Consider the function y = f(x) shown at right, trace each interval where the function behavior is A. Increasing, using a GREEN pencil Identify the interval(s) ___B. Decreasing, using a RED pencil Identify the interval(s) ___ C. Constant, using a YELLOW pencil Identify the interval(s) ___ D. State the Domain of the function ___ E. State the Range of the function ___ F. What thoughts do you have about the intervals stated above? Did you use brackets (closed/included points) or parentheses (open/non-included points)? Why or why not?
Answers
You have a function f(x). To identify the increasing interval and decreasing interval of f(x), you consider that an increasing interval is determined by the values of x in which the value of f(x) increases. For the decreasing interval you focus on the values of x in which the values of f(x) decreases.
You can notice in the given graph:
The increasing interval is (-8 , -4) U (3 , 6)
The decreasing interval is (-4 , -2)
The constant interval is (-2 , 3)
The domain of the function is (-8 , 6)
The previous interval is given by the available values of x
The range of the function is (-4 , 8)
The previos interval is given by the values of f(x) for the values of x in the domain.
The following image is a sketch of the graph with the respective intervals.
Related Questions
For an arc length s, area of sector A, and central angle θ of a circle of radius r, find the indicated quantity for the given value. r= 6.45 in, θ= 5 pi\6, s=?
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Calculate the arc length by using the following formula:
[tex]s=r\theta[/tex]Replace the values of r and θ and simplify:
[tex]\begin{gathered} s=(6.45in)(5\frac{\pi}{6})=(6.45)(\frac{5}{6})(3.14) \\ s=16.8775in \end{gathered}[/tex]Hence, the arc length is 16.8775 in
The endpoints of diameter in a circle form an angle with point C. What is the measure of angle BCD?
Answers
Answer:
90 degrees
Explanation:
Please note that whenever a triangle is inscribed in a circle and one side of the triangle is a diameter of the circle as in the given figure, then the angle that is opposite the diameter of the circle is a right angle;
[tex]\therefore\angle BCD=90^{\circ}[/tex]The order in which you write the ratio is ____ to the meaning.
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The ratio is defined as fraction in which one number is numertor and other number is denominator.
For example the ratio 2/3 has 2 in numerator and 3 in denominator, but if we write the ratio as 3/2 then it is different from previous ratio 2/3. So in ratio order is important in which you write the ratio.
Thus answer is,
The order in which you write the ratio is important to the meaning.
Jodie is an event planner who believeseach person requires 3.75 feet ofpersonal space at her events. Her nextevent will be at a venue that measures40 feet by 75 feet. How many peopleshould she include on the guest list?
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The venue measures 40 ft by 75 ft . This means the venue has the shape of a rectangle. A rectangle
247474647447x4747474747
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Answer:
1174879639277360520909 in exact form
or
in decimal form 1.17487963 x 10^21
Step-by-step explanation:
Section 5.2-10. Solve the following system of equations by substitution or elimination. Enter your answer as (x,y).-2x+3y = 15-x-3y = 12
Answers
1)-2x2)
[tex]-2x+3y-(-2x-6y)=15-2\times12\Rightarrow-2x+3y+2x+6y=15-24\Rightarrow9y=-9\Rightarrow y=-1[/tex]y=-1 implies
[tex]-2x+3\times(-1)=15\Rightarrow-2x-3=15\Rightarrow-2x=18\Rightarrow x=-9[/tex]Hence the solution is
[tex](-9,-1)[/tex]Your brother is buying textbooks for college. He has to buy 3 math textbooks and 2 science textbooks. The total cost of his textbooks is $487. Write a linear equation to represent the cost of his textbooks.
Answers
Let's define the following variables,
x: cost of a math textbook
y: cost of a science textbook
He has to buy 3 math textbooks and 2 science textbooks, that is,
Total cost = 3x + 2y
The total cost of his textbooks is $487, then the linear equation is,
487 = 3x + 2y
How many modes does the following dataset have? 9,29,13,4,2,16,10,14,27
Answers
Given:
[tex]9,29,13,4,2,16,10,14,27[/tex]To find- the mode of the given dataset.
Explanation-
We know that the mode is the most occuring frequency of the dataset. Let us arrange the data in ascending order first, and we get
[tex]2,4,9,10,13,14,16,27,29[/tex]Since there is no repeated frequency, we can say that there is no mode for the given data set.
The answer is 0.
Good evening, I need help on this questions. Thanks :)
Answers
Answer:
A and B ---> decreasing
B and C ---> constant
C and D ---> decreasing
D and E ---> increasing
Explanation:
A function is increasing if we go from left to right and the graph goes up, it is constant when it is a horizontal line and it is decreasing if when we go from left to right the graph goes down.
