Answer:
1) multiplicative inverse of i = -i
2) Multiplicative inverse of i^2 = -1
3) Multiplicative inverse of i^3 = i
4) Multiplicative inverse of i^4 = 1
Step-by-step explanation:
We have to find multiplicative inverse of each of the following.
1) i
The multiplicative inverse is 1/i
if i is in the denominator we find their conjugate
[tex]=1/i * i/i\\=i/i^2\\=We\,\, know\,\, that\,\, i^2 = -1\\=i/(-1)\\= -i[/tex]
So, multiplicative inverse of i = -i
2) i^2
The multiplicative inverse is 1/i^2
We know that i^2 = -1
1/-1 = -1
so, Multiplicative inverse of i^2 = -1
3) i^3
The multiplicative inverse is 1/i^3
We know that i^2 = -1
and i^3 = i.i^2
[tex]1/i^3\\=1/i.i^2 \\=1/i(-1)\\=-1/i * i/i\\=-i/i^2\\= -i/-1\\= i[/tex]
so, Multiplicative inverse of i^3 = i
4) i^4
The multiplicative inverse is 1/i^4
We know that i^2 = -1
and i^4 = i^2.i^2
[tex]=1/i^2.i^2\\=1/(-1)(-1)\\=1/1\\=1[/tex]
so, Multiplicative inverse of i^4 = 1
URGENTTTTTTT!!!!!!!!!!
Prove that circle A with center (–1, 1) and radius 1 is similar to circle B with center (–3, 2) and radius 2.
Answer:
Circle A and circle B are similar
Step-by-step explanation:
* Lets explain similarity of circles
- Figures can be proven similar if one, or more, similarity transformations
reflections, translations, rotations, dilations can be found that map one
figure onto another
- To prove all circles are similar, a translation and a scale factor from a
dilation will be found to map one circle onto another
* Lets solve the problem
∵ Circle A has center (-1 , 1) and radius 1
∵ The standard form of the equation of the circle is:
(x - h)² + (y - k)² = r² , where (h , k) are the coordinates the center
and r is the radius
∴ Equation circle A is (x - -1)² + (y - 1)² = (1)²
∴ Equation circle A is (x + 1)² + (y - 1)² = 1
∵ Circle B has center (-3 , 2) and radius 2
∴ Equation circle B is (x - -3)² + (y - 2)² = (2)²
∴ Equation circle B is (x + 3)² + (y - 2)² = 4
- By comparing between the equations of circle A and circle B
# Remember:
- If the function f(x) translated horizontally to the right
by h units, then the new function g(x) = f(x - h)
- If the function f(x) translated horizontally to the left
by h units, then the new function g(x) = f(x + h)
- If the function f(x) translated vertically up
by k units, then the new function g(x) = f(x) + k
- If the function f(x) translated vertically down
by k units, then the new function g(x) = f(x) – k
∵ -3 - -1 = -2 and 2 - 1 = 1
∴ The center of circle A moves 2 units to the left and 1 unit up to
have the same center of circle B
∴ Circle A translate 2 units to the left and 1 unit up
∵ The radius of circle A = 1 and the radius of circle B = 2
∴ Circle A dilated by scale factor 2/1 to be circle B
∴ Circle B is the image of circle A after translation 2 units to the left
and 1 unit up followed by dilation with scale factor 2
- By using the 2nd fact above
∴ Circle A and circle B are similar
help with 1-6 , please !!!!!
Answer:
sum of angles of triamgle is 180 degree
the half base× hight ue1/2×b×h
use the formula for all qusetions
what are the zeros of the polynomial function f(x)=x^3-x^2-6x
Answer:
x = -2, x = 0, and x = 3
Step-by-step explanation:
it was right lol
¿Cuál de las siguientes funciones es una función constante? a. Y=x+1 b. Y=x+2 c. X=y+3 d. Y=3
Answer:
Option D y=3
Step-by-step explanation:
The question in English is
Which of the following functions is a constant function?
we know that
A constant function is a function whose output value is the same for every input value
so
Verify each case
case A) y=x+1
This is not a constant function, this is a linear equation
Is a function whose output value is different for every input value
case B) y=x+2
This is not a constant function, this is a linear equation
Is a function whose output value is different for every input value
case C) x=y+3
This is not a constant function, this is a linear equation
Is a function whose output value is different for every input value
case D) y=3
This is a constant function
Is a function whose output value is the same for every input value
After graduating from college, Carlos receives two different job offers. Both pay a starting salary of
$62000 one job promises a $3720 raise per year. What will the salary be in one year
Answer:
$65720
Step-by-step explanation:
The job pays a starting salary of $62000, and raises $3720 per year. In one year, Carlos will be earning $62000 + $3720 = $65720
Final answer:
Carlos's salary in one year will be $65720, which is the sum of his starting salary, $62000, and the promised annual raise of $3720.
