Is (a-3) a factor of (a^3-6a^2+29)?
Answers
f(3) = 8 - 6*9 + 29
f(3) = 8 - 54 + 29
f(3) = - 17
As further "proof", here is the graph. Notice that the graph cuts the x axis around -2 , 2.5 and 4.2 (These are rough guesses). The factors are
(a+2)(a - 2.5)(a - 4.2)
Related Questions
What is the correct definition of the third quartile of a data set?
A. The third quartile is all the numbers of the data set added together and divided by 3. B. The third quartile is the difference between the maximum and median. C. The third quartile is the median of the upper half of data in the data set. D. The third quartile is the mode of the upper half of data in the data set.
Answers
The third quartile (also called the upper quartile) has 75 percent of the data below it and the top 25 percent of the data above it. The third quartile is the same as the median of the part of the data which is greater than the median.
therefore
the answer is the option
C.) The third quartile is the median of the upper half of data in the data set.
Option: C is the correct answer.
C. The third quartile is the median of the upper half of data in the data set.
Step-by-step explanation:We know that our data is divided into three quartiles:
1)
First quartile or lower quartile--
It is the median of the lower set of the data.
2)
Middle quartile or Median--
Median is the central tendency of the data and it always exist in the middle of the data set.
3)
Third quartile or upper quartile--
It is obtained by finding the median of the upper set of the data.
Hence, the answer is: Option: C
A bike ramp has a slope of 3/4. What is the angle the ramp makes with the ground?
Answers
Hope it helps !
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Galileo wanted to release a wooden ball and an iron ball from a height of 100 meters and measure the duration of their fall. He found a plane with an incline of 12 degrees that he could climb until he could get to an altitude of 100 m. How far should Galileo walk up the inclined plane? Round your final answer to the nearest hundredth.
Answers
We have to find the value of the hypotenuse.
For this we use the following trigonometric relationship:
senx = C.O / h
Where
x: angle
C.O: opposite leg
h: hypotenuse.
Substituting the values we have:
sen (12) = 100 / h
We cleared h:
h = 100 / sin (12)
h = 480.97 m
Answer:
Galileo should walk 480.97 m up the inclined plane
Galileo walk 480.97 meters up the inclined plane if Galileo wanted to release a wooden ball and an iron ball from a height of 100 meters and measure the duration of their fall.
What is the trigonometric ratio?The trigonometric ratio is defined as the ratio of the pair of a right-angled triangle.
We have:
Galileo wanted to release a wooden ball and an iron ball from a height of 100 meters.
Let's suppose Galileo walked x meters up the inclined plane.
The plane with an inclined a 12°
As we can see in the right angle triangle the sin ratio:
[tex]\rm sin24\° = \frac{100}{x}[/tex]
[tex]\rm x = \frac{100}{sin24\°}[/tex]
x = 480.97 meters (Sin12° = 0.20791)
Thus, Galileo walk 480.97 meters up the inclined plane if Galileo wanted to release a wooden ball and an iron ball from a height of 100 meters and measure the duration of their fall.
Know more about trigonometry here:
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32 to 28 is what percentage of what change an increase or decrease
Answers
There are seven black marbles and nine white marbles in a bag what is the aprroximate probability of drawing two black marbles and then a white marble without replacement
Answers
There is a probability of 43.75% to pick a black marble in the bag with 16 marbles.
If you do , there will be 6 black marbles and 9 white marbles left in the bag. The probability to pick anpther black marble is 6/15 or 40%.
If you do pick another black marble , there will be 5 black marbles and 9 white marbles left in the bag , which means the probability of you getting a white marble next is 9/14 or 64.28%.
Now we just have to multiply the probability of you picking the marbles in the right order :
0.4375 × 0.4 × 0.6428 = 0.11249
Which is approximately 11.25%
There is a probability of 11.25% of you getting two black marbles and one white marble in a bag with 7 black marbles and nine white marbles .
I hope you understood my brief explanation. And please consider marking this awnser as Branliest if you think it deserves it. Thank you :)
The approximate probability of drawing two black marbles and then a white marble without replacement is 9/80.
What is probability?Probability deals with the occurrence of a random event. The chance that a given event will occur. It is the measure of the likelihood of an event to occur.The value is expressed from zero to one.
