Answer:
[tex]f(x)=3(x+2)(x-2)(x-\frac{5}{3})[/tex]
Step-by-step explanation:
The rational roots theorem tells you that given a polynomial function with integer or whole number coefficients, a list of possible solutions can be found by listing the factors of the constant, or last term, over the factors of the coefficient of the leading term.
In your case, for the polynomial [tex]f(x)=3x^3-5x^2-12x+20:[/tex]
the last term is 20;the leading coeeficient is 3.So, possible rational roots can be among:
[tex]\pm1,\pm2,\pm4,\pm5,\pm10,\pm20,\pm\dfrac{1}{3},\pm\dfrac{2}{3},\pm\dfrac{4}{3},\pm\dfrac{5}{3},\pm\dfrac{10}{3},\pm\dfrac{20}{3}.[/tex]
Note that
[tex]f(-2)=3\cdot (-2)^3-5\cdot (-2)^2-12\cdot (-2)+20=-24-20+24+20=0.[/tex]
This means that [tex]x=-2[/tex] is a root of the polynomial and [tex]x-(-2)=x+2[/tex] is the factor. Also
[tex]f(2)=3\cdot 2^3-5\cdot 2^2-12\cdot 2+20=24-20-24+20=0.[/tex]
This means that [tex]x=2[/tex] is a root of the polynomial and [tex]x-2[/tex] is the factor. Also
[tex]f(\frac{5}{3})=3\cdot (\frac{5}{3})^3-5\cdot (\frac{5}{3})^2-12\cdot \frac{5}{3}+20=\frac{125}{9}-\frac{125}{9}-20+20=0.[/tex]
This means that [tex]x=\frac{5}{3}[/tex] is a root of the polynomial and [tex]x-\frac{5}{3}[/tex] is the factor.
Then
[tex]f(x)=3(x+2)(x-2)(x-\frac{5}{3}).[/tex]
is 25/60 a repeating decimal or terminating decimal
25/60 is repeating decimal
hope it helps you!!!!!!!!!
Plz help me with this
Answer: [tex]\bold{C)\quad y=2sin(x+\dfrac{3\pi}{4})}[/tex]
Step-by-step explanation:
A sin graph is a cosine graph shifted to the left [tex]\dfrac{\pi}{2}[/tex] units.
[tex]y=2cos(x + \dfrac{\pi}{4})\qquad \implies y=2sin(x+\dfrac{\pi}{4}+\dfrac{\pi}{2})\\\\\\.\qquad \qquad \qquad \qquad \quad \implies \large\boxed{y=2sin(x+\dfrac{3\pi}{4})}[/tex]
which one of these tables represent a non-linear function
Answer:
NUMBER3
Step-by-step explanation:
Table no 3 is representing here a non-linear function.
Why table 3 is a non-linear function?A nonlinear function, as its name suggests, is a function that is not linear. In other words, the graph of a nonlinear function is not a line, its graph can be anything other than a line
Since a nonlinear function is a function that is not a linear, its equation can be anything that is not of the form f(x) = ax+ b. One examples of nonlinear functions is, f(x) = x2 is nonlinear as it is a quadratic function.
The right answer is option 3.
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Point B is on a line that has a slope of 2. Which of these could be the coordinates of another point on the line?
I actually don't have enough information to complete this question but if you have a positive slope the line goes either up and right or down and left but when it is negative it goes down left or up right.
Answer:
Since theres no graph i cant really explain it to you. What i do know is that on TTM the answer would be (1,2)
Step-by-step explanation:
A random sample of 110 children who play instruments were asked if they prefer milk or juice. The results are shown in the table. Milk Juice Girls 18 27 Boys 23 42 Select a word or phrase from the drop-down menus to correctly complete the statements describing the association. Of the boys surveyed, more . Of the girls surveyed, more . There appear to be an association between gender and beverage preference.
Answer:
Juice, Juice, and no association
Step-by-step explanation:
Ezra works two summer jobs to save for a laptop that costs at least $1100. He decides to adjust his rates to $250 per lawn (x) for the summer and $300 per dog (y) for the summer, and to limit himself to 2 dogs.
Describe how to find a solution graphically.
Answer:
Graph in the first quadrant because x and y are nonnegative.
Shade the half-plane that does not include the origin since (0, 0) does not satisfy the inequality.