Explanation:
After graduating from college, Carlos has received two different job offers, both offering a starting salary of $62000, and one includes a promise of a $3720 raise per year. To calculate his salary in one year, we need to add this annual raise to his starting salary.
Starting salary: $62000
Raise after one year: $3720
Carlos's salary in one year: $62000 + $3720 = $65720
This computation shows that with the promised annual raise, Carlos's salary for the next year would be $65720.
(4^((-11/3))/(4^((-2)/3))
simplify the following expression
Answer:
[tex]\large\boxed{\dfrac{4^{-\frac{11}{3}}}{4^{-\frac{2}{3}}}=\dfrac{1}{64}}[/tex]
Step-by-step explanation:
[tex]\dfrac{4^{-\frac{11}{3}}}{4^{-\frac{2}{3}}}\qquad\text{use}\ \dfrac{a^n}{a^m}=a^{n-m}\\\\=4^{-\frac{11}{3}-\left(-\frac{2}{3}\right)}=4^{-\frac{11}{3}+\frac{2}{3}}=4^{-\frac{9}{3}}=4^{-3}\qquad\text{use}\ a^{-n}=\dfrac{1}{a^n}\\\\=\dfrac{1}{4^3}=\dfrac{1}{64}[/tex]
The simplification of the expression is [tex]\dfrac{1}{64}[/tex].
What are some basic properties of exponentiation?Exponentiation(the process of raising some number to some power) have some basic rules as:
[tex]a^{-b} = \dfrac{1}{a^b}\\\\a^0 = 1 (a \neq 0)\\\\a^1 = a\\\\(a^b)^c = a^{b \times c}\\\\ a^b \times a^c = a^{b+c} \\\\[/tex]
Given ;
[tex]\dfrac{(4^{-11/3})}{(4^{-2/3})}[/tex]
We know that
[tex]\dfrac{a^m}{a^n} = a^{m-n}[/tex]
[tex]\dfrac{(4^{-11/3})}{(4^{-2/3})} = 4^({-11/3 + 2/3})\\\\\\= 4 ^{-9/3}\\\\= 4^{-3}\\\\[/tex]
Hence, [tex]\dfrac{1}{4^3} = \dfrac{1}{64}[/tex]
Learn more about exponentiation here:
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Translate the following into algebraic expressions:
Divide the product of a and b by the quotient of c and d.
PLEASE HELP ASAP If mZYWZ - 17, what is mw
?
34
73
56
17
Answer:
73°
Step-by-step explanation:
Since WX = WZ then ΔWXZ is isosceles and WY is perpendicular to XZ
Hence ∠XYW = 90°
YW bisects XWZ, hence ⇒ ∠ YWX = ∠YWZ = 17°
The sum of the 3 angles in ΔWXY = 180°, hence
∠WXY = 180° - (90 + 17)° = 180° - 107° = 73°
Solve the equation over the interval [0,2pi) 4cscx + 6= -2
[tex]\bf 4csc(x)+6=-2\implies 4csc(x)=-8\implies csc(x)=\cfrac{-8}{4}\implies csc(x)=-2 \\\\\\ \cfrac{1}{sin(x)}=-2\implies \cfrac{1}{-2}=sin(x)\implies sin^{-1}\left( -\cfrac{1}{2} \right)=x\implies x= \begin{cases} \frac{7\pi }{6}\\\\ \frac{11\pi }{6} \end{cases}[/tex]
The product of a rational and irrational number is rational
Answer:
False
Step-by-step explanation:
I think this is a true or false question.
The statement is false.
Here is an example of it being false:
Choose the irrational number to be [tex]\sqrt{2}[/tex] and the rational to be 1.
The product of these numbers is [tex]\sqrt{2}[/tex] which is irrational, not rational.
