x ³ = 1
x ³ - 1 = 0
x ³ - 1³ = 0
Factorize the right side as a difference of cubes:
(x - 1) (x ² + x + 1) = 0
Then
x - 1 = 0 or x ² + x + 1 = 0
The first equation yields x = 1 as a root.
For the other equation, rearrange and complete the square to get the other two roots,
x ² + x + 1/4 = -3/4
(x + 1/2)² = -3/4
x + 1/2 = ±√(-3/4) = ± i √3/2
x = -1/2 ± i √3/2
x = (-1 ± i √3)/2
Since complex roots occurs in conjugate pairs, taking the sum of these two roots eliminates the imaginary part:
(-1 + i √3)/2 + (-1 - i √3)/2 = (-1 - 1)/2 = -2/2 = -1
and adding to 1 indeed shows that the sum of roots is zero.
At the Natural History Museum, 40% of the visitors are children. There are 36 children at the museum. How many visitors altogether are at the museum?
Answer:
90
Step-by-step explanation:
36/x * 40/100 = 3600/40x
and you get x = 90
Which of the following is the place value of the underlined digit? 35.1789
A ten-thousandths B tenths
C thousandths D hundredths
Answer:
1 = tenths place
7= hundredths place
8= thousandths place
9= ten-thousandths place
Step-by-step explanation:
What should the equations look like for each number? 17-20
Answer:
See below.
Step-by-step explanation:
17.)
[tex]x+100+120+100=360\\x+320=360\\x=40[/tex]
18.)
[tex]x+150+77+48=360\\x+275=360\\x=85[/tex]
19.)
[tex]x+122+92+76=360\\x+290=360\\x=70[/tex]
20.)
[tex]x+115+85+60=360\\x+260=360\\x=100[/tex]
The temperature of the rod was 10°C above zero. It was kept in a freezer at 2 p.m. If
its temperature decreased at the rate of 3°C per minute, at what time would be the
temperature be 8°C below zero? What would be the temperature at 3 pm ?
Solve for x. Type your answer below.
5(2x−12)=−90
Hi there!
[tex]\large\boxed{x = -3}[/tex]
Begin by distributing the 5:
5(2x) + 5(-12) = -90
Simplify:
10x - 60 = -90
Add 60 to both sides:
10x = -90 + 60
10x = -30
Divide both sides by 10:
x = -3
Answer:
x = -3
Step-by-step explanation:
Isolate the variable, x. Note the equal sign, what you do to one side, you do to the other. Do the opposite of PEMDAS.
PEMDAS is the order of operations, and stands for:
Parenthesis
Exponents (& Roots)
Multiplication
Division
Addition
Subtraction
~
First, divide 5 from both sides of the equation:
5(2x - 12) = -90
(5(2x - 12))/5 = (-90)/5
2x - 12 = -90/5
2x - 12 = -18
Next, add 12 to both sides of the equation:
2x - 12 (+12) = -18 (+12)
2x = -18 + 12
2x = -6
Finally, divide 2 from both sides of the equation:
(2x)/2 - (-6)/2
x = -6/2
x = -3
-3 is your answer for x.
~
[tex]x^2-x-6=0[/tex]
Answer:
x = 3 or x = -2
Step-by-step explanation:
x² - x - 6 = 0
(x - 3)(x + 2) = 0
x - 3 = 0 or x + 2 = 0
x = 3 or x = -2
I need help ASAP!! Please help me
Answer:
Step-by-step explanation:
Answer:
angle 1 = 80
angle 2 = 80
Step-by-step explanation:
in rhombus all sides are equal and also diagonals bisects each other
so
The radius of a circle is 5 cm. Find its area to the nearest tenth.
Answer:
78.5
Step-by-step explanation:
πr²
= π×5²
= 25π
= 78.5
what is 2x 3 -7x^{3}−7x 3
Answer:
It is given that
4x/3−7x/3=1
Step-by-step explanation:
By further calculation
−3x/3=1
So we get
−x=1
x=−1.
please help if possible
Answer:
59 cm ³
Does the answer help you?
Scale the numerator and the denominator down by a factor of 3 (divide) to write a fraction equivalent to \frac{3}{12}
12
3
.