Draw a horizontal line at y = 2 for 2 dogs.
Solutions lie on or below the part of the horizontal line that is in the shaded region.
Step-by-step explanation:
Answer:more than 3
Step-by-step explanation:
i jus did it
A cylinder and a cone have the same volume. The cylinder has a radius of 2 inches and a height of 3 inches . The cone has a radius of 3 inches. What is the height of the cone ?
Answer:
The height of the cone is [tex]4\ in[/tex]
Step-by-step explanation:
step 1
Find the volume of the cylinder
The volume of the cylinder is equal to
[tex]V=\pi (r)^{2}(h)[/tex]
substitute the values
[tex]V=\pi (2)^{2}(3)=12\pi\ in^{3}[/tex]
step 2
Find the height of the cone
The volume of the cone is equal to
[tex]V=(1/3)\pi (r)^{2}(h)[/tex]
Remember that the volume of the cone is equal to the volume of the cylinder
substitute the given values and solve for h
[tex]12\pi=(1/3)\pi (3)^{2}(h)[/tex]
Simplify
[tex]36=9(h)[/tex]
[tex]h=36/9=4\ in[/tex]
Enter the values for the following composite transformation.
Translate Answer
0,0
Incorrect units left and _____ units down, then rotate _____°.
Enter the three numbers with commas and no spaces. Example: 5,7,270
do u have the answer
A fountain shoots a water arc that can be modeled by the graph of the equation y=-0.006x^2+1.2x+10, where x is the horizontal distance (in feet) from the river's north shore and y is the height (in feet) above the river. Does the water arc reach a height of 50 feet? If so, about how far from the north shore is the water arc 50 feet above the water?
ANSWER
The water arc is 50 ft above the water approximately 42ft and 158ft from the north shore.
EXPLANATION
The water arc is modeled by the function:
[tex]y = - 0.006 {x}^{2} + 1.2x + 10[/tex]
We write this function in vertex form:
[tex]y = - 0.006 ({x}^{2} - 200x )+ 10[/tex]
[tex]y = - 0.006 ({x}^{2} - 200x + ( - 100)^{2} ) - - 0.006( - 100)^{2} + 10[/tex]
[tex]y = - 0.006 ( x- 100)^{2} ) + 60+ 10[/tex]
[tex]y = - 0.006 ( x- 100)^{2} ) +70[/tex]
The vertex of this function is at
(100,70).
This means that the water arc reached a height of 50ft.
We put y=50 and solve for x.
[tex]- 0.006 ( x- 100)^{2}+70 = 50[/tex]
[tex]- 0.006 ( x- 100)^{2} = - 20[/tex]
[tex]( x- 100)^{2} = \frac{10000}{3} [/tex]
[tex]x = 100 \pm \frac{100 \sqrt{3} }{3} [/tex]
x=42.3 or x=157.7
Hence the water arc is 50 ft above the water approximately 42ft and 158ft from the north shore.
The water arc does reach a height of 50 feet, and it is about 42.27 feet and 157.73 feet from the north shore when it is 50 feet above the water.
1.Set up the equation:
[tex]\[ -0.006x^2 + 1.2x + 10 = 50 \][/tex]
2. Simplify the equation:
Subtract 50 from both sides:
[tex]\[ -0.006x^2 + 1.2x + 10 - 50 = 0 \] \[ -0.006x^2 + 1.2x - 40 = 0 \][/tex]
3. Solve the quadratic equation:
We can use the quadratic formula
[tex]\( x = \frac{-b \pm \sqrt{b^2 - 4ac}}{2a} \), where \( a = -0.006 \), \( b = 1.2 \), and \( c = -40 \).[/tex]
[tex]\[ a = -0.006, \quad b = 1.2, \quad c = -40 \][/tex]
[tex]\[ \Delta = b^2 - 4ac \] \[ \Delta = 1.2^2 - 4(-0.006)(-40) \] \[ \Delta = 1.44 - 0.96 \] \[ \Delta = 0.48 \][/tex]
[tex]\[ x = \frac{-b \pm \sqrt{\Delta}}{2a} \] \[ x = \frac{-1.2 \pm \sqrt{0.48}}{2(-0.006)} \][/tex]
Calculate the square root of 0.48:
[tex]\[ \sqrt{0.48} \approx 0.6928 \][/tex]
Now, find the two values of x:
[tex]\[ x_1 = \frac{-1.2 + 0.6928}{-0.012} = \frac{-0.5072}{-0.012} \approx 42.27 \] \[ x_2 = \frac{-1.2 - 0.6928}{-0.012} = \frac{-1.8928}{-0.012} \approx 157.73 \][/tex]
Therefore, the water arc reaches a height of 50 feet at approximately [tex]\( x = 42.27 \) feet and \( x = 157.73 \)[/tex] feet from the north shore.
