Using the Factor Theorem and limits, the end behavior of g(x) is that the function decreases to the left and increases to the right.
What is the Factor Theorem?The Factor Theorem states that a polynomial function with roots [tex]x_1, x_2, \codts, x_n[/tex] is given by:
[tex]f(x) = a(x - x_1)(x - x_2) \cdots (x - x_n)[/tex]
In which a is the leading coefficient.
Considering the table, the roots are given as follows:
[tex]x_1 = -4, x_2 = 5, x_3 = 12[/tex]
Hence the function is:
f(x) = a(x + 4)(x - 5)(x - 12).
f(x) = a(x² - x - 20)(x - 12)
f(x) = a(x³ - 13x² - 32x + 240).
When x = 0, y = 1, hence the leading coefficient is found as follows:
240a = 1
a = 0.004167
Then:
f(x) = 0.004167(x³ - 13x² - 32x + 240).
The end behavior is given by the limits of f(x) as x goes to infinity, hence:
[tex]\lim_{x \rightarrow -\infty} f(x) = \lim_{x \rightarrow -\infty} 0.004167 x^3 = -\infty[/tex].[tex]\lim_{x \rightarrow \infty} f(x) = \lim_{x \rightarrow \infty} 0.004167 x^3 = \infty[/tex].Hence the end behavior is that the function decreases to the left and increases to the right.
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If f(x) = x2 – 2x and g(x) = 6x + 4, for which value of x does (f + g)(x) = 0?
hi
f(x) = x² -2x
g(x) = 6x+4
(f+g) (x) = x²-2x +6x+4 = x²+4x +4 = (x+2)² = (x+2) (x+2)
(f+g) (x) = 0 means = (x+2) (x+2) = 0
so x+2 = 0
x = -2
(f+g) (x) = 0 for x = -2
Which of the following expressions does sin(x + y) - sin(x - y) simplify to?
O2(sin x)(sin y)
O2(sin x)(cos y)
O2(cos x)(cos y)
O 2(cos x) (sin y)
The answer choice which sin(x + y) - sin(x - y) simplifies to is; 2(cos x)(sin y).
Which of the following expressions does sin(x + y) - sin(x - y) simplify to?It follows from the task content that the expression given in the task content can be simplified by trigonometric identities as follows;
sin(x + y) - sin(x - y) = sinxcosy + cosxsiny - (sinxcosy -cosxsiny)
= 2cosxsiny.
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1 On a trip, a family drove 270 kilometers in 3 hours. a Find how many kilometers were traveled in one hour. Express this as a rate per hour. it rate
Answer:
90 kilo per hour
Step-by-step explanation:
hope that helps!!
Here are two steps from the derivation of the quadratic formula (image w question below)
Answer:
B. Completing the square
Step-by-step explanation:
Between the first and second steps shown, the square of half the x-term coefficient was added to both sides. That is a value that makes the polynomial on the left be a "perfect square trinomial."
The process of adding the value required to make the left side a perfect square is called "completing the square."
Pizza prices by city (Data in Pizza prices) The company that sells frozen pizza to stores in four markets in the United States (Denver, Baltimore, Dallas, and Chicago) wants to examine the prices that the stores charge for pizza slices. Here are boxplots comparing data from a sample of stores in each market:
The answers to the questions are
a. No they are not the same
b. The presence of outliers are known to affect the market.
How to solve the box plot
For these areas we have
Q1 = 2.7 Q3 = 3 median = 2.8 out;ier 2.
Q1 = 2.5 Q3 = 2.7 median = 2.6 out;ier 3.1.
Q1 = 2.5 Q3 = 2.75 median = 2.65 out;ier 1.6
Q1 = 2.4 Q3 = 2.6 median = 2.5
We can see that the median prices in the markets are nearly similar except for the one that is conatined in the first market.
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You have a credit card that charges an interest rate of 16.15% compounded monthly. The table below shows your activity for the month of April. Date Activity Amount Balance April 1 Beginning Balance 1,000.00 April 5 Purchase 29.10 1,029.10 April 12 Payment −225.00 804.10 April 15 Purchase 97.25 901.35 April 23 Purchase 19.00 920.35 April 26 Purchase 28.40 948.75 April 30 Ending Balance 948.75 What is the average daily balance for this account? $ What is the finance charge for the month of April? $
1. The average daily balance for this credit card account is $187.74.
2. The finance charge for the month of April is $249.22.
How is the average daily balance calculated?The average daily balance for April is the total of the balance for every day in the billing cycle divided by the number of days in the billing cycle.
