Answers
Answer:
[tex]a^3 + 1 = 0[/tex]
Step-by-step explanation:
We start with the equation:
[tex]a + \frac{1}{a} = 1[/tex]
We want to find the value of:
[tex]a^3 + 1 =[/tex]
We can start with our previous equation and multiply both sides by a:
[tex](a + \frac{1}{a})*a = 1*a\\a^2 + 1 = a[/tex]
Now we can rewrite our initial expression as:
[tex]a = 1 - \frac{1}{a}[/tex]
Replacing that in the right side, we get:
[tex]a^2 + 1 = a = 1 - \frac{1}{a}[/tex]
Now again, let's multiply both sides by a
[tex]a*(a^2 + 1) = a*(1 - \frac{1}{a} )\\a^3 + a = a - a/a\\a^3 + a = a - 1\\a^3 = -1\\a^3 + 1 = 0[/tex]
So we can conclude that:
[tex]a^3 + 1 = 0[/tex]
Related Questions
Find the median for the following list of values:
1, 2, 4, 7
Answers
Answer:
3
Step-by-step explanation:
Since there are an even number of data points (there are 4 points), and since the data has already been written in ascending order, the median is the average of the middle two terms: (2 + 4)/2 = 3
Answer:
Median: 3
Step-by-step explanation:
Median: the number in the middle
1, 2, 4, 7
Median is between 2, 4
Therefore, the median is 3
What are the solutions of x2 - 2x +17 - 0?
O A. x = 1+2, or x = 1 - 2
O B. X = 1+4, or x = 1- 47
O c. x = 2, or x = -2
O D. x = 4; or x = -4/
Answers
Answer:
option B
Step-by-step explanation:
[tex]x^2 - 2x + 17 = 0 \ , \ [ \ where \ a = 1 , \ b = - 2 \ c = 17 \ ][/tex]
[tex]x = \frac{- b \ \pm \sqrt{b^2 - 4ac}}{2a}\\\\x = \frac{2 \ \pm \sqrt{2^2 - (4 \times 1 \times 17)}}{ 2 \times 1}\\\\x = \frac{2 \ \pm \sqrt{4 - 68}}{ 2 }\\\\x = \frac{2 \ \pm \sqrt{-64}}{ 2 }\\\\x = \frac{2 \ \pm \sqrt{8^2 \times -1}}{ 2 }\\\\x = \frac{2 \ \pm \ 8\sqrt{ -1}}{ 2 }\\\\[/tex]
[tex]x = \frac{2 \ \pm\ 8 i}{ 2 }\\\\[/tex] [tex][ \ where \ i = \ \sqrt{i} \ ][/tex]
[tex]x = 1 \ \pm \ 4i\\\\x = 1 + 4i , \ x = 1 - 4i[/tex]
Answer:
O B. [tex]x=1+4i[/tex] or [tex]x=1-4i[/tex]
Step-by-step explanation:
Use the Quadratic Formula for the Quadratic Equation!
Quadratic Equation: [tex]x^{2} -2x+17=0[/tex]
Quadratic Formula: [tex]x= \frac{-b±\sqrt{b^2-4ac} }{2a}[/tex]
**********************************************************************
Now set up the values like this!
[tex]ax^{2} +bx+c[/tex]
**********************************************************************
[tex]x=\frac{-b±\sqrt{-2^2-(4(0)(17)} }{2(0)}[/tex]
[tex]x=\frac{-b±\sqrt{4-(1)} }{0}[/tex]
x = 1 - 4i
x = 1 + 4i
The growth rate of some species of bamboo is 0.0000237 miles per hour. write this in scientific notation
Answers
Answer:
2.37 x 10 ^ -5
Step-by-step explanation:
What is the answer to 4/5 of 30?
Answers
Answer:
24
Step-by-step explanation:
[4 / 5 ] * 30 = 24
Answer:
24
Step-by-step explanation:
To get the answer you have to multiply the 4/5 x 30 to get the answer
What are solutions to the equation x^2-34=864
Answers
Answer:
x=29.9
Step-by-step explanation:
x=29.9
an estate valued at $75 000 is divided among three daughters Natasha, Natalie and Nadia in the ratio 5:8:2 respectively. Calculate the amount each receives
Answers
Answer:
Natasha: $25000
Natalie: $40000
Nadia: $10000
Step-by-step explanation:
5 : 8 : 2
5 + 8 + 2 = 15
$75000 ÷ 15
$5000
$5000 × 5 = $25000
$5000 × 8 = $40000
$5000 × 2 = $10000
what is the average rate of change from x equals negative 1 to x equals 1
Answers
Answer:
This question is incomplete, so I can not give you an exact answer, but I can give you the answer for the general case.