If you were to spin the spinner once, what is the probability of not landing on 3?
Answer:
5/6
Step-by-step explanation:
Answer:
5/6 i think
hope this helps pls if mine is right make it the brainlest thx
help me if u do u get bl :)
First picture = x ≤ 7
Second picture = y = [tex]\frac{x}{3}[/tex] - 1
Third picture = graph d
Hope this helps you
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The low temperature in Chicago was -3 °F. The low temperature in Milwaukee was -11 °F. Which statement is true?
-11 is greater than -3, so it was colder in Chicago.
-3 is greater than -11, so it was colder in Chicago.
-11 is greater than -3, so it was colder in Milwaukee.
-3 is greater than -11, so it was colder in Milwaukee.
Answer:
The statement -11 is greater than -3, so it was colder in Milwaukee is true.
Answer:
-11 is greater than -3, so it was colder in Milwaukee.
Step-by-step explanation:
Answer 1 (-11 is greater than -3, so it was colder in Chicago) is incorrect because it was -3 in Chicago, not -11.
Answer 2 (-3 is greater than -11, so it was colder in Chicago) is incorrect because -3 is not greater than -11.
Answer 3 is correct because -11 is greater than -3 and the cities are labeled correctly.
Answer 4 (-3 is greater than -11, so it was colder in Milwaukee) is incorrect because -3 is not greater than -11. Milwaukee was also -11, not -3.
I hope this helps!
Which is the graph of logarithmic function ?
Answer:
Graph C on edge
Step-by-step explanation:
I Just did the Assignment
The second graph is the graph of logarithmic function
What is a logarithm functionLogarithmic functions are the inverses of exponential functions. The logarithmic function [tex]y=1og_ax[/tex]is defined to be equivalent to the exponential equation [tex]x=a^y[/tex].
The logarithmic function is similar in shape to the square root function. To graph a logarithmic function it is better to convert the equation to its exponential form.
The second graph is the graph of logarithmic function
Find out more on Logarithm function at: https://brainly.com/question/13473114
IMPORTANT PLEASE HURRY!!
what is the surface area of a box if it’s volume is 2244 inches cubed?
I wasn’t given any measurements, just the volume.
For this case we have that if the box is cubed, then the volume is given by:
[tex]V = l ^ 3[/tex]
Where:
l: It's the side of the cube
We have to:
[tex]l ^ 3 = 2244\\l = \sqrt [3] {2244}\\l = 13,09204886[/tex]
So, l is the side of the box. The surface area of a cube is given by:
[tex]SA = 6l ^ 2\\SA = 6 * (13.09204886) ^ 2\\SA = 1028.41046012[/tex]
Rounding off we have that the surface area of the cube is:
[tex]1028.4 \ in ^ 2[/tex]
Answer:
[tex]1028.4 \ in ^ 2[/tex]
Esmeralda simplified a complex fraction her work is shown below
Answer:
Should be (-21/4) (2/3) = -42/12 = -21/6
So answer is
Esmerelda did not use the reciprocal of the divisor.
Step-by-step explanation:
Answer: Esmeralda added the numerators.
Esmeralda added the denominators.
Esmeralda did not use the reciprocal of the divisor.
Do, -1/2 of x is (4,0) (2,0) (-2,0)
im not sure but it could be (-2,0) :/
Answer:
(2,0)
The answer is obvious
Help me find the value of x!!!
The value of x is B. 8.
In Kyle’s closet, 5/10 of the shirts are blue and 3/10 of the shirts are green. How much more of the shirts are blue than green
Answer:
1/5
Step-by-step explanation:
we know that
5/10 of the shirts are blue
3/10 of the shirts are green
so
To find how much more of the shirts are blue than green, subtract the fraction of the shirts that are green from the fraction of the shirts that are blue
5/10-3/10=2/10
Simplify
2/10=1/5
Just keepin it simple. Can you please help me with this problem.