Answer:
[tex]\frac{1}{4}[/tex]
Step-by-step explanation:
Given
[tex]\frac{3}{12}[/tex] ← divide numerator and denominator by 3
= [tex]\frac{1}{4}[/tex]
∣x−18∣=5 absolute value
Answer
x = 13 or x = 23
Step-by-step explanation:
|x-18| = 5 means there are two possibilities.
x-18 can equal 5 or equal -5 because absolute value sign makes everything inside it positive.
so you can write two equations and solve
first is x-18 = 5
x-18 + 18 = 5 + 18
x = 23
the second is x - 18 = -5
x - 18 + 18 = -5 + 18
x = 13
The two solutions are 13 and 23.
What does x equal? Dpsewbskdye
Answer:
x = 7
Step-by-step explanation:
27 = 7x + 6 - 4x (Given)
27 = 3x + 6 (Simplify)
27 - 6 = 3x + 6 - 6 (Subtract 6 on both sides)
21 = 3x (Simplify)
21/3 = 3x/3 (Divide 3 on both sides)
7 = x (Simplify)
A school organised a farewell party of 100 students and school managementn decided three types of drinks distribute in the party
The answer is
i) - c
ii) - b
iii) - b
iv) - a
v) - d
how to change mixed fraction into improper fraction and improper to proper fraction easy way
Answer with Step-by-step explanation:
To change the mixed fraction into improper fraction you multiply the denominator with the whole and add to numerator.
For example: 4 1/5 = (5*4)+1/5=21/5
To change improper into proper mixed fraction,
Divide the numerator by denominator and write the remainder on numerator
For example: 7/2= 3 1/2
Find the gradient, picture below
Answer:
[tex]\frac{dy}{dx} = \frac{13}{8} [/tex]
Step-by-step explanation:
[tex] y = 2x + 6 {x}^{ - \frac{1}{2} } \\ \frac{dy}{dx} = 2 + 6( - \frac{1}{2}) {x}^{ - \frac{1}{2} - 1 } \\ \frac{dy}{dx} = 2 - 3 {x}^{ - \frac{3}{2} } \\ \frac{dy}{dx} = 2 - \frac{3}{ \sqrt{ {x}^{3} } } [/tex]
When x = 4,
[tex]\frac{dy}{dx} = 2 - \frac{3}{ \sqrt{ {4}^{3} } } \\ = \frac{13}{8} [/tex]
Answer:
Hello,
Answer 13/8
Step-by-step explanation:
[tex]y=2x+\dfrac{3}{\sqrt{x} } \\\\y'=2+6*\dfrac{-1}{2} x^{\frac{-3}{2} }\\\\y'=3-\frac{3}{\sqrt{x^3}} \\\\\\For x=4, \\\\y'(4)=2-\dfrac{3}{8} =\dfrac{13}{8}[/tex]
please solve this ASAP. I need this done but I can't figure it out
Answer:
x = 61
Step-by-step explanation:
Supplementary angles add up to 180 degrees. We can create an equation and solve for x.
(2x + 6) + (x - 9)= 180
~Combine like terms
3x - 3 = 180
~Add 3 to both sides
3x = 183
~Divide 3 to both sides
x = 61
Best of Luck!
A chef mix his salt and pepper. If he put 2/3 cup of salt and 1/2 cup of pepper in his shaker, what is the ratio of salt to pepper ?
Answer:
4 to 3
Step-by-step explanation:
The ratio of salt to pepper is
2/3 to 1/2
Multiply both fractions by 6
6 * 2/3 to 6 * 1/2
4 to 3
Write the Roman Numeral CLXIV in standard form.
A. 169
B. 166
C. 164
D. 159
Answer:
It's C, 164
Step-by-step explanation:
Answer this question
Answer:
[tex]\huge\boxed{width=12cm}[/tex]
Step-by-step explanation:
[tex]l-length\\w-width\\P-perimeter[/tex]
The formula of perimeter of the rectangle:
[tex]P=2l+2w=2(l+w)[/tex]
Substitute:
[tex]l=6w\\\\P=168cm[/tex]
[tex]168=2(6w+w)\\168=2(7w)\\168=14w\qquad|\text{divide both sides by 14}\\\\\dfrac{168}{14}=\dfrac{14w}{14}\\\\12=w\Rightarrow w=12(cm)[/tex]
Answer:
Width of rectangle = 12 cm
Step-by-step explanation:
Let us assume that,
→ Length = 6x
→ Width = x
→ Perimeter = 168 cm
Perimeter of rectangle,
→ P = 2(L + W)
Forming the equation,
→ 168 = 2(6x + x)
Now the value of x will be,
→ 168 = 2(6x + x)
→ 2 × 7x = 168
→ 14x = 168
→ x = 168/14
→ [ x = 12 ]
Then the length and width is,
→ Length = 6x = 6(12) = 72 cm
→ Width = x = 12 cm
Hence, required width is 12 cm.
