Is there a number that is exactly 3 more than its cube?
Answers
They are the solutions to (x-x^3=3).
The exact value for the real solution is:
(sqrt(239)/(2*3^(3/2))-3/2)^(1/3)+1/(3*(sqrt(239)/(2*3^(3/2))-3/2)^(1/3))
Approximately, it is x=-1.67169988...
If you are expecting integers (which was not specified), then there is none.
For a given number X, its cube is written as X^3.
Here we want to see if we can find a number that is exactly 3 more than its cube, this means that:
[tex]X = X^3 + 3[/tex]
We will see that yes, there exists a number with this property.
Then we can try to solve this to find the number with that given property.
We can rewrite it as:
[tex]-X^3 + X - 3 = 0[/tex]
Now we can solve this for X, as the question asks about existence and not for the exact number, we can graph this the above function:
[tex]f(X) = -X^3 + X - 3[/tex]
And if it crosses the x-axis, then at some point we have:
[tex]f(X) = 0[/tex]
This would imply that there exists a real number that is 3 more than its cube.
The graph can be seen below, and we can see that it intersects the X-axis, then yes, there is a number that is exactly 3 more than its cube.
And by watching the graph, we can see that the number is:
[tex]X = -1.672[/tex]
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Related Questions
A group of friends are going to see the newest action movie. The price of a ticket is $6.25. As a group, they spent $12 on refreshments. If they spent a total of $30.75 on tickets and refreshments, how many people went to the movies? Which equation represents the scenario?
Answers
Answer:
Which equation represents the scenario?
✔ 6.25x + 12 = 30.75
How many people went to the movies?
✔ 3
Step-by-step explanation:
1. There are 3 peoples go to the movie.
2. The equation to represent the scenario is,
⇒ 6.25x + 12 = 30.75
Where, x is number of people.
What is an expression?
Expression in math is defined as the collection of the number, variables and functions by using signs like addition, subtraction, multiplication, and division.
Given that;
The price of a ticket = $6.25
As a group, they spend $12 on refreshments.
Total spent money = $30.75
Now,
Let number of people go to the movie = x
Then, Total price spent on ticket = $6.25x
And, As a group, they spend $12 on refreshments.
So, Total spent money is equal to $30.75, as;
$6.25x + $12 = $30.75
This equation represents the scenario.
Now, Solve the equation for number of people as;
$6.25x + $12 = $30.75
Subtract 12 both side,
6.25x + 12 - 12 = 30.75 - 12
6.25x = 18.75
Divide by 6.25,
x = 3
Thus, There are 3 peoples go to the movie.
Therefore,
1. There are 3 peoples go to the movie.
2. The equation to represent the scenario is,
⇒ 6.25x + 12 = 30.75
Where, x is number of people.
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Part b what is the value of the smallest bond angle in xef4?
Answers
Answer:
90 degrees
Step-by-step explanation:
If the ratio of areas of two similar polygons is 25:49, what is the ratio of the corresponding side lengths
Answers
[tex]\bf \cfrac{\textit{similar shape}}{\textit{similar shape}}\qquad \cfrac{s}{s}=\cfrac{\sqrt{s^2}}{\sqrt{s^2}}=\cfrac{\sqrt[3]{s^3}}{\sqrt[3]{s^3}}\\\\ -------------------------------\\\\ \stackrel{\textit{ratio of sides}}{\cfrac{s}{s}}=\stackrel{\textit{ratio of the areas}}{\cfrac{\sqrt{s^2}}{\sqrt{s^2}}}\implies \cfrac{s}{s}=\cfrac{\sqrt{25}}{\sqrt{49}}\implies \cfrac{s}{s}=\cfrac{5}{7}[/tex]
Answer: 5:7
Step-by-step explanation:
The person above is right
I just did the test
WILL GIVE BRAINEST
Leo had $91, which is 7 times as much......
Answers
7x=91
7X(Allison's money)=91
First find f+g, f-g, f-g and f\g. Then determine the domain for each function f(x)=3×+7,g(×)=×+9 (f+g)(×)=
Answers
[tex]f(x)=3x+7[/tex]
[tex]g(x)=x+9[/tex]
[tex](f+g)(x)=(3x+7)+(x+9)=4x+16[/tex]
To find (f+g)(x), add the functions f(x) and g(x), substituting x into both functions and then adding the results together. The result is (f+g)(x) = 4x + 16.
Explanation:To find (f+g)(x), we need to add the two functions f(x) and g(x). f(x) = 3x + 7 and g(x) = x + 9. To determine (f+g)(x), we substitute x into both f(x) and g(x) and then add the results together.