3/10-2/5-3/4 would be least to greatest.
Hope this helps!
What is the measure of CAD?
I am pretty sure 52 degrees
Answer:
the answer is D
Step-by-step explanation:
because the measurements for CAD is 92
Which number completes this number sentence? [ ? ] > -6
A.-8
B.-7
C.-6
D.0
Answer:
It is 0
Step-by-step explanation:
Unlike the positive side of the number line which increases its value as it goes up in numbers, the negative side of a number line increases its value as it goes goes down in numbers as the more closer a negative number is to the positive side of infinity, the greater value it has. In this instance, zero is the greater number than -6 and all other negative numbers.
An experiment consists of randomly selecting a marble from a bag, keeping it, and then selecting another marble. The bag contains 4 blue marbles, 3 green marbles, 7 red marbles, and 1 yellow marble. What is the probability of selecting a red marble and then a blue marble? Question 3 options: 20% 13.33% 10% 16.66%
Answer:
13.33%
Step-by-step explanation:
First we need to find the total number of marbles
4 blue marbles+ 3 green marbles+ 7 red marbles+ 1 yellow marble= 15
The probability of a red marble = number of red marbles over the total marbles
P(red) = red/total = 7/15
We keep the marble. There are now 6 red marbles
4 blue marbles+ 3 green marbles+ 6 red marbles+ 1 yellow marble= 14
We have 14 marbles in the bag
The probability of a blue marble = number of blue marbles over the total marbles
P(blue) = blue/total = 4/14 = 2/7
Then we multiply the probabilities together
P(red,blue0 = 7/15 * 2/7 = 2/15 =.13333333 = 13.33%
Final answer:
The probability of selecting a red marble and then a blue marble from the bag is about 13.33%.Hence, the answer is B.
Explanation:
The probability of selecting a red marble and then a blue marble from a bag that originally contains 4 blue marbles, 3 green marbles, 7 red marbles, and 1 yellow marble involves calculating the probability of two independent events.
First, the probability of selecting a red marble is the number of red marbles over the total number of marbles, so P(Red first draw) = 7/(4+3+7+1) = 7/15.
After selecting a red marble, there is one less marble in the bag, so the new total is 14, and still 4 blue marbles. The probability of then selecting a blue marble is the number of blue marbles over the new total, so P(Blue second draw) = 4/14 = 2/7.
To find the combined probability of both events happening in sequence (red then blue), we multiply the individual probabilities: P(Red then Blue) = P(Red first draw) * P(Blue second draw) = (7/15) * (2/7) = 2/15. Converting this to a percentage gives us approximately 13.33%.
How to find angle measures and segment length
Answer:
The value of x is [tex]186\°[/tex]
Step-by-step explanation:
Part 27) we know that
The measurement of the outer angle is the semi-difference of the arcs it encompasses
In this problem
[tex]90\°=\frac{1}{2}[x\°-6\°][/tex]
Solve for x
[tex]180\°=[x\°-6\°][/tex]
[tex]x=180\°+6\°=186\°[/tex]
The box plots show the average gas mileage of cars and minivans tested by a certain company.
Josef says that the range for the car data is greater than the range for the minivan data because the box in the box plot for the car data is wider. Which explains Josef’s error?
Josef confused the range and the interquartile range.
Josef confused the range and the median.
Josef should have compared the medians and minimum values.
Josef should have compared the medians and maximum values.
Josef's error will be Josef confused the range and the interquartile range.
What is an interquartile range?The interquartile range is a measurement of a data set's "middle fifty." A range is a measurement of where a set's beginning and end are located.
Given that:-
Josef says that the range for the car data is greater than the range for the minivan data because the box in the box plot for the car data is wider.From the given statement we can conclude that Josef confused the range and the interquartile range.
Therefore Josef's error will be Josef confused the range and the interquartile range.
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please help! will give brainlist, only answer if youre 100% surre
Simplify. 1/4y+1 1/2 + 2− 13/4y − 12 Enter your answer in the box
Answer:
-3y-8 1/2
Step-by-step explanation:
1/4y-13/4y=-12/4y=-3y
1.5+2-12=-8.5 or 8 1/2
Answer:
-17y+13/4y
use m.a.t.h.w.a.y
Step-by-step explanation:
I need to find the measure of each angle indicated
1. From the given right-triangle, the side opposite to [tex]\theta[/tex] is 6.8 units.
The adjacent side to [tex]\theta[/tex] is 4 units.
