4. If z, a+bi and z, c+di represent two complex numbers with real components a, b, c and d, then which of the following represents the coefficient of i in the product of z, and z,?
(1) ac-bd
(2) ad-be
(3) ab+cd
(4) be+ad
Answer:3
Step-by-step explanation:
Before you factor you should check what two things?
Answer:
I put all the steps to factoring, hopefully this helps! ^^
Step-by-step explanation:
-Check for common factors. If the terms have common factors, then factor out the greatest common factor (GCF) and look at the resulting polynomial factors to factor further.
-Determine the number of terms in the polynomial.
-Look for factors that can be factored further.
-Check by multiplying.
Find the value of x then tell whether the side lengths form a Pythagorean triple 6 , 10 , x
Answer:
Explanation:
Use the Pythagorean theorem (
a
2
+
b
2
=
c
2
)
Lets label the right triangle such that:
a
=
12
b
=
16
c
=
x
Thus,
12
2
+
16
2
=
x
2
144
+
256
=
x
2
400
=
x
2
√
400
=
x
20
=
x
So our missing side,
c
is
20
We can now say that the sides of our triangle are
12
,
16
,
20
I've included a link that lists a couple of Pythagorean triples (a couple because they are infinitely many).
Step-by-step explanation:
Hope it helpful
Answer:
Step-by-step explanation:
a^2+b^2=c^2
6^2+10^2=x^2
36+100=x^2
136=x^2
[tex]\sqrt{136[/tex] =x
2[tex]\sqrt{34[/tex] =x
Jasmine recorded the number of minutes she spent doing homework each day during the months of March and April
The box plot shows her data for March
March
0
5
10
15
20
25
30
35
40
45
50
Time Spent Doing Homework (minutes)
Her data for April is given in the table
0 5 10 15
20 25 30 30 30
30 30 30 30
35 40 40 40 45
45 45 45 50 50 55 60 65 65 75
Select all true statements about the data
DA Jasmine spent more minutes doing homework during the month of April.
B
The mean value
greater for the month of April
C. The median value is greater for the month of April
D. Based on the interquartile range, there is greater variability for the month of April
Answer:
Option A,B,C and D is correct
Step-by-step explanation:
As we can see , the data set for April month has longer time duration taken for completing homework as compared to the time taken during the month of April. Hence, option A is correct.
Option B is also correct because most of the instance of time taken for doing homework is greater for month of April as compared to the month of March
Median value for the month of march = 25 and median value for the month of April is (30+35)/2 = 32.5. Hence, Option C is correct
There is greater variability for the month of April. Hence, option D is correct
i need help asap i don’t get it
I need help
Cristina and Kori both leave the restaurant at the same time, but in opposite directions. If Kori travels 9 mph faster than Cristina and after 6 hours they are 186 miles apart, how fast is each traveling?
Carrie left the restaurant traveling 12 mph. Then, 4 hours later, Leah left traveling the same direction at 24 mph. How long until Leah catches up with Carrie?
Paige started biking to the mall traveling 8 mph, after some time the bike got a flat so Paige walked the rest of the way, traveling 5 mph. If the total trip to the mall took 8 hours and it was 46 miles away, how long did Paige travel at each speed?
Answer:
Question 1)
Cristina is traveling 11 miles per hour and Kori is traveling 20 miles per hour.
Question 2)
Four hours.
Question 3)
Paige spent two hours biking and six hours walking.
Step-by-step explanation:
Question 1)
Let Cristina's speed be x.
Kori travels 9 miles per hour faster than Cristina. So, Kori's speed is (x + 9).
After six hours, Cristina would have traveled 6x miles and Kori would have traveled 6(x + 9) miles.
Since Kori traveled in the opposite direction, we can place a negative to represent this. So, after six hours, Kori is -6(x + 9) miles away from the restaurant while Cristina is 6x miles away from the restaurant.
Since the distance between them is 186 miles, the difference of the two expressions is 186. Hence:
[tex](6x)-(-6(x+9))=186[/tex]
Distribute:
[tex]6x-(-6x-54)=186[/tex]
Distribute:
[tex]6x+6x+54=186[/tex]
Simplify:
[tex]12x=132[/tex]
Hence:
[tex]x=11[/tex]
Cristina's speed is 11 miles per hour. Thus, Kori's speed is 20 miles per hour.
Question 2)
Let h represent the amount of time that has passed in hours.
Carrie left the restaurant traveling 12 miles per hour.
Four hours later, Leah left traveling in the same direction at 24 miles per hour.
After four hours, Carrie would have traveled 12(4) = 48 miles.
Carrie would still be traveling at 12 miles per hour. So, her distance from the restaurant is given by:
[tex]12h+48[/tex]
Since Leah just left and is traveling at a rate of 24 miles per hour, her distance from the restaurant is given by:
[tex]24h[/tex]
Leah will catch up when the two expressions are equivalent. Hence:
[tex]12h+48=24h[/tex]
Solve for h:
[tex]12h=48\Rightarrow h=4[/tex]
Leah will catch up with Carrie in four hours.
Question 3)
Let x represent the amount of hours spent biking and y represent the amount of hours spent walking.
The total trip to the mall took eight hours. Hence:
[tex]x+y=8[/tex]
The mall is a total of 46 miles away. Since Paige bikes at a rate of 8 miles per hour and walks at a rate of five miles per hour:
[tex]8x+5y=46[/tex]
Solve the system. We can use elimination. Multiply the first equation by -5:
[tex]-5x-5y=-40[/tex]
We can add this to the second equation:
[tex]3x=6[/tex]
Hence:
[tex]x=2[/tex]
Using the first equation again:
[tex](2)+y=8\Rightarrow y=6[/tex]
So, Paige spent two hours biking and six hours walking.
which of the following values are in the range of the function graphed below?
Answer:
f)0
Step-by-step explanation:
HELP PLEASE
Question: 1. Line segment AB has endpoints A(8, 3) and B(2, 6). Find the coordinates of the point that divides the line segment directed from A to B in the ratio of 1:2. 2. Line segment AB has endpoints A(6, 4) and B(2, 6). Find the coordinates of the point that divides the line segment directed from A to B in the ratio of 1:3.
Answer:
a) (6,4)
b) (5, 4.5)
Step-by-step explanation:
much like when you find them midpoint where you average the x-coordinates and the y-coordinates to find the midpoint coordinates, you'll do the same thing here.
to set context, a midpoint would break the segment into a ratio of 1:1.
so in the first part, a ratio of 1:2 means you are breaking the segment into 3-parts. So you'll do this for the coordinates:
[tex]x = \frac{8 + 2}{3} \: and \: y = \frac{3 + 6}{3} [/tex]
for the second part as the ratio is 1:3, you are breaking the segment into 4 parts.
[tex]x = \frac{6 + 2}{4} \: and \: y = \frac{4 + 6}{4} [/tex]
For the sample standard deviation(s) for situations involving means, explain whether it affects the width of a confidence interval, the center of a confidence interval, neither, or both.
Answer:
Affects the width of a confidence interval, as the margin of error is a function of the sample standard deviation.
Step-by-step explanation:
When we have the standard deviation for the sample, the t-distribution is used to solve the question.
It does not affect the center of the interval, which is a function only of the sample mean.
Width of a confidence interval:
The width of a confidence interval is a function of the margin of error, which is:
[tex]M = t\frac{s}{\sqrt{n}}[/tex]
In which s is related to the sample standard deviation. Thus, since s and M are directly proportional, a higher standard deviation makes the interval wider, lower standard deviation makes the interval narrower, and thus, the sample standard deviation affects the the width of a confidence interval.
PLEASE HELP I WILL MARK BRAINLIEST
Answer:
8 x 13 = 104 yd^2
Step-by-step explanation:
To find the area of a rectangle we use the basic formula:
L x W
In this case 13 is your width and 8 is your length, multiply the two given lengths to get your area which is 104.
The scores on an exam are normally distributed, with a mean of 82 and a standard deviation of 10. What percent of the scores are less than 62?
Answer:a
a
Step-by-step explanation:
i took the test
With sales tax, it costs $707 to buy a $700 dining room table. What is the sales tax
percentage?
Write your answer using a percent sign (%).