If we have a function f(x), the average rate of change between the values:
x = a and x = b,
is given by:
[tex]r = \frac{f(b) - f(a)}{b - a}[/tex]
So if we want to find the rate of change from:
x = -1 to x = 1
it is just:
[tex]r = \frac{f(1) - f(-1)}{1 - (-1)} = \frac{f(1) - f(-1)}{2}[/tex]
So just to show an example, if:
f(x) = 3*x^2 - 5
the average rate of change in that interval will be:
[tex]r = \frac{f(1) - f(-1)}{2} = \frac{3*1^2 - 5 - (3*(-1)^2 - 5)}{2} = \frac{-2 - (-2)}{2} = 0[/tex]
Please help me solve my problem!!!
Answers
True
Hope this helps! :)
______________
In a survey, 15 high school students said they could drive and 15 said they could not. Out of 60 college students surveyed, 30 said they could drive. Micah concluded that knowing that a person is in college means they are more likely to drive. Is Micah’s conclusion correct? Explain.
Answers
Answer:
No.
Step-by-step explanation:
#1, the sample size is not indicative of a proper high school population, unless of all there is a small amount of students in the high school (or even only 30 students in it). On a individual basis, it can vary widely, and so data analysis such as this is not correct. The data size is skewed as well for the college, especially as college campuses typically house more students then usual. To only ask 60 college students also skew the data gotten. Another sample error may be locational error, in which the location of the schools may warrant the need for a driver license, or if it is not needed, as well as the distance of the student's house and/or where needed facilities are to accommodate a student's needs and desires.
If we were to set all these problems aside and focus more on the question, 15 high school students said they could drive, and 15 said they could not, which makes the sample size of 30 high school students in all. 15 say they can drive, therefore:
15/30 = 1/2, or there is a 50% chance of obtaining a student that can drive.
On the other hand, out of 60 college students surveyed, 30 said they can drive, therefore:
30/60 = 1/2, or there is a 50% chance of obtaining a student that can drive.
∴ Micah's prediction is incorrect in obtaining a college student that can drive more easily then obtaining one that can drive in a high school.
However, remember that too small of a data size can lead to a heavy skew, and it will not represent reality as well.
~
Answer:
Sample Response: No, Micah is not correct. Since there are equal numbers in the group that drive and the group that doesn’t drive, the relative frequency for each is 50%. Because the relative frequencies are the same, there is no association between the variables.
Step-by-step explanation:
Got this from Edg 2021
Miguel and Jacqui built towers out of craft sticks.Miguel's tower had a 4-inch base.Jaquis tower had a 6-inch base.Miguels tower had a volume of 128 cubic inches and jaquis had a volume of 288.Who's tower was taller
Answers
Answer:
Height is same for both the towers
Step-by-step explanation:
The computation is as follows;
For 1st tower
The height is
= 128 ÷ 4^2
= 8 inches
And,
For the 2nd tower
The height is
= 288 ÷ 6^2
= 8 inches
So as we can see that the height of the both the tower is same i.e. 8 inches so the same should be considered
How do you find co terminal angle of -445
Answers
Answer:
275°
Step-by-step explanation:
-445+360=-85+360=275°
can somebody help plz
Answers
Answer:
(3,2)
Step-by-step explanation:
the other three ordered pairs do not lie in the shaded region
Find the missing side of the triangle. Round your answers to the nearest tenth if necessary.
15.3 m
10 m
24.6 m
22.4 m
Answers
Answer:
Solution given:
perpendicular[p]=x
base[b]=11.6m
hypotenuse[h]=19.2m
by using Pythagoras law
h²=p²+b²
19.2²-11.6²=x²
x=[tex]\sqrt{234.08}[/tex]
x=15.3m
option
a.