A billing cycle for a credit card account is usually one month.
Data and Calculations:Interest rate = 16.15% compounded monthly
Date Activity Amount Balance
April 1 Beginning Balance $1,000.00
April 5 Purchase 29.10 1,029.10
April 12 Payment −225.00 804.10
April 15 Purchase 97.25 901.35
April 23 Purchase 19.00 920.35
April 26 Purchase 28.40 948.75
April 30 Ending Balance 948.75
Total $5,632.05
Average daily balance = $187.735 ($5,632.05/30 days)
Daily interest rate = 0.04425 (16.15%/365)
Finance charge = $249.22 ($187.74 x 0.04425 30 days)
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A line passes through the point −8, 4 and has a slope of −3/4.
Answer:
y = (-3/4)x + 2
Step-by-step explanation:
y = m * x + b where m is the slope and b is the y-intercept
y = (-3/4)x + b substituting the slope
4 = 6 + b => b = 2 substituting the point given
y = (-3/4)x + 2
A solution of ibuprofen contains 150g in 800ml. What is the percent strength of this solution?
Answer:
18.75 percent
Step-by-step explanation:
150 / 800 x 100 = 18.75
The probability that a student has a Visa card (event V) is .76. The probability that a student has a Master card (event M) is .16. The probability that a student had both is .04.
Answer:
The Probability of both happening is 0.304.
Step-by-step explanation:
P(A) × P(B)
= 0.76 × 0.4
= 0.304
11) Find the mode of the data set.
O a.) 9
Ob.) 8
Oc.) 7
O d.) 6
Data:
5, 8, 12, 6, 7, 10, 14, 6, 13
4
Answer:
6
Step-by-step explanation:
The mode is the number that is repeated the most in the data set. 6 is the only number that is repeated twice, so it is the mode.
Brainliest, please :)
A sports store sells 70 pairs of running shoes per
day for $40.00 each. The owner estimates that
for each $3.00 increase in price, 3 fewer sales
are made each day. What price should be charged
to maximize profit?
Answer:
$55
Step-by-step explanation:
so, we know that each day the store will currently sell $2800 worth of shoes.
we want to know the maximum of the expression (40+3x)(70-3x), expanding we get 2800 - 9x^2 + 90x,
the maximum of this would be x = 5, so the price they should charge is 55
Determine which equation is belongs to the graph of the limacon curve below.
[-5,5] by [-5,5]
a.
r = 1 + 3 sin theta
c.
r = 1 + 3 cos theta
b.
r = 2 + 2 sin theta
d.
r = 3 + sin theta
Option a. The equation that is used to show the graph of the limacon is given as r = 1 + 3 sin theta.
How to solve for the equationWe have these ppoints [-5,5] by [-5,5]
The limacoin is used to represent a shape that may appear like that of a snail.
This is written in the form of
r = a ± b sin θ
and
r = a ± b cos θ
Given that we have the ± sign, the curve that is at the top of the horizontal; line is the + sign and the one below is the -
If a/b < 1 then a circle is within the circle that was formed as a graph.
Hence from the description that we have given here, the graph has the forms of
r = a + b sin θ
This is the equation that can be used to suit the form r = 1 + 3 sin theta
Hence option a is right.
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Tornadoes Use the frequency distribution from Exercise 12 in Section on page 49 to construct a frequency polygon. Does the graph suggest that the distribution is skewed? If so, how?
The distribution is skewed because it's on the right side of the polygon and this illustrates that's it's positively skewed.
How to illustrate the information?It should be noted that the polygon can be gotten by plotting the data.
After the analysis of the distribution, the distribution is skewed to the right.
This illustrates that it is skewed.
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Ramon is six years younger than 4 times his brothers age. Oh f his brother is 5 year old, how old is Ramon
Answer:
14
Step-by-step explanation:
The equation would be R = 5(4) - 6. Multiply 5 by 4 to get 20, then subtract 6 to get 14.
find each lettered angel measure
Answer:
a = 64°
b = 138.7°
Step-by-step explanation:
First, Let's find the measure a,
180° = 116° + a180 - 116 = aa = 64°______
Now,
90° + a + 82° + x + x + x = 360°90+ 64 + 82 + 3x = 360° 236 + 3x = 360 3x = 124/ 3x = 41.3°______
Now that we found out what x equals, let's find 'b'-
b + x = 180°b + 41.3 = 180b = 180 - 41.3b = 138.7°Consider the following sample data set of 20 numbers.