Answer:
False
Step-by-step explanation:
Ight so any irrational number times a rational number is irrational. But keep in mind that If its 0 times an irrational number, its going to be 0, which is a rational number. So irrational x rational = irrational. Irrational x 0=rational 0.
Hope this helped
PLEASE HURRY 10 POINTS What is the solution to the equation 3(2x+5)=3x+4x
A x=0
B x=4
C x=5
D x=15
Answer:
D x=15
Step-by-step explanation:
3(2x+5)=3x+4x
Distribute the 3
6x +15 = 3x+4x
Combine like terms
6x+15 = 7x
Subtract 6x from each side
6x+15 -6x = 7x-6x
15 =x
Solve 3x − 2 = 37. please help me
To solve the equation 3x - 2 = 37, you add 2 to both sides to get 3x = 39. Then, you divide by 3 to solve for x, obtaining x = 13.
Explanation:To solve the equation
3x − 2 = 37
for x, you start by moving the -2 to the other side of the equation by adding 2 to both sides. This gives you
3x = 39
. Then, you isolate x by dividing every term by 3. After dividing, you find that
x = 13
. So the solution to the equation 3x - 2 = 37 is x = 13.
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To solve the equation, add 2 to both sides and then divide by 3 to isolate the variable x. The solution is x = 13.
Explanation:To solve the equation 3x - 2 = 37, we need to isolate the variable x. Here are the steps:
Add 2 to both sides of the equation to get rid of the constant term. This gives us 3x = 39.Divide both sides of the equation by 3 to solve for x. This gives us x = 13.Therefore, the solution to the equation is x = 13.
Learn more about Solving Equations here:https://brainly.com/question/14410653
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The length of a rectangle exceeds its width by 3
inches, and the area is 54 square inches. What
are the length and width of the rectangle?
Answer:
The length is 9 and the width is 6.
Step-by-step explanation:
6*9 = 54 and 9 is 3 greater than 6.
Which of the following would be the most logical first step to solving this
quadratic equation?
2x2-x+ 2 = -11
O
A. Divide both sides by x.
O
B. Take the square root of both sides.
O
C. Set up smaller equations using the zero product rule.
O
D. Add 11 to both sides.
Answer:
D is correct option
Step-by-step explanation:
The correct option is D.
The standard quadratic equation is ax²+bx+c=0
Where a and b are coefficients and c is constant.
It means that constant are on the L.H.S and there is 0 on the right hand side.
Therefore to make it a quadratic equation first of all you have to add 11 at both sides so that the R.H.S becomes 0.
The given equation is:
2x2-x+ 2 = -11
If we add 11 on both sides the equation will be:
2x2-x+ 2 +11= -11+11
2x^2-x+13=0
Thus the correct option is D
You can further solve it by applying quadratic formula....
Final answer:
The most logical first step to solve the quadratic equation 2x² - x + 2 = -11 is to set up smaller equations using the zero product rule and then applthe quadratic formula. The correct option is c.
Explanation:
The most logical first step to solve the quadratic equation 2x² - x + 2 = -11 is to:
C. Set up smaller equations using the zero product rule.
Once the equation is rearranged, apply the quadratic formula to determine the values of x.
Using the quadratic formula yields the solutions by substituting the values of a, b, and c correctly.
A single die is rolled twice. Find the probability of rolling a 2 the first time and a 5 the second time.
Answer:
[tex]\frac{1}{36}[/tex]
Step-by-step explanation:
All die rolls have a 1 in 6 chance of landing on any specific number (because they have 6 equal sides). In probability, two independent events with probabilities a and b will occur concurrently [tex]a*b[/tex] of the time. In this case, [tex]a=b=\frac{1}{6} \to p=a*b=\frac{1}{6}*\frac{1}{6}=\frac{1}{36}[/tex]
Answer:
Required probability = 1/36
Step-by-step explanation:
It is given that,single die is rolled twice
The outcomes of rolling a die are
1, 2, 3, 4, 5, and 6
Total = 6
To find the probability
Probability of getting 2 = 1/6
Probability of getting 5 = 1/6
Therefore probability of rolling a 2 the first time and a 5 the second time. = 1/6 * 1/6 = 1/36
A pathway divides a rectangular garden into two parts as shown. Find the measure of angle A
Answer:
m < A = 101 degrees.