15.3 m
Answer:
15.3 m
Step-by-step explanation:
c refers to the longest side (hypotenuse) whereas a and b referes to the two other smaller sides of atriangle.
pythagoras theorem
a^2 + b^2 = c^2
11.6^2 + x^2 = 19.2^2
134.56 + x^2 = 368.64
x^2 = 368.64 - 134.56
x^2 = 234.08
x=[tex]\sqrt{234.08[/tex]
x=15.29
x=15.3 m
Please help :( The picutre is right below worth 20 pionts and will mark brainliest :)
oh and the question is right in the picture too also with the rest
Answers
Answer:
perpendicular
Step-by-step explanation:
peripenducular looks like a plus sign. HOPE THIS HELPS!
Branliest...
Jane and Tannic split the cost of buying a video game. The game costs$25, and the sales is 6% markup. How much do they each pay?
Answers
Given:
The cost of game = $25
Sales markup = 6%
To find:
How much do they each pay?
Solution:
The sales markup is 6% of the cost.
[tex]\text{Sales markup}=25\times \dfrac{6}{100}[/tex]
[tex]\text{Sales markup}=1.5[/tex]
Now, the total cost after sales markup is:
[tex]25+1.5=26.5[/tex]
Jane and Tannic split the cost of buying a video game. It means they divide the cost in two equal parts. So, the amount paid by each one is
[tex]\dfrac{26.5}{2}=13.25[/tex]
Therefore, Jane and Tannic will pay $13.25 each .
slope = 4, point (3,-2) is on the line
Answers
Answer:
y = 4x + b
Step-by-step explanation:
We know that (3, -2) is on this line. So 3 = m(-2)+b.
This leaves us with two variables the slope (m) and the y intercept (b).
But wait a minute, the slope is given to us since it says slope = 4.
Our equation is now, 3 = 4(-2)+b
3 = -8 + b
b = 11.
Our final equation is now y = 4x + b.
(y,x) is a point on this line.
Hope this helped!
JoeLouis2
what is the difference of the polynomials?
{m^2n^2-7}-(mn+4)
Answers
Answer:
[tex]m^{2} n^{2} - mn-11[/tex]
Step-by-step explanation:
Simplify the expression.
Runelle collected river water for an experiment. She poured it into 8 jars. Each jar had the mixed number two and three fourths pints of water. What is the total amount of river water Runelle collected?
Answers
Answer: 22 pints of water
Step-by-step explanation:
Runelle collected river water and poured in eight jars such that each jar had 2³/₄ of water.
The total amount of water collected by Runelle from the river will therefore be the sum of all the water in the 8 jars and because they are the same, we can simply multiply the quantity in one jar by 8 to see the sum:
= Amount of water in one jar * 8 jars
= 2³/₄ * 8
= 11/4 * 8
= 22 pints of water
suppose y varies inversely with x, and y=39 when x=1/3.what is the value of y when x=26
Answers
Answer:
y = 1/2
Step-by-step explanation:
Varies inversely
xy = k
------------------------
Find the constant of variation
y = 39 when x = 1/3
k = 1/3 * 39
k = 13
-----------------------
what is the value of y when x=26
26y = 13
y = 13/26
y = 1/2
Answer:
y = [tex]\frac{1}{2}[/tex]
Step-by-step explanation:
Given y varies inversely with x then the equation relating them is
y = [tex]\frac{k}{x}[/tex] ← k is the constant of variation
To find k use the condition y = 39 when x = [tex]\frac{1}{3}[/tex] , then
39 = [tex]\frac{k}{\frac{1}{3} }[/tex] ( multiply both sides by [tex]\frac{1}{3}[/tex] )
[tex]\frac{1}{3}[/tex] × 39 = k
13 = k
y = [tex]\frac{13}{x}[/tex] ← equation of variation
When x = 26 , then
y = [tex]\frac{13}{26}[/tex] = [tex]\frac{1}{2}[/tex]
Worth 20 points Il will mark brainiest! :)
The picture is included too oh and the question is already in the picutre but just incase you cant see what it says it says this
In the diagram below lines, AB and CD are . sorry if the picture is a bit dark
Answers
A. Perpendicular!
Because they cross with a 90 degree angle :]
Answer: Perpendicular
Step-by-step explanation: Hope this helps
What is the volume of this. Pyramid
720 cm2
1080cm2
1440 cm2
2160 cm2
Answers
Answer:
Option (1)
Step-by-step explanation:
To calculate the volume of the given pyramid,
Formula to be used,
Volume = [tex]\frac{1}{3}(\text{Area of the triangular base)}(\text{Height})[/tex]
Area of the triangular base = [tex]\frac{1}{2}(\text{Base})(\text{Height})[/tex]
= [tex]\frac{1}{2}(9)(15)[/tex]
= 67.5 cm²
Now volume of the pyramid = [tex]\frac{1}{3}(67.5)(32)[/tex]
= 720 cm³
Therefore, Option (1) will be the correct option.
