Answer: A
Step-by-step explanation:
Points 1 to 6To present y=-x^3+3x^2, 9 points must be selected, point 1: Domain, 2: zeros of the function, 3: period and symmetry, 4: sign of the function, 5: going to the edge of the function, 6: asymptotes, 7: monotony and extreme values, 8: concavity and convexity, 9: to present the function graphically.
ANSWERS
1. Domain: all real values
2. Zeros: 0 (with multiplicity 2) and 3
3. Not periodic. Symmetric about the point (1, 2)
4. Positive for x < 3; negative for x > 3
5. f → ∞ as x → -∞; f → -∞ as x → ∞
6. none
EXPLANATION
1. The domain of a function is the set of all the x-values for which the function exists. In this case, we have a polynomial function and, therefore, the domain is all real values.
2. To find the zeros of the function, we have to solve,
[tex]-x^3+3x^2=0[/tex]First, factor x² and -1 out. To do so, we have to divide each term by x² and by -1 - or, in other words, divide by -x²,
[tex]\begin{gathered} -x^2\left(\frac{-x^3}{-x^2}+\frac{3x^2}{-x^2}\right)=0 \\ \\ -x^2(x^{3-2}-3x^{2-2})=0 \end{gathered}[/tex]So, we have,
[tex]-x^2(x-3)=0[/tex]In this equation, we can see that if x = 0, then the equation is true. Also, if x = 3 the equation is true. So, these are the two zeros, with the particularity that x = 0 has multiplicity 2. This is because the factor related to that zero is x squared.
Hence, the zeros are 0 and 3. 0 has multiplicity 2.
3. As mentioned before, this is a polynomial function, which means that it is not a periodic function. A cubic function is an odd function, and it is symmetric about the origin. However, this function is not the parent function, x³, but it is symmetric about the point (1, 2).
4. We know that the function is zero at x = 0 and at x = 3. For x < 0, the function is positive,
[tex]with\text{ }x=-1:\text{ }y=-(-1)^3+3(-1)^2=-(-1)+3\cdot1=1+3=4[/tex]For 0 < x < 3, the function is also positive. This is because x = 0 with multiplicity 2.
Then, since the function crosses the x-axis at x = 3 and that zero has multiplicity 1, we can conclude that the function is negative for x > 3.
Hence, is the function is positive for x < 3 and negative for x > 3.
5. As mentioned in part 4, the function is positive for all values of x less than 3, which means that the function goes to infinity as x goes to negative infinity.
Since for x > 3 the function is always negative, it goes to negative infinity as x goes to infinity.
6. A polynomial function has no restrictions in the domain and, therefore, has no asymptotes.
What is the effect on the volume of a cylinder if the radius is doubled while the height is halved?A. The volume is halved.B. The volume remains the same.C. The volume is multiplied by 4.D. The volume is doubled.
Given that
There is a cylinder and we have to find the change in its volume if the radius is doubled and the height is halved.
Explanation -
Let the Initial radius be r and the height be h. Then the initial volume will be
[tex]v=\pi\times r^2\times h-----------(i)[/tex]Now applying the given changes,
new radius = 2 x r
new height = h/2
Then the new volume will be V,
[tex]\begin{gathered} V=\pi\times(2r)^2\times\frac{h}{2} \\ \\ V=\pi\times4r^2\times\frac{h}{2} \\ \\ V=2\times\pi\times r^2\times h \\ \\ On\text{ substituting v = }\pi\times r^2\times h \\ \\ V=2\times v \end{gathered}[/tex]Hence volume will be doubled. And option D is correct.
Final answer -
Therefore the final answer is OPTION D.What does it mean to say that a number is a perfect square? Give one example of a number that is a perfect square and one that is not. Explain your examples.
A perfect square is a number that is gotten by multiplying it by itself.
An example of a perfect square is 25 and one that is not is 7.
What is a perfect square?A square number, sometimes known as a perfect square, is an integer that is the square of another integer; in other words, it is the product of another integer and itself. For instance, 9 is a square number since it equals 3² and may be expressed as 3 × 3.