Step-by-step explanation:
The transverse line crosses 2 parallel lines (opposite angles of a rectangle are parallel) , so the same side angles add up to 180 degrees.
m < A + 79 = 180
m < A = 101 degrees.
Answer:
A=101°
Step-by-step explanation:
The two lengths of the rectangle are parallel and therefore the sides of the path form two parallel transversals.
The angle marked 79° and the angle marked A are supplementary ( they add up to 180°)
A+79=180°
A=180-79
=101°
when you use ____ you form general ideas and rules based on your experiences and observations
a. symmetry
b. logic
c. deduction
d. induction
Induction is the correct answer; when you use induction form general ideas and rules based on your experiences and observations. I hope this will help you! Have a wonderful day!
Answer:
d. induction
Step-by-step explanation:
When you use induction you form general ideas and rules based on your experiences and observations.
The volume of the spheres is 500/3 pie cubic units What is the value of X?
Answer:
125
Step-by-step explanation:
500 ÷ 4 = 125
I think this is the right answer. sorry if I'm wrong.
Answer:
x=5 assuming that x is the radius.
x is the radius?
Step-by-step explanation:
[tex]V=\frac{4}{3} \pi r^3[/tex] is the volume of a sphere.
We are given [tex]V=\frac{500}{3} \pi[/tex] cubic units.
We are asked to find the value of x. If x is not the radius, please correct me:
[tex]V=\frac{4}{3}\pi r^3[/tex] with [tex]V=\frac{500}{3} \pi[/tex] and the assumption that x is r.
[tex]\frac{500}{3}\pi=\frac{4}{3}\pi x^3[/tex]
If you multiply both sides by 3, then you would have:
[tex]500 \pi=4 \pi x^3[/tex]
If you divide both sides by [tex]\pi[/tex] you will have:
[tex]500=4x^3[/tex]
If you divide both sides by 4, you will have:
[tex]125=x^3[/tex]
The last step would be to take the cube root of both sides:
[tex]\sqrt[3]{125}=x[/tex]
[tex]5=x[/tex]
[tex]x=5[/tex]
For f(x)=3x+1 and g(x)=x•x-6,find (f - g)(x)
Answer:
[tex]\large\boxed{(f-g)(x)=-x^2+3x+7}[/tex]
Step-by-step explanation:
[tex](f-g)(x)=f(x)-g(x)\\\\f(x)=3x+1,\ g(x)=x^2-6\\\\(f-g)(x)=(3x+1)-(x^2-6)=3x+1-x^2+6=-x^2+3x+7[/tex]
Write a function rule for the table
For this case we must construct a function of the form [tex]y = f (x)[/tex] taking as reference the values of the table.
It is observed that if we evaluate the following function we have:
[tex]f (x) = x + 4[/tex]
Different signs are subtracted and the sign of the major is placed.
[tex]f (-3) = - 3 + 4 = 1\\f (-2) = - 2 + 4 = 2\\f (-1) = - 1 + 4 = 3\\f (0) = 0 + 4 = 4[/tex]
So, the function is:[tex]f (x) = x + 4[/tex]
Answer:
[tex]f (x) = x + 4[/tex]
Jennifer stores her fishing pole in a cylindrical case. The cylinder has a diameter of 5 inches and a height of 50 inches.Which is closest to the volume, in cubic inches, of the cylinder?
Answer:
Volume of Cylinder = 981.75 cubic inches
Step-by-step explanation:
There is no answer choice shown, but i will answer this using formula for volume of cylinder and round the answer to 2 decimal places.
You match it with the choices that u have.
The volume of a cylinder is given by the formula [tex]V=\pi r^2 h[/tex]
Where
V is the volume
r is the radius (half of diameter)
h is the height
We know diameter is 5, so radius is 2.5
also, the height is 50
We simply plug it in the formula and solve:
[tex]V=\pi r^2 h\\V=\pi (2.5)^2 (50)\\V=981.75[/tex]
find the area of a sector with a central angle of 170° with the radius of 17 mm. Round to the nearest 10th.
This circle is centered at the point (3, 2), and the length of its radius is 5. What
is the equation of the circle?