Which equation shows the point-slope form of the line that passes through (3, 2) and has a slope of 1/3
Answers
Answer:
y-y1=m(x-x1)
y-2=1/3(x-3)
y=1/3x+1
Line q has a slope of -8/9 , Another line r has the slope of 9/8.Are line q and line r parallel or perpendicular?
Answers
Answer:
perpendicular
Step-by-step explanation:
parallel => both lines have the same value of slope
perpendicular => the product of both slope values are -1
=> -8/9 x 9/8 = -1
If Line q has a slope of -8/9 , Another line r has the slope of 9/8.Then both lines are perpendicular but not parallel
What is Slope of Line?The slope of the line is the ratio of the rise to the run, or rise divided by the run. It describes the steepness of line in the coordinate plane.
The slope intercept form of a line is y=mx+b, where m is slope and b is the y intercept.
The slope of line passing through two points (x₁, y₁) and (x₂, y₂) is
m=y₂-y₁/x₂-x₁
Two lines are parallel when the slope of two lines is same, so 1 and r are not parallel.
Two lines are said to be perpendicular when the product of two slopes is minus 1.
Line q has a slope of -8/9
Let m₁=-8/9
r has the slope of 9/8
m₂=9/8
Now let us multiply m₁ and m₂
m₁ ×m₂
-8/9×9/8
-1
The product of slopes of q and r is -1. The lines are perpendicular.
Hence Line q and line r are perpendicular but not parallel.
To learn more on slope of line click:
https://brainly.com/question/14511992
#SPJ2
which graph is a function of x?
Answers
Answer:the one to the left
Step-by-step explanation:
Which expressions are equivalent to the on below select all that apply 9x
Answers
Answer:
B and D
Step-by-step explanation:
Multiplying exponents just adds them.
Answer:
B + D
Step-by-step explanation:
On a coordinate plane, a line goes through points (negative 2, 1) and (0, negative 3). Y = negative StartFraction 2 Over 9 EndFraction x + 2.
Two separate linear functions are expressed by the graph and by the equation. Select all that apply.
The slope is negative for both functions.
The equation has a steeper slope than the line in the graph.
The slope of the line in the graph is -2.
The graph and the equation express an equivalent function
Answers
Answer:Using the formula for the area of the composite shape, Area of composite shape = Area of rectangle + area of the square. ⇒ Area of composite shape = 14+9 = 23 square inches.
Step-by-step explanation:
Answer:
Using the formula for the area of the composite shape, Area of composite shape = Area of rectangle + area of the square. ⇒ Area of composite shape = 14+9 = 23 square inches.
Step-by-step explanation:
got it right on the quiz!!!
Find the volume.
I need this in now like ASAP 10 points
Answers
Answer:
0.48 m^3
Step-by-step explanation:
volume = length * breadth * height
=6m * 4m * 0.02m
=0.48 m^3
For the image below, state the line of reflection:
Answer choices:
y = -2
x-axis
y-axis
x = -1
Answers
Answer:20
Billions
Step-by-step explanation:
Answer:
Kjxiycdafgousdgkuafveligfasa
If AD = 5.1cm, find the height (in cm) of the triangle.
Answers
Answer:
I. AC = 15 cm
II. h = 7.4 cm
Step-by-step explanation:
I. Determination of AC
AB = 9 cm
BC = 12 cm
AC =?
The length AC can be obtained by using pythagoras theory as illustrated below:
AC² = AB² + BC²
AC² = 9² + 12²
AC² = 81 + 144
AC² = 225
Take the square root of both side
AC = √225
AC = 15 cm
II. Determination of the height.
AB = 9 cm
AD = 5.1 cm
BD = h =?
The height of the triangle can be obtained by using pythagoras theory as illustrated below:
AB² = AD² + BD²
9² = 5.1² + h²
81 = 26.01 + h²
Collect like terms
h² = 81 – 26.01
h² = 54.99
Take the square root of
h = √54.99
h = 7.4 cm
Work out the perimeter of this semicircle.
Take a to be 3.142
10 cm
Answers
Answer:
perimeter=1/2*2πr
Step-by-step explanation:
1/2*2*3.142*10
=31.42