Therefore, for each part of the function, we get
A and B ---> decreasing
B and C ---> constant
C and D ---> decreasing
D and E ---> increasing
-2(6.× -8 - 8 × 4)^0
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Every number raised to the power of zero is equal to one.
[tex]-2\cdot1=-2[/tex]The final expression is -2
Debra will rent a car for the weekend. She can choose one of two plans. The first plan has an initial fee of $50 and costs anadditional $0.15 per mile driven. The second plan has an initial fee of $59 and costs an additional $0.11 per mile driven.for what amount of driving do the two plans cost the same? i need the answer for miles and cost
Answers
First plan cost is modeled as:
50 + 0.15x
where x are the miles driven
Second plan cost is modeled as:
59 + 0.11x
If the two plans cost the same, then:
50 + 0.15x = 59 + 0.11x
0.15x - 0.11x = 59 - 50
0.04x = 9
x = 9/0.04
x = 225 miles
which corresponds to a cost of:
50 + 0.15*225 = $83.75
this lettuce i have is 25 calories per serving. serving size is 85 grams. i had 27 grams. how many calories would that be??
Answers
Answer:
7.94117647059 Calories
Step-by-step explanation:
25 Calories = 85 Grams
25/85 = 0.294117647059
0.294117647059 = 1 Gram
0.294117647059 times 27 = 7.94117647059
2. (5 points) A very special island is inhabited only by knights and knaves. Knights always tell
the truth, and knaves always lie. You meet two inhabitants: Sue and Marge. Sue says that
Marge is a knave. Marge claims. "Sue and I are not the same." Determine who is a knight and
who is a knave.
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Answer:
Sue is knave and Marge be knightStep-by-step explanation:
Let Sue be knight and Marge be knave.
Sue says: "Marge is a knave". Since Sue is knight, she is right and Marge should lie.
Marge says: "Sue and I are not the same." - this is right answer too, so this is not a correct response and our assumption is wrong.
Now, let Sue be knave and Marge be knight. Then Marge's response is right and Sue's is wrong. This is a match and this assumption is correct.
Solve the following/3x=7-3/x
Answers
Value of x is 8.46 for equation 3x=7-3/x
What is Equation?Two or more expressions with an Equal sign is called as Equation
The given equation is 3x=7-3/x
3x+3/x=7
3x²+3=7x
3x²-7x+3=0
Use quadratic equation formula
a=3, b=-7, c=3
x=-b±√b²-4ac/2a
x=7±√49-4(3)(3)/2(3)
x=7±√49-36/6
x=7±√13/6
x=7±√2.16
x=7+1.46
x=8.46
Hence value of x is 8.46 for equation 3x=7-3/x
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a^2 - b^4 Evaluate is a= -5 and b= 2
Answers
21
Explanations:Given the expression
[tex]a^2-b^4[/tex]We are to find the resulting value given that a = -5 and b = 2
[tex]\begin{gathered} =(-5)^2-(2)^2 \\ =25-4 \\ =21 \end{gathered}[/tex]Hence the value of the expression if a = -5 and b = 2 is 21
Melissa wants to rent a boat and spend at most $38. The boat costs $6 per hour, and Melissa has a discount coupon for $4 off. What are the possible numbers of hours Melissa could rent the boat?Use t for the number of hours.Write your answer as an inequality solved for t.
Answers
ANSWER:
[tex]t\leq7[/tex]EXPLANATION:
Given:
Melissa wants to rent a boat and spend at most $38
Cost of boat per hour = $6
Discount coupon off = $4
Let t represent the number of hours
We can go ahead and set up the below inequality;
[tex]6t-4\leq38[/tex]Let's add 4 to both sides of the inequality;
[tex]\begin{gathered} 6t-4+4\leq38+4 \\ 6t\leq42 \end{gathered}[/tex]Let's divide both sides by 6;
[tex]\begin{gathered} \frac{6t}{6}\leq\frac{42}{6} \\ t\leq6 \end{gathered}[/tex]So Melissa can rent the boat for up to 7 hours
The standard normal curve is grafted below. Shade the region under the standard normal curve to the left of x=1.00Use the table to find the area under the standard normal curve to the left of x=1.00
Answers
Explanation
Part A
The shaded area under the standard normal curve to the left of z=1.00 can be seen below.
Part B
Using the z table, the area under the standard normal curve to the left of z.=1.00 is
Answer: 0.8413
For the following set of data, find the number of data within 2 population standard deviations of the mean.28, 65, 114, 74, 68, 75, 70, 69, 64
Answers
To determine the data that is within 2 population standard deviations of the mean, let's calculate the mean first.
To determine the mean, let's add all the data and divide the result by the total number of data.
[tex]28+65+114+74+68+75+70+69+64=627[/tex][tex]627\div9=69.66667[/tex]The mean is 69.66667.
Let's now calculate the standard deviation. Here are the steps:
1. Subtract the mean from each data, then square the result.
[tex]\begin{gathered} 28-69.66667=(-41.66667)^2=1,736.1114 \\ 65-69.66667=(-4.66667)^2=21.7778 \end{gathered}[/tex][tex]\begin{gathered} 114-69.66667=(44.33333)^2=1,965.4441 \\ 74-69.66667=(4.33333)^2=18.7777 \end{gathered}[/tex][tex]\begin{gathered} 68-69.66667=(-1.66667)^2=2.7778 \\ 75-69.66667=(5.33333)^2=28.4444 \end{gathered}[/tex][tex]\begin{gathered} 70-69.66667=(0.33333)^2=0.1111 \\ 69-69.66667=(-0.66667)^2=0.4444 \\ 64-69.66667=(-5.66667)^2=32.1111 \end{gathered}[/tex]2. Add the results in step 1.
[tex]1,736.1114+21.7778+1,965.4441+18.7777+2.7778=3,744.8888[/tex][tex]28.4444+0.1111+0.4444+32.1111=61.111[/tex][tex]3,744.8888+61.111=3,805.9998[/tex]The sum is 3, 805.9998.
3. Divide the sum by the total number of data.
[tex]3,805.9998\div9=422.8889[/tex]4. Square root the result in step 3.
[tex]\sqrt{422.8889}\approx20.56[/tex]The standard deviation is approximately 20.56.
So, the data that are within 2 population standard deviations of the mean are between:
[tex]\begin{gathered} 69.67-(2)(20.56)=28.55\approx29 \\ 69.67+(2)(20.56)=110.79\approx111 \end{gathered}[/tex]The data that are within 2 population standard deviations of the mean are between 29 and 111. Based on the given data, the data that are between 29 and 111 are the following: 64, 65, 68, 69, 70, 74, and 75. There are 7 data that are within 2 population standard deviations of the mean.
Use the times and corresponding closing prices of the stock to create coordinate pairs. Let X represent the number of weeks since the first at a point, and Y represent the closing price of each time. So, X equals zero represents the data point from five years ago. There are 52 weeks in a year, and you can write the time for each closing price recorded in terms of weeks that have passed since five years ago, when X equals zero. Fill in the table to represent your data as coordinate pairs
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Combining both tables we get:
hi, can you help me answer this question please, thank you!
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The correct option is B
Explanation:The given statement shows that there is a 95% chance that the mean of a sample of 29 gadgets will be between 12.8 and 34.9
2.) Part A: complete the following table for the functions
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Complete the following table for the functions:
[tex]\begin{gathered} f(x)=x^2+1 \\ g(x)=f(x-5) \\ h(x)=f(x+3) \end{gathered}[/tex]The below function represents the transformation of the independent variables:
[tex]\begin{gathered} f(x)=x^2+1 \\ g(x)=f(x-5)\ldots\ldots\text{.f(x) will decrease by 5 units} \\ h(x)=f(x+3)\ldots\ldots.f(x)\text{ will increase by 3 units} \end{gathered}[/tex]I WILL BE MARKING BRAINLIEST
The general form of an ellipse is 15x2+4y2+30x−16y−29=0.
What is the standard form of the ellipse?
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The equation of ellipse in standard form is (x + 1)² / 4 + (y - 2)² / 15 = 1.
How to determine the standard form of the ellipseIn this problem we find the equation of an ellipse in general form, whose standard form can be found by algebra properties. The general form of the equation of an ellipse centered at (h, k) is introduced below:
(x - h)² / a² + (y - k)² / b² = 1
Where:
a, b - Lengths of the semiaxes.(h, k) - Coordinates of the center.The complete procedure is now presented:
15 · x² + 4 · y² + 30 · x - 16 · y - 29 = 0
(15 · x² + 30 · x) + (4 · y² - 16 · y) = 29
15 · (x² + 2 · x) + 4 · (y² - 4 · y) = 29
15 · (x² + 2 · x + 1) + 4 · (y² - 4 · y + 4) = 29 + 15 · 1 + 4 · 4
15 · (x + 1)² + 4 · (y - 2)² = 29 + 15 + 16
15 · (x + 1)² + 4 · (y - 2)² = 60
(x + 1)² / 4 + (y - 2)² / 15 = 1
The equation of ellipse is (x + 1)² / 4 + (y - 2)² / 15 = 1.