Answer:
(x-3)² + (y-2)² = 25
Step-by-step explanation:
A circle's equation is (x-h)² + (y-k)² = r². When centered at the origin, h and k equal 0. If you shift the circle, say, one unit up, then k equals 1, and the equation is x² + (y-1)² = r².
So for your circle, the equation would be (x-3)² + (y-2)² = 5² or (x-3)² + (y-2)² = 25.
Kiemanh is solving the equation 15r- 6r=36. What is the value of r?
Answer:
r equals 4- this is the value of r
hope this helps
Step-by-step explanation:
Answer:
[tex]\large\boxed{r=4}[/tex]
Step-by-step explanation:
In this question, we're going to need to solve the equation for r.
This means that we need to get the r by itself to see what it equals to.
Lets solve:
[tex]15r- 6r=36\\\\\text{Subtract 15r and -6r}\\\\9r=36\\\\\text{Now you will divide}\\\\r=4[/tex]
When you're done solving, you should get r = 4
This means that the value of r is 4 (or r = 4)
I hope this helped you out.Good luck on your academics.Have a fantastic day!The original price of a skateboard was reduced by $15. The new price is $49.
Answer:
The original price of a skateboard is $64
Step-by-step explanation:
Let
x ----> the original price of a skateboard
y ----> the new price of a skateboard
we know that
The linear equation that represent this problem is equal to
y=x-15 ----> equation A
y=49 ---> equation B
substitute equation B in equation A and solve for x
49=x-15
Adds 15 both sides
49+15=x
64=x
Rewrite
x=$64
After eating lunch together, Jay and Paul start walking in opposite directions. Jay walks 0.75 miles every 15 minutes and Paul power walks 2.5 miles every 30 minutes. In miles, how far apart are they after 1.5 hours?
Answer:
12 miles
Step-by-step explanation:
Jay walks 0.75 miles in 15 minutes, or 1/4 hour, so his speed is:
0.75 mi / 0.25 hr = 3 mi/hr
Paul walks 2.5 miles in 30 minutes, or 1/2 hour, so his speed is:
2.5 mi / 0.50 hr = 5 mi/hr
After 1.5 hours, Jay has walked a distance of:
3 mi/hr × 1.5 hr = 4.5 mi
And Paul has walked a distance of:
5 mi/hr × 1.5 hr = 7.5 mi
So the total distance between them is:
4.5 mi + 7.5 mi = 12 mi
WILL GIVE BRAINLEIST DUE AT 9:45 P.M. PLS HURRY SUPER EASY. Bella rollerblades 8 miles in one hour. The function rule that represents this situatrion is 8x, where x is the numger of hours. Make a table to find how many hours she had skated when she traveled 16,24, and 32 miles. Then graph the function. After refer to the exercise. How many miles would Bella travel if she skated for 7 hours?
Hours ] 8x ] Miles
? ] ? ] ]
? ] ? ] ]
? ] ? ] ]
Answer:
I hope this helps! <3
Step-by-step explanation:
Which of the following expressions are equivalent? Justify your reasoning.
4√x3
1
x−1
10√x5•x4•x2
x
1
3
•x
1
3
•x
1
3
Answer:
b and d
Step-by-step explanation:
b. 1/x^-1
=(1/x)^-1
=x
d. x^1/3 * x^1/3 * x^1/3
=x^1/3+1/3+1/3
=x^3/3
=x^1
=x....
If g(x) = xsquared +2, find the g (3)
Answer:
g(3)=11 I think
Step-by-step explanation:
Since x is 3, you substitute it in for the x. So it would be 3 squared +2.
I'm not sure if this is right but I tried helping.
Answer:
g(3) =11
Step-by-step explanation:
g(x) = x^2 +2
Let x =3
g(3) = 3^2 +2
= 9+2
= 11
Determine algebraically whether f(x) = x^2(x^2 + 9)(x^3 + 2x) is even or odd.
[tex]f(x) = x^2(x^2 + 9)(x^3 + 2x)\\\\f(-x) = (-x)^2((-x)^2 + 9)((-x)^3 + 2\cdot(-x))\\f(-x)=x^2(x^2+9)(-x^3-2x)\\f(-x)=-x^2(x^2+9)(x^3+2x)\\\Large f(-x)\not =f(x)\implies\text{not even}\\\\-f(x)=-x^2(x^2+9)(x^3+2x)\\ -f(x)=f(-x)\implies \text{odd}[/tex]