For the given situation,
Number of black marbles = 7
Number of white marbles = 9
The event of drawing two black marbles from seven black marbles is
⇒ [tex]\frac{7C_{2} }{16C_{2} }[/tex]
[tex]7C_{2} =\frac{(7)(6)}{(1)(2)}[/tex]
⇒ 21
[tex]16C_{2}=\frac{(16)(15)}{(1)(2)}[/tex]
⇒ 120
Now, [tex]\frac{7C_{2} }{16C_{2} }=\frac{21}{120}[/tex]
Total number of balls, after drawing 2 black balls without replacement is
⇒ 16 - 2 = 14
The event of drawing a white marble without replacement from nine white marbles is
[tex]\frac{9C_{1} }{14C_{1} } = \frac{9}{14}[/tex]
Thus, the approximate probability of drawing two black marbles and then a white marble without replacement is
P(E) = [tex](\frac{21}{120}) (\frac{9}{14} )[/tex]
⇒ 9/80
Hence we can conclude that the approximate probability of drawing two black marbles and then a white marble without replacement is 9/80.
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The following table gives the science scores and times spent studying for 10 students:
Name Scores (%) Time Spent
Studying (hrs)
Angela 90 4
Brad 70 2
Curt 80 3
Dozer 60 1
Enda 50 1
Frank 40 2
Gill 100 4
Hailey 100 3
Intra 50 1
John 80 3
Describe the correlation between the score and time spent studying.
Answers
When identifying the independent and dependent quantities, we think about what would cause the other to change. The score on the test would not cause the number of hours spent studying to change; rather, the number of hours spent studying would cause the score to change. This means that the number of hours studying would be the independent quantity and the score would be the dependent quantity.
Plotting the graph with the time studying on the x-axis (independent) and the score on the y-axis (dependent) gives you the graph shown. You can see in the image that there seems to be a positive correlation; the data seem to generally be heading upward.
As per the table, the given science scores and time data for studying about 10 hours are given.
A positive correlation can be seen between the number of hours spent studying and the scores. This states that the no. of hours of studying could be on the independent and the score would be the dependent quantity. When on the graph with the time studying on the x-axis and the y-axis gives you the graph the line seems to be going up hence a positive correlation.Learn more about the gives the science scores and times spent studying.
brainly.com/question/25299087.
Does anyone know what the system of equations for this would be?
Answers
rewrie as:
a = 10 pounds - b
0.75a + 0.50 b = $6.00
replace a with the above equation:
0.75(10-b) +0.50b = 6.00
distribute the(10-b):
7.50 - 0.75b + 0.50b = 6.00
combine like terms:
7.50-0.25b = 6.00
subtract 7.50 from each side:
-0.25b = -1.50
divide both sides by 0.25 to find b
b = -1.50 / -0.25
b = 6
she bought 6 pounds of bananas and 4 pounds of apples
What is the vertex of the graph of y = x2 + 4x?
(–2, –12)
(–2, –8)
(–2, –6)
(–2, –4)
Answers
Answer:
(-2, -4)
Step-by-step explanation:
Let's remember how to calculate the vertex of a parabola:
If we have the equation of the parabola given in the form y = ax^2 + bx + c, the x-coordinate of the vertex is x = -b/2a. For the y-coordinate we just replace the x of the equation with -b/2a and do the calculation.
In this case, a = 1, b = 4, c = 0.
The x-coordinate of the vertex is x = -4/2*1 = -2
The y-coordinate is y = (-2) ^2 + 4*(-2) = 4 - 8 = -4
Therefore, the vertex is (-2, -4)
AC is tangent to circle O at A. If mBY =24, what is m
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we know that
the inscribed angle measures half of the arc it comprises.
then
m∠YAB=(1/2)*m∠BY-------------> m∠YAB=(1/2)*24°=12°
m∠YAC=90°-m∠YAB=90°-12°=78°
the answer is the option C) 78°
PLEASE HELP ME ON THIS
Answers
8x+12y<96
x+y>10
Please help ASAP!! Super appreciated!!! <3
Answers
Your school drama club is putting on a play and hopes to raise $600 from ticket sales. They sell adult tickets for $8 each and student tickets for $5 each. Let x represent the number of adult tickets and y represent the number of student tickets. The equation to represent the number of tickets sold to reach their goal, 8x+ 5y = 600, is graphed below. If 40 adult tickets are sold, how many student tickets must be sold to reach their goal?