The mean of data set A is 43.5 and the MAD is 3.7. The mean of data set B is 12.8 and the MAD is 4.1. What differences would you expect to see when comparing the dot plots of the two data sets?
Answer:
MAD - mean absolute deviation is indication of the distance of data points from the mean.
Data set B shows the greater variability since has greater MAD.
It means the B data set is more spread compared to A data set.
Determine if this
graph is an
example of a
function??
Answer:
A function is a set of ordered pairs where there is exactly one y value for each x value.
This is the case with this graph, so this graph IS a function.
Let me know if this helps!
We are planning a reception for our daughter. The hall that we are renting charges a $50 cleanup fee. In
addition to the cleanup fee, they charge $20 per guest for food and drinks.
If we have $3,700.00 available, what is the maximum number of guest we can invite without going over ou
budget?
Answer:
The answer is 235
Step-by-step explanation:
it's just basic long divistion.
$108.75 for working 15 hours as a holiday helper wrapping gifts. At this rate, how much money will she earn if she works 18 hours the next week. Explain.
Jesse travels 3.0 meters east and then turns and travels 4.0 meters north. The trip requires 35 seconds. What is his velocity?
Using Pythagorean triplet
[tex]\\ \sf\longmapsto AB^2=AC^2-BC^2[/tex]
[tex]\\ \sf\longmapsto AB^2=4^2-3^2[/tex]
[tex]\\ \sf\longmapsto AB^2=16-9[/tex]
[tex]\\ \sf\longmapsto AB^2=7[/tex]
[tex]\\ \sf\longmapsto AB=\sqrt{7}[/tex]
Now time=35[tex]\\ \sf\longmapsto Velocity=\dfrac{Displacement}{Time}[/tex]
[tex]\\ \sf\longmapsto Velocity=\dfrac{\sqrt{7}}{35}[/tex]
[tex]\\ \sf\longmapsto Velocity=\dfrac{2.6}{35}[/tex]
[tex]\\ \sf\longmapsto Velocity=0.07m/s[/tex]
A circle has a circumference of 1{,}133.541,133.541, comma, 133, point, 54 units.
What is the diameter of the circle?
Answer: Radius is 21.2537 units, to 6 sig figs
Step-by-step explanation:
I'll assume the circumference is simply 133.541 units^2. Circumference (C) is C = 2*pi*R, where R is the radius. Thus, R = C/(2*pi),
R = (133.541/2*(3.14159) to 6 sig figs
R = 21.2537 units
i think i got the hang of it but i still need help
pls help !
Answer:
50
Step-by-step explanation:
The sum of interior angles in a triangle is equal to 180 degrees
since one of the angle is given as 80 the remaining is 100
The given is an isosceles triangle which means two of its side length and so its angles are equal in measure so 100/2 = 50
Answer:
4/5 t
Step-by-step explanation:
why?
80%xt by definition of p%=p/100
80/100t
80/100t reduce the fraction with 20
so the answer is;
4/5 t
Hope it helps
help pleasseeeeeeeee
Answer:
-1
Step-by-step explanation:
I know that i^4 = 1
i^10 = i^4 * i^4 * i^2
= 1 * 1 * i^2
We know that i^2 = -1
=1 *1 *-1
= -1
Simplify xy-5x+y^2xy−5x+y 2 if x = -3 and y = 5.
The simplification of the expression [tex]xy-5x+y^2xy-5x+y ^2[/tex] gives - 335.
What is a simplification of an expression?Usually, simplification involves proceeding with the pending operations in the expression.
Simplification usually involves making the expression simple and easy to use later.
Given;
[tex]xy-5x+y^2xy-5x+y ^2[/tex]
Substitute x = -3 and y = 5.
[tex]-3\times 5-5\times -3+5^2\times -3\times 5-5\times -3+5 ^2[/tex]
= -15 + 15 - 375 + 15 + 25
= -335
Learn more about simplification;
https://brainly.com/question/17579585
#SPJ1
For what values of does the equation (2 + 1)^2 + 2 = 10 − 6 have two real and equal roots?
Answer:
(2 + 1)^2 + 2 = 10 - 6
Falso
Step-by-step explanation:
109 / 5000
El lado izquierdo
11
no es igual al lado derecho
4
, lo que significa que la declaración dada es falsa.
Falso