A perfect square is a number that can be written as the product of two integers or as an integer's second exponent. 25 is a perfect square because it is the product of the integer 5 and itself, 5 × 5 = 25. A perfect square is a positive integer formed by multiplying an integer by itself.
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Here are 5 lines on a coordinate grid: Write equations for lines a,b,c,d and e a: b: c: d: e:
The equations of each of the given lines are:
Line a is: x = -4
Line b is: x = 4
Line c is: y = 4
Line d is: y = -2
Line e is: y = -¾x + 1
How to Write the Equation of a Line?If we determine the slope value, m, and the y-intercept value, b, the equation of a line can be written as y = mx + b in slope-intercept form by plugging in the values of the determined variables.
For a vertical line, the equation is expressed as x = b, where b is the x-intercept of the line.
For a horizontal line, the equation would be y = b, where b is the line's y-intercept value.
Equation of line a (vertical line):
The x-intercept is -4. This means that, the equation of line a is: x = -4
Equation of line b (vertical line):
The line's x-intercept is 4. To write the equation of the line, substitute the value of the x-intercept into x = b.
Therefore, the equation of line b is: x = 4
Equation of line c (horizontal line):
The y-intercept (b) = 4. Substitute the b = 4 into y = b.
The equation of line c is: y = 4
Equation of line d (horizontal line):
y-intercept (b) = -2. Substitute b = -2 into y = b.
Equation of line d is: y = -2
Equation of line e:
Slope (m) = rise/run = -3/4
y-intercept (b) = 1
To write the equation of the line, substitute m = -¾, and b = 1 in the equation y = mx + b
y = -¾x + 1
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I need help with #10 It says to also round to the nearest hundredth. Please help!
In general, one can obtain the volume of a sphere and a cube using the formulas below
[tex]\begin{gathered} V_{cube}=l^3 \\ l\rightarrow\text{ side of the cube} \\ V_{sphere}=\frac{4}{3}\pi r^3 \\ r\rightarrow\text{ radius} \end{gathered}[/tex]In our case, we need to subtract the volume of the hollow sphere from the volume of the cube, as shown below
[tex]\begin{gathered} V_{cube}=18^3 \\ and \\ V_{sphere}=\frac{4}{3}\pi(9)^3 \\ \Rightarrow V_{foam}=V_{cube}-V_{sphere} \\ \Rightarrow V_{foam}=2778.371... \end{gathered}[/tex]Rounding to the nearest hundredth,
[tex]\Rightarrow V_{foam}\approx2778.37[/tex]The answer is 2778.37in^3
Consider the function f(x)= -2x-8.What is the value of f(-5) ?
substitute the -5 in the place of x in the expression -2x-8 and simplify
[tex] = - 2( - 5) - 8 \\ = 10 - 8 \\ = 2[/tex]
[tex]f( - 5) = 2[/tex]
ATTACHED IS THE SOLUTION
Austin makes a
commission of 20% on
his sales each week.
Last week, his sales
were $520. How much
was Austin’s
commission?
Answer:
His commission is 104$.
Step-by-step explanation:
1. Find 20% of 520$, which is 104$.
That's the answer! Please mark me as the brainliest!
Solve for y:
2x+4y=32
Answer:
Step-by-step explanation:
2x+4y=32
Get Y on one side of equation by itself
(subtract 2x on both sides)
leaves 4y = 32 - 2x
Divide by 4 to get Y alone (without coefficient)
4y = 32 - 2x
4
y = 8 - 1/2x
4. WATER Mr. Williams pays $40 a month
for city water, no matter how many
gallons of water he uses in a given
month. Let x represent the number of
gallons of water used per month. Let y
represent the monthly cost of the city
water in dollars. What is the equation of
the line that represents this information?
What is the slope of the line?
+0
The equation of the line that represents the information is y = $40.
The slope of the line is 0.
What is the equation and the slope?The equation that represents the total amount paid by Mr. Williams for the city water can be represented with a linear equation. A linear equation is an equation that is made up of a single variable that is raised to the power of one.