Diagram can be shown here:
https://static.k12.com/eli/bb/343/3_23939/2_15013_4_23943/d7066d09bfa7bf4e8df2b2c0b508a3e8ba21c76d/media/b1cd8381087979f1dffbcd6f3efef158a61fbd57/mediaasset_649354_1.gif
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The measure of a minor arc is equal to the measure of __________
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PLEASE HELP ME ON THIS
QUICKLY!!!!!!!!!!!!!!!!!
~BRAINLIEST AVAILABLE
Answers
Next, let's look at the y values again, and test out the common ratios given. First, let's use 0.6. If it's a common ratio of 5, 3, 1.8, and 1.08, then we can find that out by multiplying it by 5 first.
5 x 0.6 is 3.
Then, 3 x 0.6 is 1.8.
Finally, 1.8 x 0.6 is 1.08.
Therefore, B is correct. The table represents a geometric sequence because the successive y-values have a common ratio of 0.6, since multiplying the values by 0.6 equals the next value down.
Please help will give Brainliest!! 1.Find the length of line segment AB when A=(2, 0) and B=(2, 6)
2.Find the length of CD: C(12, -10) and D(0, -6)
3.Find the length of EF: E(-3, 2) and F(6, 2)
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Try to work it out but if you still need help then ill be be happy to do so :)
Can someone please help me out on this?
Answers
If GH = 3 and HJ = 5, then G ___ J.
Choose the relationship symbol that would make a true statement.
Answers
Step-by-step explanation:
The given equation is as follows.
GH = 3 and HJ = 5
Therefore, simplify for H from both the equations as follows.
H = [tex]\frac{3}{G}[/tex] .......... (1)
and, H = [tex]\frac{5}{J}[/tex] .......... (2)
Equating both equation s(1) and (2), we get the following.
[tex]\frac{3}{G}[/tex] = [tex]\frac{5}{J}[/tex]
G = [tex]\frac{3J}{5}[/tex]
or, G = 0.6J
This means that J will be 0.6 times greater than G.
Thus, we can conclude that G < J.
PLEASE HELP ASAAAAPPPPPP
Answers
15. The following statements concerning the location of an extreme value of a twice-differentiable function, f, are all true. Which statement also includes the correct justification?
(A) The function has a maximum at x=5 because f'(5)=0.
(B) The function has a maximum at x=5 because f'(x)<0 for x<5 and f'(x)>0 for x>5.
(C) The function has a minimum at x=3 because the tangent line at x=3 is horizontal.
(D) The function has a minimum at x=3 because f'(x)<0 for x<3 and f'(x)>0 for x>3.
(E) The function has a minimum at x=3 because f"(3)<0.,
Answers
The mean of the data set is 18 what’s the missing number 21,11,blank,27,22,13,16
Answers
9514 1404 393
Answer:
16
Step-by-step explanation:
The sum of the 7 numbers needs to be 7·18 = 126.
Then the missing number is ...
126 -21 -11 -27 -22 -13 -16 = 16
Factor completely x2 - 8x + 16
A. (x+4)(x+4)
B. (x-4)(x-4)
C. (x+4)(x-4)
D. (x-2)(x-8)
Answers
When you take -4+-4, you will get -8 and when you multiply -4 x -4, you will get 16
Rotate this image 90 clockwise around the point (-1 1 )
Answers
In this case given the point (-1, 1), the image will be (1, -(-1)) or (1, 1)
Answer: You didn't put options A, B, C, OR D
no picture either
Step-by-step explanation:
The table below shows the data collected on the number of car washes, y, each day since the Auto Spa opened, x.
Days Since Auto Spa Opened 0 20 40 60 80 100
Number of Car Washes 29 35 18 31 28 14
The owner of the new Auto Spa created a line of best fit for the data that can be modeled by the following equation.
y = -0.12x + 31.76
Match the slope and y-intercept with the correct description for the given situation.
titles
the number of cars washes on the day the Auto Spa opened
the ratio of car washes to the number of days since the Auto Spa opened
the number of car washes
the total number of days since the Auto Spa opened
the ratio in the number of days since the Auto Spa opened to the total profit
pair
y-intercept
slope
Answers
Explanation:
This line of best fit is in slope intercept form: y=mx+b, where m is the slope and b is the y-intercept.
