that uses the equals sign to represent the equality of two expressions.
Main Body:
For [tex]-x^{2} +y = 1[/tex]
We make y the subject to obtain
[tex]y = x^{2} +1[/tex]
We can easily graph this function, because we just have to transform the graph [tex]y = x^{2}[/tex] of by shifting the intercept up to 1.
As for the straight line, -x +y = 2
We find the intercepts as follows,
When y = 0 , x = -2
When x = 0 , y = 2
We plot the points (-2,0) and (0,2).
We now draw the two graphs on the same graph sheet. The intersection of the two graphs gives the solution to be
x= -0.62 or x= 1.62
See graph
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.
Radioactive Strontium The half-life of strontium-90 is 28 years. How long will it take a 50- mg sample to decay to a mass of 32 mg?
Answers
The time taken is obtained as 3 years.
What is the time taken?We know that radioactivity has to do with the fact that a substances does disintegrate gradually over a period of time.
Let us recall the formula;
N/No = (1/2)^t/t1/2
N = The mass of radioactive atoms at time t
No = The mass of radioactive atoms initially present
t = time taken
t/12 = half life of the radioactive nucleus
Then;
32/50 = (1/2)^t/28
0.64 = (1/2)^t/28
log 0.64 = t/28 log0.5
t/28 = log(0.64/0.5)
t = 28 * log(0.64/0.5)
t = 3 years
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If A = (6,7,8,11) and B = {(7,6,7,9), list the elements of A U B.
Answers
The elements of AUB is {6, 7, 8, 9, 11} when A = {6,7,8,11} and B = {7,6,7,9}.
According to the question,
We have the following information:
A = {6,7,8,11} and B = {7,6,7,9}
Now, we know that the elements of AUB means that all the elements which are there in both sets but the elements are not supposed to be repeated.
(Please that AUB can also be found using Venn diagram and questions are asked where the question has to be solved by making Venn diagram and representing all the elements in it.)
So, we have the following expression:
AUB = {6,7,8,9,11}
(Now, note that numbers however repeated in sets are not repeated here.)
Hence, the elements of AUB is {6, 7, 8, 9, 11} when A = {6,7,8,11} and B = {7,6,7,9}.
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Please help 18points
Answers
All the options are correct
George invest $500 in his friend's startup company. his friend agrees to give him 8% of the original investment each year for the next 3 years. write a linear function for this situation.
Answers
The linear function for the situation is :-
Amount at the end of 3 years = Original investment + original investment*Rate*Time/100
It is given in the question that:-
Investment of George's friend in startup company = $ 500.
Interest percent = 8 %
Time period of investment = 3 years
We have to find the linear function for this situation.
As this interest is on original investment, the interest will be simple.
Hence,
The linear function for the situation will be :-
Amount at the end of 3 years= Original investment + original investment*Rate*Time/100
Amount at the end of 3 years = 500 + 500*8*3/100 = 500 + 120 = $ 620
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consider the line y= 5/2x+5
1. find the equation of the line that is perpendicular to this line and passes through the point (-5,6)
2. find the equation of the line that is parallel to this line and passes through the point (-5,6)
Answers
Answer:
Step-by-step explanation:
1
y-6 = -2/5(x-(-5)
y - 6 = -2/5(x+5)
y -6 = -2/5 x -2
y = -2/5 x -2 + 6
y = -2/5 x + 4
2
y-6 = 5/2 (x-(-5)
y-6 = 5/2 (x+5)
y - 6 = 5/2 x + 25/2
y = 5/2 x + 25/2 + 6
y = 5/2 x + (25+12)/2
y = 5/2 x + 37/2
use eulers method with step size 0.5 to compute the approximate y values y1 y2 y3 and y4 of the solution of the intitial value problem y'=y 2x y(3)=0
Answers
Answer:
[tex]y_1=\boxed{-3}[/tex]
[tex]y_2=\boxed{-8}[/tex]
[tex]y_3=\boxed{-16}[/tex]
[tex]y_4=\boxed{-28.5}[/tex]
Step-by-step explanation:
Given:
[tex]y'=y-2x, \;\;y(3)=0[/tex][tex]h=0.5[/tex]Use Euler’s method with h = 0.5 to find approximate values for the solution of the initial value problem:
[tex]y'=y-2x, \;\;y(3)=0[/tex]
at x = 3.5, 4, 4.5, 5.
Therefore:
[tex]f(x,y)=y-2x, \quad x_0=3 \;\;\text{and}\; \;y_0=0[/tex]
Euler's Method
[tex]\boxed{y_{n+1}=y_n+hf(x_n,y_n)}[/tex]
[tex]\begin{aligned}\implies y_1&=y_0+hf(x_0,y_0)\\&=0+(0.5)f(3,0)\\&=0+0.5[0-2(3)]\\&=0+0.5(-6)\\&=-3\end{aligned}[/tex]
[tex]\begin{aligned}\implies y_2&=y_1+hf(x_1,y_1)\\&=-3+(0.5)f(3.5,-3)\\&=-3+0.5[-3-2(3.5)]\\&=-3+0.5(-10)\\&=-3-5\\&=-8\end{aligned}[/tex]
[tex]\begin{aligned}\implies y_3&=y_2+hf(x_2,y_2)\\&=-8+(0.5)f(4,-8)\\&=-8+0.5[-8-2(4)]\\&=-8+0.5(-16)\\&=-8-8\\&=-16\end{aligned}[/tex]
[tex]\begin{aligned}\implies y_4&=y_3+hf(x_3,y_3)\\&=-16+(0.5)f(4.5,-16)\\&=-16+0.5[-16-2(4.5)]\\&=-16+0.5(-25)\\&=-16-12.5\\&=-28.5\end{aligned}[/tex]
[tex]\begin{array}{|c|c|c|}\cline{1-3} \text{Step}\;(n) & x_n&y_n\\\cline{1-3} 0&3&0\\\cline{1-3} 1&3.5&-3\\\cline{1-3} 2&4&-8\\\cline{1-3} 3&4.5&-16\\\cline{1-3} 4&5&-28.5\\\cline{1-3} \end{array}[/tex]