So, (f+g)(x) = f(x) + g(x) = (3x + 7) + (x + 9) = 4x + 16.
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Olivia started her banking account with $100 and is increasing the account $20 per month. The independent variable
Answers
The independent variable is the amount of months.
Answer:
Wee is the independent variable, and deposit is the dependent variable
Step-by-step explanation:
Given that Olivia started her banking account with $100 and is increasing the account $20 per month.
Here the variable which changes independently is the independent variable
Hence no of weeks elapsed would be the independent variable
The dependent variable would be the variable which changes whenever number of weeks changes.
Here dependent variable is the total balance in the account in a particular week
D=100+20n wbere n= no of weeks that eapsed
and D= depositisin in the bank
Central City High School's robotics team is at a competition. In the last round, the team earned 80 points for their robot climbing over an obstacle and an additional 12 points for each ball the robot shot through a hoop. They won the round with 344 total points. Write an equation in the form a = bx + c that can be used to find the number of balls, x, their robot shot through the hoop. Fill in a, b, and c to complete the equation for this situation. Big fraction Parentheses Vertical bars Square root Root Superscript (Ctrl+Up) Subscript (Ctrl+Down) Plus sign Minus sign Middle dot Multiplication sign Equals sign Less-than sign Greater-than sign Less-than or equal to Greater-than or equal to Pi Alpha Beta Epsilon Theta Lambda Mu Rho Phi Sine Cosine Tangent Arcsine Arccosine Arctangent Cosecant Secant Cotangent Logarithm Logarithm to base n Natural logarithm Bar accent Right left arrow with under script Right arrow with under script Angle Triangle Parallel to Perpendicular Approximately equal to Tilde operator Degree sign Intersection Union Summation with under and over scripts Matrix with square brackets
Answers
Answer:
[tex]344=12x+80[/tex]
[tex]a=344[/tex]
[tex]b=12[/tex]
[tex]c=80[/tex]
Step-by-step explanation:
Let x be number of balls shot through the hoop by Central City High School's robot.
We have been given an equation [tex]a=bx+c[/tex] and we are asked to find the values of a, b and c.
We are told that Central City High School's team earned an additional 12 points for each ball the robot shot through a hoop. So the points earned by shooting x balls through the hoop will be 12x.
The team also earned 80 points for their robot climbing over an obstacle. So total number of points earned by team will be equal to [tex]12x+80[/tex].
We are also told that the team won the round with 344 total points. We can represent this information in an equation as: [tex]344=12x+80[/tex]
Upon comparing this equation with our given equation we will get,
[tex]a=344[/tex]
[tex]b=12[/tex]
[tex]c=80[/tex]
Therefore, the equation [tex]344=12x+80[/tex] can be used to find the number of balls, x, team's robot shot through the hoop.
seven less than the product of 3 and a number is -16
Answers
If you wanted to answer that you would add 7 to both sides,
which would be
-9 = 3x
Divide both sides by 3
x = -3
The product of three and a number, means you multiply 3 and x where x=the unknown number.
Is -16 means that is is equal to -16.
Let's put it all together.
3x - 7 = -16
If you want to solve for x:
3x - 7 = -16
Add 7 to both sides.
3x = -9
Divide 3 on both sides.
x = -3
Hope this helps!
Calculate the perimetet of the quadrilateral
Answers
Perimeter means an outline of a shape. You just need to add all the sides of the quadrilateral.
Perimeter of quadrilateral = [tex]2+2+3+5 = 12cm[/tex]
Hope I helped (:
Have a great day!
you roll a number cube twice. what is the probability of rolling a 2 first and then rolling an odd number
Answers
The probability of rolling a 2 on a die and then rolling an odd number on a second roll is 1/12.
The probability of rolling a 2 on a die is 1/6 because there are six sides on a die, each with an equal chance of landing face up. When rolling the dice a second time, there are three odd numbers (1, 3, and 5), so the probability of rolling an odd number is 3/6, or 1/2. To find the combined probability of both events occurring in sequence (rolling a 2 first and then an odd number), we multiply the individual probabilities: (1/6) × (1/2) = 1/12.
At noon, ship A is 170 km west of ship B. Ship A is sailing east at 40 km/h and ship B is sailing north at 20 km/h. How fast is the distance between the ships changing at 4:00 PM?
Answers
At 4:00 PM, the distance between the ships is changing at a rate of 6160 km/h.
Explanation:To find the rate at which the distance between the ships is changing, we can use the concept of relative velocity. At 4:00 PM, ship A has been sailing east for 4 hours, covering a distance of 40 km/h * 4 h = 160 km. Ship B has been sailing north for 4 hours, covering a distance of 20 km/h * 4 h = 80 km.