In this equation, m corresponds with -0.12 and b corresponds with 31.76.
The slope is the ratio of change in y to change in x. The y-coordinate of each point represents the number of car washes and the x-coordinate represents the number of days since Auto Spa opened; the ratio of change in y to change in x is then the ratio of the number of car washes to the number of days since Auto Spa opened.
The y-intercept is the point where the data crosses the y-axis; at this point, and all on the y-axis, the x-coordinate is 0. In this problem, the x is the number of days since Auto Spa opened; if it is 0, this means 0 days since it opened, which would be its opening day. Thus the y-intercept is the number of car washes on opening day.
Answer:
The slope is the ratio of car washes to the number of days since Auto Spa opened; and the y-intercept is the number of car washes on the day the Auto Spa opened.
Step-by-step explanation:
What is the maximum number of real zeros that a function with degree 5?
Answers
y = (x - 22)(x - 1)(x + 1)(x - 2)(x+2)
Rules that govern the ways that logarithms are simplified and combined are going to be very similar to simplifying and combining rules for what other family of functions?
Exponential
Linear
Rational
Polynomial
Answers
Rules that govern the ways that logarithms are simplified and combined are going to be very similar to simplifying and combining rules for the exponential family of function.
This comes from the definition of logarithm itself which says that a logarithm is a quantity representing the power to which a fixed number (the base) must be raised to produce a given number.
Let us illustrate this by way of an example. We know that 100 can be represented as [tex] 10^2 [/tex]. Here 10 is the base, 2 is the power and 100 is the given number. Therefore,
[tex] 10^2=100 [/tex]
Likewise, we can represent 1000 as [tex] 1000=10^3 [/tex]
Now, if we multiply [tex] 10^2 [/tex] and [tex] 10^3 [/tex] we will get: [tex] 10^2\times 10^3=10^{2+3}=10^5 [/tex]. We added the powers. Therefore, the logarithm of [tex] 10^5 [/tex] to the base 10 is 5.
Let us see if we will get the same result by using the rules of logarithms.
[tex] log(10^2\times 10^3)=log(10^2)+log(10^3)=2log(10)+3log(10)=2+3=5 [/tex]
As we can see we got the same result by using the logarithm and the exponential rule, thus, verifying our answer. Similar results can be obtained for other operations of the logarithmic rule.
A grocery store sells chili peppers at $2.04 for a dozen. At this rate, what's the cost per pepper? A. $0.17 B. $1.70 C. $0.07 D. $1.07
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For which data representation is the median the better measure of center
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In all but the 3 graphs, the data is perfectly symmetrical. This means that the mean and the median would be the same.
However, in the second graph the data is skewed to the right. This means that the mean would also be skewed to the right due to the larger scores there. Using the median in this case would give a clearer picture of the data.
Convert the fraction to decimal and decimal into the fraction 10.222
Answers
I'm not sure if that's what you were looking for but I hope this helps!
Answer:
10 and 222/1000
Step-by-step explanation:
(x 2 + 2x - 1)(x 2 + 2x + 5) Please help asap!
Answers
To solve this equation, we can use distributive property.
I listed the terms you have to multiply :
x² × x² = x^4
x² × 2x = 2x³
x² × 5 = 5x²
2x × x² = 2x³
2x × 2x = 4x²
2x × 5 = 10x
-1 × x² = -x²
-1 × 2x = -2x
-1 × 5 = -5
Add all of them....
x^4 + 2x³ + 5x² +2x³ + 4x² + 10x - x² - 2x - 5
add up the like terms to simplify
x^4 + 4x³ + 8x² + 8x - 5
Hope this helped! :)
Line AB intersects line DF. Which statement shows that the two lines are perpendicular?
Line AB and line DF are on the same plane.
Line AB and line DF intersect only once.
Line AB and line DF intersect at a 90° angle.
Line AB and line DF intersect at a 180° angle.
Answers
Line AB and line AD intersect at a 90° angle
Explanation:
Two lines are said to be perpendicular if the angle between the two lines is 90 degrees.
If the angle between the two lines is 180, the two lines are said to be supplementary angles
The first and second options do not imply that the lines are perpendicular as the angle formed between them could be less or more that 90°.
Hope this helps :)