24 30 4 42 40 26 23 36 12 45 29 21 34 16 47 28 32 54 19 9
1.
Create a relative frequency table and a frequency histogram with the bin width 8.
2.
Find the sample mean. (Round to the nearest hundredth.)
3.
Find the sample standard deviation
. (Round to the nearest hundredth.)
The mean = 28.55, while the standard deviation is 13.16
1. The histogram is an attachment
How to calculate for the mean of the data setWe have the following numbers
24 30 4 42 40 26 23 36 12 45 29 21 34 16 47 28 32 54 19 9
The sum of these numbers is given as
571
The total numbers = 20
The mean = 571/20
= 28.55
2 = How to find the standard deviation= (24 - 28.55)2 + ... + (9 - 28.55)/20 - 1
= 3292.95/19
= 173.31315789474
s = √173.31315789474
= 13.164845532506
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Can you help with this question? I'm not sure if the black highlighted choice is right
Answer:
See below
Step-by-step explanation:
Remember... when you square a negative number, you get a positive result
AND you cannot divide by zero AND you cannot have the sqrt of a negative number so:
-2 > x > 2 (looks like 'D' but there is a negative sign missing)
please help me i included the images of the questions, ill give brainliest
Answer:
1: r^5, 2: st^2, 3: qr, 4: 1, 5: m, 6: x, 7: 1/z, 8: a, 9: d^4f^2 10: 1, 11: cd^2, 12: b, 13: 1, 14: st^2, 15: 1/mn.
Step-by-step explanation:
1 explanation: Cancel the common factor of r^6 and r.
2 explanation: Simplify the expression.
3 explanation: simplify the expression.
4 explanation: Simplify the expression.
5 explanation: simplify the expression.
6 explanation: Cancel the common factor of x^2 and x.
7 explanation: Cancel the common factor of z^4 and z^5.
8 explanation: Cancel the common factor of a^2 and a.
9 explanation: simplify the expression.
10 explanation: simplify the expression.
11 explanation: simplify the expression.
12 explanation: simplify the expression.
13 explanation: simplify the expression.
14 explanation: simplify the expression.
15: simplify the expression.
I am odd I am less than 40 both of my digits are perfect squares t-u=0
Answer:
19 or 14
Step-by-step explanation:
Since the number is odd you can disqualify all even numbers up to 40 including 0.
Next since this number has 2 digits you can take out all 1 digit numbers.
After that, find perfect squares that also are 1 digit each.
Lastly merge the combination of the numbers as each digit on each sides in such a way that the result is less than 40.
A diver begins at 90 feet below sea level. She descends at a steady rate of 6 feet per minute for 6 minutes. Then, she ascends 20 feet. This expression shows her current depth in feet.
Negative 90 minus 6 (6) + 20
What is her current depth?
Negative 596 feet
Negative 556 feet
Negative 146 feet
Negative 106 feet
Which is the graph of the inequality?
5y+x>−10
Number graph ranging from negative twenty to twenty in increments of two on the x and y axes. A dotted line with a positive slope is drawn in the fourth quadrant of the graph. The area above the line is shaded gray.
Number graph ranging from negative ten to ten on the x and y axes. A solid line passes through (negative one, zero) and (zero, three). The area to the left of the line is shaded gray.
Number graph ranging from negative twenty to twenty in increments of two on the x and y axes. A solid line passes through (zero, negative fourteen) and (two, zero). The area to the right of the line is shaded gray.
Number graph ranging from negative ten to ten on the x and y axes. A dotted line passes through (zero, negative two) and (five, negative three). The area above the line is shaded gray.
We can simplify the inequality to:
y > (-1/5)*x - 2
From that, we conclude that the correct option is the last one.
Which is the graph of the given inequality?
Here we have the inequality:
5y + x > -10
If we isolate y, we get:
y > (-10 - x)/5
y > (-1/5)*x - 2
Then the inequality will be a dashed/dotted line with a negative slope, that passes through the point (0, -2), such that the region above and to the right of the line is shaded.
From that we conclude that the correct option is the last one:
"Number graph ranging from negative ten to ten on the x and y axes. A dotted line passes through (zero, negative two) and (five, negative three). The area above the line is shaded gray."
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whats the correct answer
Answer:
C
Step-by-step explanation:
The first part of this is to represent the center.