To find the distance between the ships at 4:00 PM, we can use the Pythagorean theorem. The distance between the ships is the hypotenuse of a right triangle with legs of 170 km and 80 km. Using the theorem, we find that the distance between the ships is √(170^2 + 80^2) ≈ 186.45 km.
To find the rate at which the distance is changing, we can use the derivative of the distance formula. Let D be the distance between the ships. Then, D^2 = (170 + 40t)^2 + (80 + 20t)^2, where t is the time in hours. Taking the derivative of D^2 with respect to t and solving for dD/dt, we get: dD/dt = (170 + 40t)(40) + (80 + 20t)(20).
Substituting t = 4 into the expression, we find that dD/dt = (170 + 40(4))(40) + (80 + 20(4))(20) = 6160 km/h. Therefore, the distance between the ships is changing at a rate of 6160 km/h at 4:00 PM.
A plumber charges a flat fee of $79 to visit a home and examine a clogged drain. The plumber charges an additional $21 per hour spent fixing the drain. The total cost, c (in dollars), for fixing a drain that takes, h hours is given by the following function.
C(h)=79+21h
(a) What is the total cost for fixing a drain that takes 7 hours?
(b) If the plumber charges a total of $310, how many hours did he spend fixing the drain?
Answers
Final answer:
The total cost for fixing a drain that takes 7 hours is $226. If the plumber charges a total of $310, he spent 11 hours fixing the drain.
Explanation:
The cost function given by the plumber is C(h) = 79 + 21h, where C represents the total cost and h represents the number of hours spent fixing the drain.
To find the total cost of fixing a drain that takes 7 hours, we substitute h with 7 in the given equation: C(7) = 79 + 21(7). Calculating this, we get C(7) = 79 + 147, which equals $226. Therefore, the total cost for fixing a drain that takes 7 hours is $226.To find out how many hours the plumber spent fixing the drain when the total charge is $310, we set C(h) equal to 310 and solve for h: 310 = 79 + 21h. Subtracting 79 from both sides gives us 231 = 21h. Dividing both sides by 21 yields h = 11 hours. Thus, the plumber spent 11 hours fixing the drain.Write a real-life situation that can be modeled by the expression .
5 x 3/4
Answers
Answer:
On Zira's birthday Lizzy, Amy Wilson Amara, and Ria want only 3/4 inches of the cake how much cake do you need for all of them?
Solutions 5 x3/4 = 3.75 inches of cake
Step-by-step explanation:
a receipe calls for 3 1/3 cup of heavy cream, If i double the receipe and want to make 2 1/2 times the amount how much heavy cream do I have to use?
Answers
(10/3)(5/2) cups = 25/3 cups, or 8 1/3 cups.
For 2 1/2 times the doubled recipe, starting with an initial amount of 3 1/3 cups of heavy cream, the total amount needed would be 16 2/3 cups of heavy cream.
To calculate how much heavy cream is needed, we must first understand the initial amount required and then apply the necessary adjustments to upscale the recipe.
If the original recipe calls for 3 1/3 cups of heavy cream and we want to double the recipe, we would need 2 x 3 1/3 cups which is 2 x (10/3) cups = 20/3 cups or 6 2/3 cups.
Now, if we want to make 2 1/2 times the amount of the doubled recipe, we multiply 6 2/3 cups by 2 1/2 (5/2), resulting in (20/3) x (5/2) cups. Simplifying this, we get:
(20/3) x (5/2) = (100/6) cups = 16 2/3 cups.
Therefore, for 2 1/2 times the doubled recipe, you would need 16 2/3 cups of heavy cream.
Which is the image of Triangle ABC for a 180° counterclockwise rotation about P?
Answers
Answer:
Triangle GHI is rotating 180° counterclockwise .
Step-by-step explanation:
Given : Triangles.
To find : Which is the image of Triangle ABC for a 180° counterclockwise rotation about P.
Solution : We have triangle ABC .
If we Rotate GHI triangle in counterclockwise 180 degree we get triangle ABC.
We can prove it by rotating triangle ABC in clockwise direction 180° We get triangle GHI.
Therefore, Triangle GHI is rotating 180° counterclockwise .
Ron sees 3 dogs at the park. Hal sees twice as many dogs as Ron. How many dogs do they see in all?
Answers
Hal 2(3) =6
3+6 =9
they saw 9 dogs all together
John must have at least 289 test points to pass his math class. He already has test scores of 72, 78, and 70. Which inequality will tell him at least how many more points he needs to pass the class?