Recall the mnemonics, SOH-CAH-TOA.
We use the tangent ratio to obtain:
[tex]\tan \theta=\frac{Opposite}{Adjacent}[/tex]
[tex]\tan \theta=\frac{4}{6.8}[/tex]
[tex]\tan \theta=\frac{10}{17}[/tex]
[tex]\implies \theta=\tan^{-1}(\frac{10}{17})[/tex]
[tex]\implies \theta=30.5\degree[/tex] to the nearest tenth.
2. This time we were given the hypotenuse to be 15.7 units and the adjacent side is 6 units.
We use the cosine ratio to obtain:
[tex]\cos \theta=\frac{Adjacent}{Hypotenuse}[/tex]
[tex]\cos \theta=\frac{6}{15.7}[/tex]
[tex]\cos \theta=\frac{60}{157}[/tex]
[tex]\implies \theta=\cos^{-1}(\frac{60}{157})[/tex]
[tex]\implies \theta=67.5\degree[/tex] to the nearest tenth.
Answer:
25). 55.02°
26). 30.46°
Step-by-step explanation:
Points to remember
Trigonometric ratios
Sin θ = Opposite side/Hypotenuse
Cos θ = Adjacent side/Hypotenuse
Tan θ = Opposite side/Adjacent side
To find the answer of question 25
Cos θ = Adjacent side/Hypotenuse
= 9/15.7 = 0.573
θ = Cos⁻¹(0.573) = 55.02°
To find the answer of question 26
Tan θ = Opposite side/Adjacent side
= 4/6.8 = 0.588
θ = Tan⁻¹(0.588) = 30.46°
Plz help me with this
Answer: B) A = 750(1.04)ⁿ
Step-by-step explanation:
The formula for compounded annually is: A = P(1 + r)ⁿ where
A (amount accrued) = unknownP (amount invested) = $750r (interest rate) = 4% -->(0.04)t (time in years) = unknownA = 750(1 + 0.04)ⁿ
= 750(1.04)ⁿ
Write the correct inequality for each graph.
1.) x>2
2.)x≤3
3.)x<4
4.)x≥5
Hope this helps:)
Find the missing lengths of the sides
ANSWER
The correct answer is C
EXPLANATION
The given triangle is a right triangle. Since two angles are equal, it is a right isosceles triangle.
This implies that, x=8 units.
Using Pythagoras Theorem,
[tex] {y}^{2} = {8}^{2} + {8}^{2} [/tex]
This implies that:
[tex]{y}^{2} = 64 + 64[/tex]
[tex]{y}^{2} =128[/tex]
Take positive square root,
[tex]{y} = \sqrt{128} [/tex]
[tex]{y} = 8 \sqrt{2} [/tex]
The correct answer is C
Answer:
Correct choice is C. [tex]x=8[/tex], [tex]y=8\sqrt{2}[/tex].
Step-by-step explanation:
Apply formula [tex]\sin\left(\theta\right)=\frac{opposite}{hypotenuse}[/tex]
[tex]\sin\left(45^o\right)=\frac{8}{y}[/tex]
[tex]\frac{1}{\sqrt{2}}=\frac{8}{y}[/tex]
[tex]y=8\sqrt{2}[/tex]
Apply formula [tex]\tan\left(\theta\right)=\frac{opposite}{adjacent}[/tex]
[tex]\tan\left(45^o\right)=\frac{8}{x}[/tex]
[tex]1=\frac{8}{x}[/tex]
[tex]x=8[/tex]
Hence correct choice is C. [tex]x=8[/tex], [tex]y=8\sqrt{2}[/tex].
Jackson works as a veterinarian technician and earns $12.20 per hour Jackson normally works 40 hours a week in a normal week what is his total pay before taxes and other deductions Jackson works as a veterinarian technician earns $12.20 per hour Jackson normally works 40 hours a week in normal week what is his total pay before taxes and other deductions
Answer:
Multiply $12.40 times 40. Remember to use a dollar sign in your answer.
Step-by-step explanation: