[tex](1+i)^2-3(2-i)^3=1+2i-1-3(8-12i-6+i)=2i-6+33i=\boxed{-6+35i}[/tex].
Hope this helps.
What is the answer to a10/a3 ?
Answer:
a^7
Step-by-step explanation:
[tex]\frac{a^{10}}{a^3}\\\\\mathrm{Apply\:exponent\:rule}:\quad \frac{x^a}{x^b}=x^{a-b}\\\frac{a^{10}}{a^3}=a^{10-3}\\\\=a^7[/tex]
Find all unit vectors that are orthogonal to the vector u = 1, 0, −4 .
Answer:
Step-by-step explanation:
Given:
u = 1, 0, -4
In unit vector notation,
u = i + 0j - 4k
Now, to get all unit vectors that are orthogonal to vector u, remember that two vectors are orthogonal if their dot product is zero.
If v = v₁ i + v₂ j + v₃ k is one of those vectors that are orthogonal to u, then
u. v = 0 [substitute for the values of u and v]
=> (i + 0j - 4k) . (v₁ i + v₂ j + v₃ k) = 0 [simplify]
=> v₁ + 0 - 4v₃ = 0
=> v₁ = 4v₃
Plug in the value of v₁ = 4v₃ into vector v as follows
v = 4v₃ i + v₂ j + v₃ k -------------(i)
Equation (i) is the generalized form of all vectors that will be orthogonal to vector u
Now,
Get the generalized unit vector by dividing the equation (i) by the magnitude of the generalized vector form. i.e
[tex]\frac{v}{|v|}[/tex]
Where;
|v| = [tex]\sqrt{(4v_3)^2 + (v_2)^2 + (v_3)^2}[/tex]
|v| = [tex]\sqrt{17(v_3)^2 + (v_2)^2}[/tex]
[tex]\frac{v}{|v|}[/tex] = [tex]\frac{4v_3i + v_2j + v_3k}{\sqrt{17(v_3)^2 + (v_2)^2}}[/tex]
This is the general form of all unit vectors that are orthogonal to vector u
where v₂ and v₃ are non-zero arbitrary real numbers.
[tex]\left ( \frac{1}{\sqrt{17}},0, \frac{-4}{\sqrt{17}}\right )[/tex]
A vector is a quantity that has both magnitude and direction.
Two vectors are said to be orthogonal if they are perpendicular to each other.
Unit vectors orthogonal to [tex]u=\left ( a,b,c \right )[/tex] are given by [tex]\left ( \frac{a}{\sqrt{a^2+b^2+c^2}},\frac{b}{\sqrt{a^2+b^2+c^2}},\frac{c}{\sqrt{a^2+b^2+c^2}} \right )[/tex]
So, vectors orthogonal to [tex]u=\left ( 1,0,-4\right )[/tex] are [tex]\left ( \frac{1}{\sqrt{1^2+0^2+(-4)^2}},\frac{0}{\sqrt{1^2+0^2+(-4)^2}},\frac{-4}{\sqrt{1^2+0^2+(-4)^2}} \right )[/tex]
[tex]\left ( \frac{1}{\sqrt{1^2+0^2+(-4)^2}},\frac{0}{\sqrt{1^2+0^2+(-4)^2}},\frac{-4}{\sqrt{1^2+0^2+(-4)^2}} \right )=\left ( \frac{1}{\sqrt{17}},0, \frac{-4}{\sqrt{17}}\right )[/tex]
So, unit vector orthogonal to [tex]u[/tex] is [tex]\left ( \frac{1}{\sqrt{17}},0, \frac{-4}{\sqrt{17}}\right )[/tex]
For more information:
https://brainly.com/question/17108011?referrer=searchResults
If x = 2 and y = 4, then (2x + 3y) ÷ 4 - 2 = A) 10 B) 9 C) 8 D) 2
Answer:
[tex] \boxed{ \bold{ \huge{ \boxed{ \sf{2}}}}}[/tex]
Option D is the correct option.
Step-by-step explanation:
Given, x = 2 and y = 4
[tex] \sf{(2x + 3y) \div 4 - 2}[/tex]
plug the value of x and y
⇒[tex] \sf{ (2 \times 2 + 3 \times 4) \div 4 - 2}[/tex]
Multiply the numbers which are inside the bracket
⇒[tex] \sf{(4 + 12) \div 4 - 2}[/tex]
Add the numbers which are inside the bracket
⇒[tex] \sf{16 \div 4 - 2}[/tex]
Divide 16 by 4
⇒[tex] \sf{4 - 2}[/tex]
Subtract 2 from 4
⇒[tex] \sf{2}[/tex]
Hope I helped!
Best regards! :D
Answer:
2 (D)
Step-by-step explanation:
(2x+3y)÷4-2 you replace the variables with the matching numbers, and then multiply them by the number next to them.
(4+12)÷4-2 you add the numbers together
16÷4-2 you divide 16 by 4
4-2 you subtract to
2 this is your answer
The domain and target set of functions f and g isR. The functions are definedas:(b)•f(x) = 2x+ 3•g(x) = 5x+ 7(a)f◦g?(b)g◦f?(c) (f◦g)−1?(d)f−1◦g−1?(e)g−1◦f−1?
Step-by-step explanation:
The domain and target set of functions f and g given is expressed as;
f(x) = 2x+3 an g(x) = 5x+7 on R. To calculate the given functions, the following steps must be followed.
a) f◦g
f◦g = f(g(x)]) = f(5x+7)
To solve for the function f(5x+7), the variable x in f(x) will be replaced with 5x+7 as shown;
f(x) = 2x+3
f(5x+7) = 2(5x+7)+3
f(5x+7) = 10x+14+3
f(5x+7) = 10x+17
Therefore the function f◦g is equivalent to 10x+17
b) For the composite function g◦f
g◦f = g(f(x)])
g(f(x)) = g(2x+3))
To drive the functon g(2x+3), the variable x in g(x) will be replaced with 2x+3 as shown;
g(x) = 5x+7
g(2x+3) = 5(2x+3)+7
g(2x+3) = 10x+15+7
g(2x+3) = 10x+22
This shoes that the composite function g◦f = 10x+22
c) To get the inverse of the composite function f◦g i.e (f◦g)⁻¹
Given (f◦g) = 10x+17
To find the inverse, first we will replace (f◦g) with variable y to have;
y = 10x+17
Then we will interchange variable y for x:
x = 10y+17
We will then make y the subject of the formula;
10y = x-17
y = (x-17)/10
Hence (f◦g)⁻¹ = (x-17)/10
d) For the function f⁻¹◦g⁻¹
First we need to calculate for the inverse of function f(x) and g(x) as shown:
For f⁻¹(x):
Given f(x)= 2x+3
To find the inverse, first we will replace f(x) with variable y to have;
y = 2x+3
Then we will interchange variable y for x:
x = 2y+3
We will then make y the subject of the formula;
2y = x-3
y = (x-3)/2
f⁻¹(x) = (x-3)/2
Similarly for the function g⁻¹(x):
Given g(x)= 5x+7
To find the inverse, first we will replace g(x) with variable y to have;
y = 5x+7
Then we will interchange variable y for x:
x = 5y+7
We will then make y the subject of the formula;
5y = x-7
y = (x-7)/5
g⁻¹(x) = (x-7)/5
Now to get f⁻¹◦g⁻¹
f⁻¹◦g⁻¹= f⁻¹(g⁻¹(x))
f⁻¹(g⁻¹(x)) = f⁻¹((x-7)/5)
Since f⁻¹(x) = (x-3)/2
f⁻¹((x-7)/5) = [(x-7)/5)-3]/2
= [(x-7)-15/5]/2
= [(x-7-15)/5]/2
= [x-22/5]/2
= (x-22)/10
Hence f⁻¹◦g⁻¹= (x-22)/10
e) For the composite function g⁻¹◦f⁻¹
g⁻¹◦f⁻¹= g⁻¹[f⁻¹x)]
g⁻¹[f⁻¹(x)] = g⁻¹((x-3)/2)
Since g⁻¹(x) = (x-7)/5
g⁻¹(x-3/2) = [(x-3/2)-7]/5
= [(x-3)-14)/2]/5
= [(x-17)/2]/5
= (x-17)/10
Therefore the composite function g⁻¹◦f⁻¹= (x-17)/10
Solve for w
-4+w = -10
Answer:
w = -6
Step-by-step explanation:
Adding 4 to both sides (we do this to get rid of the -4) gives us:
-4 + w + 4 = -10 + 4
w = -6
Answer:
[tex]\Huge \boxed{w=-6}[/tex]
Step-by-step explanation:
[tex]-4+w=-10[/tex]
To solve for [tex]w[/tex], we need to isolate the variable on one side of the equation.
Adding 4 to both sides.
[tex]-4+w+4=-10+4[/tex]
Simplifying the equation.
[tex]w=-6[/tex]
5p-8/2=7p+4/2
Please help.
Answer:
p=-3
Step-by-step explanation:
Answer:
-4/2=2p
Step-by-step explanation:
5p - 8/2 = 7p +4/2
-5p -5p
-8/2 = 2p + 4/2
-4/2 -4/2
-4/2 = 2phope it helps =)200 + 10x = 120 + 15x now solve the equation to find x, the number of hours that both companies will charge the same ammount
Answer:
16
Step-by-step explanation:
Given the equation, [tex] 200 + 10x = 120 + 15x [/tex], let's solve for x as follows,
Subtract 200 from both sides
[tex] 200 + 10x - 200 = 120 + 15x - 200 [/tex]
[tex] 10x = - 80 + 15x [/tex]
Subtract 15x from both sides
[tex] 10x - 15x = - 80 + 15x - 15x [/tex]
[tex] -5x = - 80 [/tex]
Divide both sides by -5
[tex] \frac{-5x}{-5} = \frac{-80}{5} [/tex]
[tex] x = 16 [/tex]
Two hikers are 77 miles apart and walking toward each other. They meet in 10 hours. Find the rate of each hiker if one hiker walks 5.5 mph faster than the other.
The rate of the slower hiker is 1.1 mph and the rate of the faster hiker is 6.6 mph
Explanation
One hiker walks 5.5 mph faster than the other.
Suppose, the speed of the slower hiker is (x) mph.
So, the speed of the faster hiker will be:
(x+5.5)mph
Both hikers are walking toward each other and meet in 10 hours.
We know that, Distance = speed * time
So, the distance walked by the slower hiker in 10 hours = 10x miles and the distance walked by the faster hiker in 10 hours = 10(x + 5.5) miles.
Given that, they were 77 miles apart in the beginning. So the equation will be ...
10x + 10(x + 5.5) = 77
10x + 10x + 55 = 77
20x = 77 - 55 = 22
x = 22/20 = 1.1
Thus, the rate of the slower hiker is 1.1 mph and the rate of the faster hiker is (1.1 + 5.5) mph = 6.6 mph
Complete the equation for the horizontal line that passes through (5, –7).
Answer:
y = -7.
Step-by-step explanation:
It is horizontal so it will pass through the y axis where y = -7. It is parallel to the x axis so will never pass through it.
What’s the area and hurry:)
Find the equation of a line containing the given points (2,6) and (5,3). Write the equation in slope-intercept form.
Answer:
Step-by-step explanation:
(3-6)/(5-2) = -3/3= -1
y - 6 = -1(x - 2)
y - 6 = -x + 2
y = -x + 8
Anybody know the answer to this?
====================================================
Explanation:
Set A = {4,5,6,7,8,9} since these values are larger than 3 and smaller than 10. We only consider whole numbers in this range.
Set B = {1,2,3,4,5,6,7} represents positive whole numbers less than 8
To find the set [tex]A \cap B[/tex] we need to see which values are in both A and B at the same time. Those values are {4,5,6,7}
So [tex]A \cap B = \{4,5,6,7\}[/tex]
--------
side note: the notation [tex]A \cap B[/tex] means "A intersect B", so we're looking at where the two sets intersect or overlap (ie what they have in common).
A fourth-grade class earned snow cones for reading the most number of books. Each snow cone cost $1.47. If the total cost for the snow cones was $32.34, how many fourth graders are in the class?
Answer:
22 fourth graders
Step-by-step explanation:
Set up an equation, with the total amount on one side and the amount per cone on the other. Let x represent the unknown number of students:
[tex]1.47x=32.34[/tex]
Now we need to solve for x. Do this by isolating it:
Undo the multiplication on the left side by dividing both sides by 1.47:[tex]\frac{1.47x}{1.47} =\frac{32.34}{1.47}[/tex]
The 1.47 on the left now cancels each other out. Simplify:
[tex]x=22[/tex]
x equals 22, so there are 22 fourth graders in the class.
:Done
The value of the angle 5/4 π radians converted to degrees is:
Answer:
The answer is
[tex]225\degree[/tex]Step-by-step explanation:
In order to convert radians to degrees multiply the the value by
[tex] \frac{180\degree}{\pi} [/tex]So for the value above we have
[tex] \frac{5\pi}{4} \times \frac{180}{\pi} \\ = \frac{5 \times 180}{4} \\ = \frac{900}{4} [/tex]We have the final answer as
[tex]225\degree[/tex]Hope this helps you
You are working on an assignment for your statistics class. You need to estimate the proportion of students at your college who delay taking their first math class for at least one year. Which sampling plan will produce the most reliable results
Answer:
A simple random technique used to choose let's say 100 students can be adopted
Step-by-step explanation:
Because it give each student equal opportunity of being selected to avoid bias
A piece of wire 2/5 m long is to be cut into six pieces of the same length what is the length of each piece
Answer:
each peice will be 1/15 m long.
Step-by-step explanation:
Answer:
you got this
Step-by-step explanation:your smart try to figure it out by yourself
Write the polynomial in standard form. Then name the polynomial based on its degree and number of terms.
x²+2-7x
Write the polynomial in standard form.
Answer:
x²-7x+2
Step-by-step explanation:
x²+2-7x in standard form is
x²-7x+2
find the value of x
Answer:
[tex]x=12[/tex]
Step-by-step explanation:
First, note that the angles shown are vertical angles. In other words, the two equations are equivalent to each other.
Therefore, set the equations equal to each other and solve for x;
[tex]6x+7=8x-17[/tex]
Add 17 to both sides:
[tex]6x+24=8x[/tex]
Subtract 6x from both sides:
[tex]24=2x[/tex]
Divide both sides by 2:
[tex]x=12[/tex]
Therefore, the value of x is 12.
And we're done!
Answer:
12
Step-by-step explanation:
a line parallel to y=5x+2
Answer:
Step-by-step explanation:
y=-1/5x+4
----------
The slope of the perpendicular line is always the opposite reciprocal of the original line
For example: the opposite reciprocal of 5 is -1/5
Can anyone help me with this?
Answer:
x = 12
Step-by-step explanation:
they are virtical menaing they are the same value
6x + 7 = 8x - 17
6x + 24 = 8x
24 = 2x
12 = x
Answer:
x = 12
Step-by-step explanation:
Opposite angles are equal, so 6x + 7 = 8x - 17.
6x + 7 = 8x - 17
7 = 2x - 17 (take away 6x from both sides)
2x = 24 (Add 17 to Both Sides)
x = 12 (answer)
Sebastian was in a hotel lobby and took the elevator up 7 floors to his room. Then he took the elevator down 9 floors to the parking garage. He described his movement with the expression 9+ (-7). What is Sebastian's error?
Answer:
Sebastian didn't interpret the numbers correctly (See explanation)
Step-by-step explanation:
If you go up an elevator, you are gaining floors, so the number is positive.
If you go down an elevator, you are losing floors, so the number is positive.
Looking at the statement, he went 7 floors up to his room, then 9 floors down to the parking garage this can be represented as [tex]7 - 9[/tex], since the 7 is positive and the 9 is negative.
Sebastian described the movement as [tex]9 + -7[/tex], which is wrong - 9 should be -9 and -7 should be 7.
Hope this helped!
Answer:
Step-by-step explanation:
Let the lobby level be the reference point for Seb's movement.
The following describes his motion: +7 - 9. This puts him 2 floors below the lobby level.
Seb's "9 + (-7)" is incorrect because it indicates an upward trip, whereas the actual direction was downward. Similarly, "-7" indicates a downward trip, whereas the action direction was upward.
please help me out :)
Answer:
-2
Step-by-step explanation:
So we want to find the value of:
[tex](-6)+(4)[/tex]
Simply add:
[tex](-6)+4=-2[/tex]
Thus, drop the word SUM on -2.
Further notes:
To use the number line to solve, first start by placing your point on -6.
Since we are adding 4 to -6, we move to the right. Thus, move from -6 four spaces to the right.
If you do so correctly, you will end up at -2, the same answer we acquired previously.
Answer:
[tex]\Huge \boxed{-2}[/tex]
Step-by-step explanation:
The sum is the result from adding two or more numbers to each other.
[tex]-6 + 4 = - 2[/tex]
-6 is the starting point on the number line.
4 is added to -6, so an arrow from -6 goes 4 units to the right of the number line.
The arrow stops at -2.
Chicken eggs can be categorized as large if they weigh at least 2 ounces. Clare weighs 48 large eggs and finds that they have a mean weight of 2.1 ounces and a mean absolute deviation of 0.08 ounces. Interpret 0.08 ounces in this situation.
Answer:
Kindly check explanation
Step-by-step explanation:
Given the following :
Large eggs : ≥2 ounces
Mean of 48 large eggs = 2.1 ounces
Mean absolute deviation = 0.08 ounces
0.08 ounces here is the mean absolute deviation of the 48 large eggs weighed, meaning that:
The average of the sum of the absolute differences in each individual egg and the mean value of all eggs weighed is 0.08.
This means that the average difference, variability or deviation in the weight of large eggs weighed is 0.08 ounces around the mean value of all eggs weighed.
Mean Absolute Deviation (MAD) :
Σ|xi - mean| / n
xi = each individual value
n = number of values
HELP!
Factor x2 - x - 30.
1.( x - 7)( x - 3)
2.( x + 9)( x - 3)
3.( x + 5)( x - 6)
4.( x + 4)( x - 8)
Answer:
3.) (x + 5) (x - 6)
Step-by-step explanation:
Factor the following:
x^2 - x - 30
Hint: | Factor x^2 - x - 30 by finding two numbers whose product is -30 and whose sum is -1.
The factors of -30 that sum to -1 are 5 and -6. So, x^2 - x - 30 = (x + 5) (x - 6):
Answer: (x + 5) (x - 6)
3.5 - (n + 21) - 4n = -45
Answer:
[tex]n = \frac{11}{2} = 5.500[/tex]
The fastest pizza box folder can assemble 2 pizza boxes in 5 seconds. At this rate, how long would it take to assemble 20 pizza boxes?
Answer:
50 seconds in order to assemble 20 pizza boxes
Step-by-step explanation:
there are two ways to solve this the first way is divide 20 by 2 which is 10 and then multiply 10 by 5 the reason to this is because we know that for every 2 it takes 5 seconds.
the second way takes longer but you write:
2, 2, 2, 2, 2, 2, 2, 2, 2, 2,
5, 5, 5, 5, 5, 5, 5, 5, 5, 5,
so here were basically writing the number 2 10 times because when u count that u can see that it equals 20 and then since for every 2 boxes it takes 5 seconds u put the 5 under each 2 so then you would count the 5s, like 5, 10 15, 20... and so on and u will see that its 50 which means 50 seconds.
The Sky Ranch is a supplier of aircraft parts. Included in stock are 6 altimeters that are correctly calibrated and two that are not. Three altimeters are randomly selected, one at a time, without replacement. Let the random variable x represent the number that are not correctly calibrated. Complete the probability distribution table; report probabilities accurate to 4 decimal places.
x 0 1 2 3
P (x)
Answer:
For x = 0, P(x = 0) = 0.35
For x = 1, P(x = 1) = 0.54
For x = 2, P(x = 2) = 0.11
For x = 3, P(x = 3) = 0
Step-by-step explanation:
We are given that the Sky Ranch is a supplier of aircraft parts. Included in stock are 6 altimeters that are correctly calibrated and two that are not. Three altimeters are randomly selected, one at a time, without replacement.
Let X = the number that are not correctly calibrated.
Number of altimeters that are correctly calibrated = 6
Number of altimeters that are not correctly calibrated = 2
Total number of altimeters = 6 + 2 = 8
(a) For x = 0: means there are 0 altimeters that are not correctly calibrated.
This means that all three selected altimeters are correctly calibrated.
Total number of ways of selecting 3 altimeters from a total of 8 = [tex]^{8}C_3[/tex]
The number of ways of selecting 3 altimeters from a total of 6 altimeters that are correctly calibrated = [tex]^{6}C_3[/tex]
So, the required probability = [tex]\frac{^{6}C_3}{^{8}C_3}[/tex]
= [tex]\frac{20}{56}[/tex] = 0.35
(b) For x = 1: means there is 1 altimeter that is not correctly calibrated.
This means that from three selected altimeters; 1 is not correctly calibrated and 2 are correctly calibrated.
Total number of ways of selecting 3 altimeters from a total of 8 = [tex]^{8}C_3[/tex]
The number of ways of selecting 2 correctly calibrated altimeters from a total of 6 altimeters that are correctly calibrated = [tex]^{6}C_2[/tex]
The number of ways of selecting 1 not correctly calibrated altimeters from a total of 2 altimeters that are not correctly calibrated = [tex]^{2}C_1[/tex]
So, the required probability = [tex]\frac{^{6}C_2 \times ^{2}C_1 }{^{8}C_3}[/tex]
= [tex]\frac{30}{56}[/tex] = 0.54
(c) For x = 2: means there is 2 altimeter that is not correctly calibrated.
This means that from three selected altimeters; 2 are not correctly calibrated and 1 is correctly calibrated.
Total number of ways of selecting 3 altimeters from a total of 8 = [tex]^{8}C_3[/tex]
The number of ways of selecting 1 correctly calibrated altimeters from a total of 6 altimeters that are correctly calibrated = [tex]^{6}C_1[/tex]
The number of ways of selecting 2 not correctly calibrated altimeters from a total of 2 altimeters that are not correctly calibrated = [tex]^{2}C_2[/tex]
So, the required probability = [tex]\frac{^{6}C_1 \times ^{2}C_2 }{^{8}C_3}[/tex]
= [tex]\frac{6}{56}[/tex] = 0.11
(d) For x = 3: means there is 3 altimeter that is not correctly calibrated.
This case is not possible, so this probability is 0.
Determine the payback period (in years) for a project that costs $120,000 and would yield after-tax cash flows of $20,000 the first year, $22,000 the second year, $25,000 the third year, $27,000 the fourth year, $31,000 the fifth year, and $37,000 the sixth year.
Answer: luis is 28
Step-by-step explanation:
first you need to set up an equation. if luis age is equal to four years added to colleens age we can substitute colleens age with a variable (i’m gonna use the letter c) and luis’s age for a different variable (i’ll use L). your equation would be C + 4 = L. our second equation would be both of their ages is equal to 52, giving us C + L = 52 as our equation. since our other equation tells us that what L equals (it would equal C plus 4), we can substitute out the L in the second equation for C + 4. the equations would change from C+L= 52, to C + C + 4 = 52. then we would solve like any regular equation for our variable. first we can simplify the 2 c’s together to get
2c + 4 = 52. next you would take your + four and do the opposite sign to both sides of the equation. so you do + 4 minus 4 and then 52 minus four. this leaves you with the equation 2c = 48. lastly you do the opposite function to both sides with your coefficient. you would do 2c divides by 2 (to cancel out your two because it’s being multiplied by c). and then 48 divided by 2 leaving you with C = 24. that tells us that colleens age is 24, and then you plug this into your first equation to get 24 + 4 = L telling you that luis’s age is 28. to fact check you would just add the two ages together to see if you got your total
number. these are called like two step equations with substitution i believe
what is decimal of 2 2/9
Answer:
2.22
Step-by-step explanation:
To get 2 2/9 in decimal form, we basically convert the mixed number to a fraction and then we divide the numerator of the fraction by the denominator of the fraction. Here are the detailed math steps we use to convert 2 2/9 mixed number to decimal form:
Step 1: Multiply the whole number by the denominator:
2 × 9 = 18
Step 2: Add the product you got in Step 1 to the numerator:
18 + 2 = 20
Step 3: Divide the sum from Step 2 by the denominator:
20 ÷ 9 = 2.222222
That's it! The answer to 2 2/9 in decimal form is displayed below:
2 2/9 ≈ 2.22
Alma is 3 years older than Liz.
Let a = Alma's age.
Then ?
=
Liz's age.
Lucy
Answer:
12 hope you understand the answer
Answer:
A-3
Step-by-step explanation:
Since Alma is 3 years older than Liz then Liz would be A-3