A. 72 + 78 + 70 + x ≤ 289 B. 72 + 78 + 70 + x > 289 C. 72 + 78 + 70 + x < 289 D. 72 + 78 + 70 + x ≥ 289
Answers
John needs to use the inequality 72 + 78 + 70 + x ≥ 289 to determine the minimum number of additional test points required to pass his math class.
Explanation:The student, John, needs to determine how many more test points he requires to pass his math class. Given his current test scores, the inequality to represent this scenario should account for the minimum points he needs to achieve the threshold.
Therefore, the inequality should include an 'at least' condition, meaning the total points must be greater than or equal to the pass mark of 289. Adding his current scores of 72, 78, and 70 gives a total of 220, so the inequality will include an unknown variable, x, which represents the additional points needed. The correct inequality is D. 72 + 78 + 70 + x ≥ 289.
Final answer:
John needs to use the inequality 72 + 78 + 70 + x ≥ 289, which simplifies to x ≥ 69, to determine he requires at least 69 more points to pass. Option D
Explanation:
John needs to determine how many more points he requires to pass his math class, with a target score of at least 289 points. He already has test scores of 72, 78, and 70. To find out the least number of additional points he needs, he should use an inequality that allows for the sum of his scores and an unknown quantity x (representing the points he needs) to be at least as great as 289. This is represented by the inequality 72 + 78 + 70 + x ≥ 289. This can be simplified to x ≥ 69, which means John needs at least 69 more points to pass the class.
Evaluate 3f(2) = .
what does this equal
Answers
Answer:
The answer is 12
Step-by-step explanation:
Make a table of ordered pairs for the equation.
y=−1/3x+1
Answers
x = -6, y = −1/3(-6) +1 = 3
x = -3, y = −1/3(-3) +1 = 2
x = 0, y = 1
x = 3, y = −1/3(3) +1 = 0
x = 6, y = −1/3(6) +1 = -1
Table
x y
-6 3
-3 2
0 1
3 0
6 -1
Answer:
The answer is the next table:
x y
0 1
3 0
6 -1
9 -2
Step-by-step explanation:
In order to determine the table with ordered pairs, we have to know about replacing values.
In a linear function, there are two variables, the dependent variable (y) and the independent variable (x). If we replace any value in the "x" variable, we get the "y" value. The process is called "replacing value".
To get the table, we choose some value to replace in the "x" variable:
[tex]x=0\\y=-\frac{1}{3}(0)+1=1\\[/tex]
[tex]x=3\\y=-\frac{1}{3}(3)+1=-1+1=0[/tex]
[tex]x=6\\y=-\frac{1}{3}(6)+1=-2+1=-1[/tex]
[tex]x=9\\y=-\frac{1}{3}(9)+1=-3+1=-2[/tex]
The table with some ordered pairs is:
x y
0 1
3 0
6 -1
9 -2
I have attached an image that shows a graph with the ordered pairs.
what is the estimate of 8.354
Answers
Can u simplify and convert these please and thank you
Answers
1/13 = 0.0769 = 7.7%
9/26 = 0.346 = 34.6%
5/26 = 0.192 = 19.2%
1/13=.08=8%
9/26=.35=35%
5/26=.19=19%
Find the probability that the sample mean deviates from the population mean μ = 108 by no more than 2.
Answers
0.05 is 1/10 the value of?
Answers
Answer
0.5
Explanation
0.05 is 1/10 the value of?
In other words the question is asking, what must be multiplied by 1/10 to give 0.05.
let that value be X.
1/10 × X = 0.05
X/10 = 0.05
X = 0.05 × 10
= 0.5
The value that must be multiplied by 1/10 which gives 0.05 would be 0.5.
What is the fundamental principle of multiplication?If an event can occur in m different ways and if following it, a second event can occur in n different ways, then the two events in succession can occur in m × n different ways.
We need to find the value that must be multiplied by 1/10 which gives 0.05.
Let that value be X.
1/10 × X = 0.05
X/10 = 0.05
X = 0.05 × 10
= 0.5
Thus, the value that must be multiplied by 1/10 which gives 0.05 would be 0.5.
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Which of the following is a like radical to 3x sqrt 5?
X(3sqrt 5)
Sqrt 5y
3(3sqrt 5x)
Y sqrt 5
Answers
The like radicals to 3x√5 from the given options is: D. y√5.
What are Like Radicals?Like radicals can be defined as radicals having the same root number (i.e. square) and also have the same radicand.
Given, 3x√5, the root here is a square, while the radicand is 5. Thus, like radicals to 3x√5 will have same root and radicand.
Therefore, the like radicals to 3x√5 from the given options is: D. y√5.
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The like radical to 3x sqrt 5 is y sqrt 5.