The form of a linear equation is:
y = ax + b
Where:
a = slope = which measures the rate of change of the equationb = intercepty = $40 + (x × 0)
y = $40
When shown on a graph, a linear equation can either slope upward, downward or have a slope of zero.
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Represent the following sentence as an algebraic expression, where “a number” is the letter x. You do not need to simplify 3 is multiplied by the difference of seven and a number
The given statement can be written algebraically as follow:
3(7 - x)
3 means '3 is multipled by' and the factor (7-x) means 'the difference of seven and a number'
according to government data, 51% of employed women have never been married. rounding to 4 decimal places, if 15 employed women are randomly selected: a. what is the probability that exactly 2 of them have never been married? b. that at most 2 of them have never been married? c. that at least 13 of them have been married?
a) The probability that exactly 2 of them have never been married is[tex]0.0026 \text{ or }2.6*10^{-3}[/tex]
b) The probability that at most 2 of them have never been married is[tex]0.0029\text{ or }2.9*10^{-3}[/tex]
c) The probability that at least 13 of them have been married is [tex]0.0046 \text{ or } 4.6*10^{-3}[/tex]
a) What is the probability that exactly 2 of them have never been married?
By applying binomial probability distribution method,
[tex]P(x)=^{n}C_{x}p^{x}q^{n-x}[/tex]
Substitute,
P(x) =Binomial probability = 51% = 0.51
x = No. of times of an outcome = 2
n = No. of trials = 15
q = Probability of failure = 49% = 0.49
[tex]^{n}C_{x}[/tex] = No. of combinations
[tex]P(2)=^{15}C_{2}*(0.51)^{2}*(0.49)^{15-2}\\\\P(2)=\frac{15!}{13!2!} *(0.51)^{2}*(0.49)^{13}\\\\P(2)=0.0026 \text{ or }2.6*10^{-3}[/tex]
b) What is the probability that at most 2 of them have never been married?
By applying binomial probability distribution method,
[tex]P(x)=^{n}C_{x}p^{x}q^{n-x}[/tex]
Substitute,
P(x) =Binomial probability = 51% = 0.51
x = No. of times of an outcome = 0,1,2
n = No. of trials = 15
q = Probability of failure = 49% = 0.49
[tex]^{n}C_{x}[/tex] = No. of combinations
[tex]P(0-2)=^{15}C_{0}*(0.51)^{0}*(0.49)^{15-0}+^{15}C_{1}*(0.51)^{1}*(0.49)^{15-1}+^{15}C_{2}*(0.51)^{2}*(0.49)^{15-2}\\\\P(0-2) = 2.253*10^{-5}+15*0.51*4.59987*10^{-5}+2.563*10^{-3}\\\\P(0-2)=0.0029 \text{ or }2.9*10^{-3}[/tex]
c)What is the probability that at least 13 of them have been married?
By applying binomial probability distribution method,
[tex]P(x)=^{n}C_{x}p^{x}q^{n-x}[/tex]
Substitute,
P(x) =Binomial probability = 51% = 0.51
x = No. of times of an outcome = 13,14,15
n = No. of trials = 15
q = Probability of failure = 49% = 0.49
[tex]^{n}C_{x}[/tex] = No. of combinations
[tex]P(13-15)=^{15}C_{13}*(0.51)^{13}*(0.49)^{15-13}+^{15}C_{14}*(0.51)^{14}*(0.49)^{15-14}+^{15}C_{15}*(0.51)^{15}*(0.49)^{15-15}\\\\P(13-15)= 105*(0.51)^{13}*(0.49)^{2}+15* (0.51)^{14}*(0.49)+(0.51)^{15}\\\\P(13-15)= 0.0046 \text{ or } 4.6*10^{-3}[/tex]
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Determine which set of side measurements could be used to form a triangle.
12, 23, 7
10, 7, 2
8, 3, 11
5, 11, 8
Answer:
5, 11, 8
Step-by-step explanation:
I did the quiz and got it correct :]
Stella needed to get her computer fixed. She took it to the repair store. The technician
at the store worked on the computer for 4 hours and charged her $59 for parts. The
total was $359. Which tape diagram could be used to represent the context if z
represents the cost of labor per hour?