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Suppose you are choosing at random from the numbers 1 through 12 (inclusive). If the event E is "the number is even," find the set representing E. Express your answer as a bracketed set in the form {a,b,c,d}.
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The set numbers from 1 to 12(inclusive) is:
1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12
The set even numbers are:
2, 4, 6, 8, 10, 12
Given that the event E is "the number is even"
Therefore, the set representing the event E as a bracketed set is:
[tex]E=\mleft\lbrace2,4,6,8,10,12\mright\rbrace[/tex]
The padlock for your gym locker uses a 3 number sequence to open the lock. If the numbers go from 1 to 27, how many different sequences are there on the dial without repeating a number?A. 17,550B. 33,696C. 16,848D. 8,775
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SOLUTION:
We want to the different sequences possible without repeating a number.
For the first number, there are 27 ways to select it.
Since we aren't allowed to repeat numbers;
There are 26 ways to select the second number.
There are also 25 ways to select the third number.
Therefore, the different sequences possible are;
[tex]No\text{. of ways =}27\times26\times25=17550\text{ ways}[/tex]Find the distance between:(4,-9) and(-8,0)Round your answer to the nearest hundredth.
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The distance between 2 points (x1, y1) and (x2, y2) is calculated as:
[tex]\text{distance}=\sqrt{(x_2-x_1)^2+(y_2-y_1)^2}[/tex]So, if we replace (x1, y1) by (4, -9) and (x2, y2) by (-8,0), we get:
[tex]\begin{gathered} \text{distance}=\sqrt{(-8-4)^2+(0-(-9))^2} \\ \text{distance}=\sqrt{(-12)^2+(9)^2} \\ \text{distance}=\sqrt{144+81} \\ \text{distance}=\sqrt{225} \\ \text{distance}=15 \end{gathered}[/tex]Answer: the distance is 15
CASSANDRA WENT FOR A JO9.SHE RAN AT A PACE OF 7.3 MILESPER HOUR. IF SHE RAN FOR 0.75HOURS, HOW FAR DID CASSANDRARUN?
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We can use one simple formula, that is d=vt
d=distance
v=pace
t=time
So,
d=(7.3miles per hour)(0.75 hours)=5.475 miles
when graphed on a coordinate plane,Bumby Avenue can be represented by the equation y=-4x-7. primrose can be represented by the equation 8x+2y=17. Are these streets parallel ?
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Answer:
The lines are not parallel because their slopes are opposite reciprocals.
Explanation:
The lines:
[tex]\begin{gathered} y=-4x-7 \\ \text{and} \\ 8x+2y=17 \end{gathered}[/tex]are not parallel because their slopes are not the same
Note:
Two straight lines are said to be parallel when their slopes are the same, and have different y-intercepts.
what is the solution set for the inequality
A. x ≤ -5
B. x ≤ 5
C. x ≤ 1
d. x ≤ -14
Answers
The solution set to the inequality, 4x + 12 ≤ -8, is determined as: A. x ≤ -5.
How to Find the Solution Set of an Inequality?The solution set is the value of x that would make an inequality statement true. To find the value of x, solve as you would solve a normal equation.
Using the key to the given model in the diagram, we can write the inequality as follows:
On the left, we would have, 4x + 12.
On the right, we would have, -8.
The inequality would be expressed as:
4x + 12 ≤ -8
Solve for x
4x + 12 - 12 ≤ -8 - 12 [subtraction property of equality]
4x ≤ -20
4x/4 ≤ -20/4
x ≤ -5
The solution set is: A. x ≤ -5.
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QUESTION 31 POINTThe area of a triangle is 18. The base is 6 inches. What is the height? Do not include units in your answer.
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ANSWER:
6
STEP-BY-STEP EXPLANATION:
The area of a triangle is given by the following equation:
[tex]A=\frac{b\cdot h}{2}[/tex]We replace and solve for h (height)
[tex]\begin{gathered} 18=\frac{6\cdot h}{2} \\ h=\frac{18\cdot2}{6} \\ h=6 \end{gathered}[/tex]The height of the triangle is 6 inches
Hello, I had a question on how to find the leading coefficient and the degree.
Answers
Given:
given polynomial is
[tex]23v^5-2v+4v^8-18v^4[/tex]Find:
we have to find the leading coefficient and degree of the polynomial.
Explanation:
The lewading coefficient is the coefficient of highest power term of the polynomial.
Highest power of v is 8 and its coefficient is 4.
Therfore, leading coefficient is 4.
and the degree of the polynomial is equal to the highest power of v in the polynomial, which is 8.
Therefore, the leading coefficient of polynomial is 4 and degree is 8.