Explanation:Given the expression 3x sqrt 5, we can see that the square root is applied only to 5 and not to 3x. To find a like radical, we need to find an expression in which the square root is also applied only to the same number.
Looking at the options, the only expression that matches this criterion is y sqrt 5. The square root is applied only to 5, just like in the original expression. Therefore, y sqrt 5 is the like radical to 3x sqrt 5.
Carol, Ann, and Liz each bought a toy fish. Carol’s fish is 9 inches longer than Ann’s fish. Liz’a fish is 9 inches longer than twice the length of Ann’s fish. Ann’s fish is 17 inches long. Find the length of each toy fish.
Answers
Carol= 17+9
Liz= (17x2) +9
Ann- 17 in.
Carol-26 in.
Liz- 34+ 9= 43 in.
A survey was taken of 100 potential voters, asking them which candidate they would vote for in a local election. The results are given in the table below.
CANDIDATE X Y Z
NUMBER OF SUPPORTERS 63 17 20
If 5000 people vote in the actual election, which is the best prediction for the number of votes for candidate X, based on the results of this poll?
630
850
1000
3150
Answers
So candidate X won 63% of the votes in the poll.
This means that candidate X is expected to win the elections by a percentage close to 63%.
63% of the voters is (63/100)*5000=63*50=3150 voters
Answer: 3150
Kyle saves 8% of his income for a new car this year his salary was $2000 less than in the previous year and he saved $3000 what was his salary in the previous year
Answers
First let us calculate for his salary this year. We know that 3000 is only 8% of his salary, hence:
0.08 * salary = 3000
salary = 3000 / 0.08
salary = 37,500
Therefore his previous salary is:
previous salary = 37,500 + 2,000
previous salary = $39,500
Answer:
First let us calculate for his salary this year. We know that 3000 is only 8% of his salary, hence:
0.08 * salary = 3000
salary = 3000 / 0.08
salary = 37,500
Therefore his previous salary is:
previous salary = 37,500 + 2,000
previous salary = $39,500
Step-by-step explanation:
Mel Company has a net income, before taxes, of $95,000. The treasurer of the company estimates 45% of net income will have to be paid for federal and state taxes. The tax for both federal and state is:
Answers
☺☺☺☺
Answer:
The tax will be $42,750.
Step-by-step explanation:
Mel Company has a net income, before taxes, of $95,000.
The treasurer of the company estimates 45% of net income will have to be paid for federal and state taxes.
So, the tax for both federal and state is:
[tex]0.45\times95000=42750[/tex] dollars
Therefore, the tax will be $42,750.
How do you find the x intercepts of 3x^(5/3) - 4x^(7/3)
Answers
3x^(5/3) - 4x^(7/3) = 0. Factor out x^(5/3): x^(5/3) [3 - 4x^(2/3)] = 0
Then either x^(5/3) = 0, or 3 - 4x^(2/3) = 0.
In the latter case, 4x^(2/3) = 3.
To solve this: mult. both sides by x^(-2/3). Then we have
4x^(2/3)x^(-2/3) = 3x^(-2/3), or 4 = 3x^(-2/3). It'd be easier to work with this if we rewrote it as
4 3
--- = --------------------
1 x^(+2/3)
Then
4
--- = x^(-2/3). Then, x^(2/3) = (3/4), and x = (3/4)^(3/2). According to my 3 calculator, that comes out to x = 0.65 (approx.)
Check this result! subst. 0.65 for x in the given equation. Is the equation then true?
My method here was a bit roundabout, and longer than it should have been. Can you think of a more elegant (and shorter) solution?
[tex]\bf 3x^{\frac{5}{3}}-4x^{\frac{7}{3}}=0\implies \stackrel{common~factor}{x^{\frac{5}{3}}}(3-4x^{\frac{2}{3}})=0\\\\ -------------------------------\\\\ x^{\frac{5}{3}}=0\implies \boxed{x=0}\\\\ -------------------------------\\\\ 3-4x^{\frac{2}{3}}=0\implies 3=4x^{\frac{2}{3}}\implies (3)^3=\left(4x^{\frac{2}{3}}\right)^3 \\\\\\ 27=64x^2\implies \cfrac{27}{64}=x^2\implies \sqrt{\cfrac{27}{64}}=x\implies \boxed{\cfrac{3\sqrt{3}}{4\sqrt{4}}=x} \\\\\\ 0.64951905283832898507\approx x[/tex]
Dilate using a scale factor of 2
(2,3) (5,2) (3,-2)
Answers
(2,3) times 2= (4,6)
(5,2) times 2= (10,4)
(3,-2) times 2= (6,-4)
Hope this helps!