Answer: 75 per hour
Step-by-step explanation:
find the measures of the copleentary angles that satisfy each case angles have equal measure
Answer:
The measures of this complementary angles is:
45°
Step-by-step explanation:
Complementary angles sum 90°
∡A + ∡B= 90°
∡A = ∡B
Then:
∡A + ∡A = 90°
2∡A = 90°
∡A = 90/2
∡A = 45°
∡B = 45°
A teacher kept track of what students consumed at a school picnic. For three grades, the ratios of the amount of water consumed to the amount of fruit juice consumed were equivalent. Complete the table.
Based on the ratios of water consumed to the fruit juice consumed, the missing figures in the completed table would be:
24 water : 28 gallons of fruit juice 18 water : 21 gallons of fruit juice How to find the ratios?The ratio of water gallons consumed to fruit juice gallons is equivalent which means that at their simplest, they will always have the ratio of 6 : 7 as is the case in the 5th grade.
The missing ratio for Juice in 6th grade is:
= (Water gallons x Juice gallons in 5th grade) / water gallons in 5th grade
= (24 x 7) / 6
= 28 gallons of fruit juice
The missing ratio for water in 6th grade is:
= (18 x 7) / 6
= 21 gallons of fruit juice
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a political candidate has asked you to conduct a poll to determine what percentage of people support her. a) suppose the candidate believes that the percentage that support her is approximately 73%. if we want a 6% margin of error at a 94% confidence level, what size sample is needed?
The sample size needed will be equal to n = 149.
The (1 - α)% confidence interval for population proportion is given by
CI = p ± z(α/2)√p (1 - p)/n
The margin of error will be given as
MOE = z(α/2)√p (1 - p)/n
We know that approximately 73% people support the candidate and margin of error is 0.06.
The critical value of z for confidence level 94% is given by z = 1.65. Now, using the formula of Margin of Error.
MOE = z(α/2)√p (1 - p)/n
n = [z(α/2)√p (1 - p)/MOE]²
n = [1.65√0.73 (1 - 0.73)/0.06]²
n = 148.84
n = 149 approximately which is the required sample size.
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Which of the following is equivalent to 3/8 A) 0.3 B) 0.45 C) 0.6 D) 0.375
SOLUTION
Given the question in the image, the following are the solution steps to answer the question.
STEP 1: Write the given fraction
[tex]\frac{3}{8}[/tex]STEP 2: Convert to decimal
[tex]\frac{3}{8}=0.375[/tex]Hence, the equivalent is 0.375
Solve: -3+12x=-3x+27
Answer:
the answer is 2 and one fourth
Step-by-step explanation:
because the 3s cancel out
For the function f(x)= x^2+4x-1, what is the range of f (x) for the domain {-2,0,1}?
The range of the given function is {-5,-1,4} which is the B option.
Given function:-
[tex]f(x) = x^2+4x-1[/tex]
Domain = {-2,0,1}
We have to find the range of the given function for the given domain.
Putting x = -2 in the given function, we get,
[tex]f(-2) = (-2)^2+4(-2)-1[/tex]
f(-2) = 4 - 8 - 1 = -5
Putting x = 0 in the given function, we get,
[tex]f(0) = (0)^2+4(0)-1[/tex]
f(0) = 0 + 0 -1 = -1
Putting x = 1 in the given function, we get,
[tex]f(1) = (1)^2+4(1)-1[/tex]
f(1) = 1 + 4 - 1 = 4
Hence, the range of the given function is {-5,-1,4}.
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bricklayer brenda would take nine hours to build a chimney alone, and bricklayer brandon would take 1010 hours to build it alone. when they work together, they talk a lot, and their combined output decreases by 1010 bricks per hour. working together, they build the chimney in 55 hours. how many bricks are in the chimney?
When seen as a function, a relationship exists between a set of inputs and outputs.
The number of bricks in the chimney exists 900.
What is meant by functions?A function in mathematics from a set X to a set Y allocates exactly one element of Y to each element of X. The sets X and Y are collectively referred to as the function's domain and codomain, respectively.
Simply described, a function is an input-output connection where each input is coupled to exactly one output range, codomain, and domain are included in each function. A function exists generally denoted by f(x) where x exists the input.
Let x be the number of bricks in the chimney. The work done exists the rate multiplied by the time.
Using w = rt, we get
[tex]$x=\left(\frac{x}{9}+\frac{x}{10}-10\right) \cdot 5[/tex]
Expanding the above equation, we get
[tex]$\left(\frac{x}{9}+\frac{x}{10}-10\right) \cdot 5: \quad \frac{19 x}{18}-50$[/tex]
x = (19x / 18) - 50
Multiply both sides by 18
[tex]$x \cdot 18=\frac{19 x}{18} \cdot 18-50 \cdot 18[/tex]
Simplifying the above equation,
x × 18 = 19x - 900
Subtract 19x from both sides
x × 18 - 19x = 19x - 900 - 19x
Simplifying the above equation, we get
-x = -900
Divide both sides by -1
[tex]$\frac{-x}{-1}=\frac{-900}{-1}[/tex]
x = 900
Therefore, the value of x exists 900.
The complete question is:
Bricklayer Brenda would take nine hours to build a chimney alone, and bricklayer Brandon would take hours to build it alone. When they work together, they talk a lot, and their combined output decreases by bricks per hour. Working together, they build the chimney in hours. How many bricks are in the chimney?
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A paper company needs to ship paper to a large printing business. The paper will be shipped in small boxes and large boxes. The volume of each small box is 6 cubic feet and the volume of each large box is 15 cubic feet. There were 2 more small boxes shipped than large boxes and the total volume of all boxes was 243 cubic feet. Write a system of equations that could be used to determine the number of small boxes shipped and the number of large boxes shipped. Define the variables that you use to write the system.
The Number of small and large boxes shipped are 10 and 5 respectively.
Large boxes :
Volume = 18 cubic feets
Let number of large boxes = b
Small boxes :
Volume = 10 cubic feets
Number of small boxes = 2b
Total volume shipped = 190 cubic feet
To obtain total volume shipped :
(Number of small boxes × volume of small boxes) + (Number of large boxes × volume of large boxes
Writing as a system of equation :
(10 × 2b) + (18 × b)
20b + 18b = 190 cubic feets
38b = 190
b = 190 ÷ 38
b = 5
Hence,
Number of large boxes = 5
Number of small boxes = 2(5) = 10
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YAbisects ZXYZ. Which statement is false?A. YXYZB. ZXYA and ZZYA each measure 63º.C. ZXYA: ZZYAD. The total measure of ZXYA and ZZYA is 126º.
Given that
[tex]\vec{YA}\text{ bisesects}\angle XYZ[/tex]Then,
[tex]\begin{gathered} \angle XYA\text{ and }\angle ZYA\text{ each measure 63degr}ees \\ \angle XYA\cong\angle ZYA \\ \text{ The total measure of }\angle XYA\text{ and }\angle ZYA\text{ }is\text{ }63+63=126^{\text{0}} \end{gathered}[/tex]Therefore, the statement
[tex]\begin{gathered} \bar{YX}\cong\bar{YZ}\text{ is false} \\ The\text{ answer is Option A} \end{gathered}[/tex]Solve the unequality
10 is greater than X over six
Answer:
x25 - 24.1x square would be your answer
Step-by-step explanation:
Suppose Juan places $6000 in an account that pays 12% interest compounded each year.Assume that no withdrawals are made from the account.Follow the instructions below. Do not do any rounding.(a) Find the amount in the account at the end of 1 year.(b) Find the amount in the account at the end of 2 years.su
1) Since this investment has been in an account with 12% compound interest per year, then we can write out the following:
a) Note that there was no withdrawal during this first year.