It sits at (1,-1), so the left hand part of the equation is
(x - 1)^2 + (y + 1) = r^2
That means the answer has to be either B or C. D gets knocked out of the running because of the minus sign in the middle. D does not give a circle.
B is wrong because the y value should be plus. So the answer is C. Notice because the question is multiple choice you don't need to solve for r since all answers give r^2 = 36
Name the figure below in two different ways.
Y
Symbol:
and
M
A
The line segment in the figure can be named as: IYM and MYI.
How to Name a Line Segment?If we have three points on a line segment, the point on the middle will be the alphabet in the center when naming the line, while the alphabets of both endpoints can be written either at the beginning or ending.
Given the figure above, Y will be at the center. The endpoints are I and M. Therefore, the line segment can be named as: IYM and MYI.
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What is the absolute value of –6? Use the number line to help answer the question.
Answer:
6
Step-by-step explanation:
Absolute value is a number's distance from 0, another way to think of it is that it makes any number positive, so |-6|, the absolute value of -6 would be 6.
Answer:
6
Step-by-step explanation:
The absolute value is always positive, since it's the number's distance from zero.
Thus, the absolute value of -6 is 6.
Done !!
which of the following functions is graphed below?
The function that's illustrated in the graph is function D.
How to explain the function?First, you look at the left side of the graph. You can tell by the shape that it is an x³ function.
Also, the filled-in circle means inclusive. so we know that when x is less than or equal to a number.
The answer that illustrates the information explained is D.
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Answer:
B.
Step-by-step explanation:
An open circle means to exclude the point.
A closed circle means to include the point.
In this graph we see a part of a parabola with an open circle above. The parabola starts at x = 1, but does not include x = 1, and the x values of the parabola increase.
A parabola has an x squared in the equation.
The solution has to have an equation with an x² as its greatest exponent, and also must include x > 1.
The lower part of the graph is a third degree polynomial, so it must have an x cube term, x³. Also, the greatest x value for the x³ function is x = 1, but x = 1 is included. Then all x values tot he left of x = 1 are also included, so for the cubic polynomial, the domain (x values) must be x ≤ 1.
The answer is B.
The sides of a rectangle are enlarged by a scale factor of 2. Write
down the scale factor that the area is enlarged by.
Answer:
4
Step-by-step explanation:
both sides are multiplied by 2 which means its the original area*2*2 which means it's the original area*4
Question 1 (3 points)
Solve the following linear system:
y = -2x - 5
y = 2/3x + 3
as an ordered pair (x,y)
Answer:
Step-by-step explanation:
hello : y = -2x - 5
y = 2/3x + 3
means : -2x-5 = 2/3 x+3
-6x-15 = 2x +9
-8x=24 so : x = -3
put the value for : x in the first equation :y = -2(-3)-5 =1
the ordered pair (-3;1) is solution
Explain how to draw a line segments that measures 2 7/16 inches.
Answer: draw the line using a ruler on which you have identified points 2 7/16 inches apart.
Step-by-step explanation: On your ruler graduated in inches with marks at 1/16-inch intervals, locate the 0 mark and the mark 1/16 inch before the half-inch mark between 2 and 3 inches.Draw your line along the edge of the ruler between the two marks you have identified: 0 and 2 7/16. The line will be 2 7/16 inches long.
Find the interquartile of the data set that consists of 8,18,4,2,3,7,11,13,5,1 answers 11,8,6,3
Answer:
I.Q.R = 11 - 3
I.Q.R = 9
the interquartile range = 9
Time: ~15 minutes
Materials: pencil/paper or whiteboard/marker
Task: Two men and two women want to take a rowboat to an island. The boat has a maximum capacity of one man or two women. Someone must always be in the boat when it’s moving. How can all four of them get to the island?
The four of them can get to the island if the two women begins the journey first. Detail below:
How can the four of them get to the island?From the question given, we were told that:
The boat has a maximum capacity of one man or two women.Someone must always be in the boat when it’s moving.With the above information in mind, we can determine how the four of them can get to the island by following the steps listed below:
The two women will take the boat to the island.One of the women will return with the boat to meet with the other two men leaving the other woman on the island.One of them men will then take the boat to the island to meet the other women on the island.The woman on the island will return with the boat to meet the other man and woman.The two women will take the boat to meet the other man on the island.One of the women will return with the boat to meet with the other man.The last man will take the boat to meat the other man and woman on the island.The woman on the island will return with the boat to meet the last woman.Finally, the two women will take the boat to meet the two men on the islandLearn more about riddles:
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