[tex]\begin{gathered} F=P(1+\frac{r}{n})^{nt} \\ F=6000(1+\frac{0.12}{1})^{1\cdot1} \\ F=6000(1.12)^1 \\ F=6720 \end{gathered}[/tex]b) To find out the amount of money over a course of this time 2 years, then we can write out the following:
[tex]\begin{gathered} F=P(1+\frac{r}{n})^{nt} \\ F=6000(1+\frac{0.12}{1})^{1\cdot2} \\ F=7526.4 \end{gathered}[/tex]In this case, it is also compounded per year. Just the period (t) is greater than the other one.
So, we can tell the following about the earnings of this investment:
[tex]a)\$6720,b)\$7526.40[/tex]Plssss help due tomorrow!!
Answer:
y = -1/3x +1
Step-by-step explanation:
You want the slope-intercept form equation of the line through the points (-3, 2) and (-9, 4).
SlopeThe slope is given by the formula ...
m = (y2 -y1)/(x2 -x)
m = (4 -2)/(-9 -(-3)) = 2/-6 = -1/3
Y-interceptThe y-intercept is given by the formula ...
b = y1 -m(x1)
b = 2 - (-1/3)(-3) = 1
Slope-intercept equationThe slope-intercept equation of the line is ...
y = mx +b
y = -1/3x +1
Five less than a number is at least eight
What.
is it 13?
.......................
the average depth of the arctic ocean is 3.953x10^3 feet while the average depth of the atlantic ocean is 1.2851x10^4 feet. approximately how many times deeper is the atlantic ocean than the arctic ocean
By taking the quotient between the average depth of the oceans, we conclude that the atlantic ocean is 3.251 times deeper.
How many times deeper is the Atlantic Ocean?We know that the average depth of the arctic ocean is 3.953x10^3 feet and the average depth of the atlantic ocean is 1.2851x10^4 feet
Notice that both of these are in scientific notation.
To see how many times deeper is the atlantic ocean than the artic ocean we need to take the quotient between the average depth of the atlantic ocean and the average depth of the arctic ocean, this gives:
(1.2851x10^4)/(3.953x10^3) = (1.2851/3.953)*(10^4/10^3)
= 0.3251*(10^1) = 3.251
The atlantic ocean is 3.251 times deeper than the artic.
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Hi can somebody help me with this?
Answer:
Step-by-step explanation:
Jane is selling handmade hair bows for $5.25 each. A woman came by to buy some for the girls in her daughter's girl scout troop. She spent $84. How many hairbows did she buy? Show Your Work
We know that each bow cost $5.25.
We also know that the woman spent a total of $84.
Lets call x the number of bows she bought.
Then, we can write:
[tex]\begin{gathered} 5.25\cdot x=84 \\ x=\frac{84}{5.25}=16 \end{gathered}[/tex]The woman bought 16 bows.
the snowy tree cricket is sometimes called the temperature cricket because the frequency of it chirps varies based on the temperature. the number of chirps per minute is 148 less than 4 times the outside temperature in degrees fahrenheit. write an equation that relates the number of chirps per minute, x, and the outside temperature in degrees fahrenheit, f. whatiis the outside temperature if a snowy tree cricket chirps 100 times a day?
The equation that relates the number of chirps per minute x, and the outside temperature in degrees Fahrenheit is x = 4f -148. If the snowy tree cricket chirps 100 times in a minutes, the the outside temperature is 62 degrees Fahrenheit.
The number of chirps per minute is 148 less than 4 times the outside temperature in degrees Fahrenheit.
The number of chirps per minute = x
The outside temperature in degrees Fahrenheit = f
Then the linear equation will be
x = 4f - 148
Given that x = 100 chirps per minutes
Substitute the values in the equation
100 = 4f -148
4f = 100+148
4f = 248
f = 248/4
f = 62 degrees Fahrenheit.
Hence, the equation that relates the number of chirps per minute x, and the outside temperature in degrees Fahrenheit is x = 4f -148. If the snowy tree cricket chirps 100 times in a minutes, the the outside temperature is 62 degrees Fahrenheit.
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