Answer:
1%
Step-by-step explanation:
707-700=7 tax
700 x tax percentage=7
tax percentage =7/700
Tax percentage= .01 0r 1%
Find the circumference of a circle with diameter,
d
= 6cm.
Give your answer in terms of
π
.
Answer:
6π cm
Step-by-step explanation:
Special Right Triangles
Guided Practice
Find the values of x and y.
A. x=30, y=10V3
B. x= 10, y=30V3
C. x= 30 V3, y=10
D. x=10V3, y=30
y
30°
2013
Need help ASAP
Answer:
A.
x = 30
y = 10√3
Step-by-step explanation:
Reference angle = 30°
Opposite = y
Adjacent = x
Hypotenuse = 20√3
✔️To find x, apply CAH:
Cos 30 = Adj/Hyp
Cos 30 = x/20√3
20√3 × Cos 30 = x
20√3 × √3/2 = x (cos 30 = √3/2)
(20√3 × √3)/2 = x
(20 × 3)/2 = x
60/2 = x
30 = x
x = 30
✔️To find y, apply SOH:
Sin 30 = Opp/Hyp
Sin 30 = y/20√3
20√3 × Sin 30 = y
20√3 × ½ = y (sin 30 = ½)
(20√3 × 1)/2 = y
(20√3)/2 = y
10√3 = y
y = 10√3
Please help I will Mark if your right
Answer:
Line DC.
Step-by-step explanation:
Point D and Point C are not connected and, therefore, do not form a line.
Geometry
DC is not a line, due to it not being connected.
A ball is thrown straight down from the top of a building at a velocity of 16 ft/s. The building is 480 feet tall, and the acceleration due to gravity is 32 ft/s2.
This problem can be represented using the following equation.
How much time will the ball take to reach the ground? (1/2)32t^2+16t=480
Answer:
Time, t = 5 seconds.
Step-by-step explanation:
Given the following data;
Initial velocity = 16 ft/s
Height = 480 ft
Acceleration due to gravity = 32 ft/s²
To find how much time it will take the ball to reach the ground, we would use the kinematic equation given by the formula;
[tex] d = V_{i}t + \frac {1}{2}at^{2} [/tex]
Where;
d is the displacement.Vi is the initial velocity.a is the acceleration or acceleration due to gravity.t is the time measured in seconds.Substituting into the equation, we have;
[tex] 480 = 16t + \frac {1}{2}*32t^{2} [/tex]
[tex] 480 = 16t + 16t^{2} [/tex]
Dividing all through by 16, we have;
[tex] 30 = t + t^{2} [/tex]
Re-arranging the quadratic equation, we have;
[tex] t^{2} + t - 30 = 0 [/tex]
We would solve the quadratic equation by factorization;
[tex] t^{2} + 6t - 5t - 30 = 0 [/tex]
[tex] t(t + 6) - 5(t + 6) = 0[/tex]
[tex] (t + 6)(t - 5) = 0 [/tex]
t = -6 or 5
Since we know time can't be negative, we would ignore the value of -6.
Therefore, time = 5 seconds
Si 3 alumnos inasistentes de un curso corresponde al 10%. ¿Cuántos alumnos tiene el curso?
a)13 b) 27 c) 30 d) 110
Question 1 of 10
A density curve for all the possible ages between 0 years and 25 years is in
the shape of a triangle. What is the height of the triangle?
A. 0.04
B. 0.08
C. 0.02
D. 0.16
Step-by-step explanation:
A density curve for all the possible ages between 0 years and 25 years on the shape of a triangle. 0.04
Which of these are polygons?
On
А
B
o
D
F
G
G
Answer:
B C and F
Step-by-step explanation:
Polygons are closed shaped with straight lines
D and E have curves therefore they cannot be classified as polygons
A is not closed therefore it A is not a polygon
B, C and F are closed and use only straight lines therefore those 3 are polygons
Hawkeye Elementary School is having a raffle for students who are in sports. The school leaders are voting to choose between the two options below.
i. Option 1: Raffle off two items and include all boys and girls in each raffle.
ii. Option 2: Have a separate raffle for boys and a separate raffle for girls.
Not in sports In sports Total
Girls 17 18 35
Boys 17 21 38
Total 34 39 73
Required:
If you get to vote and you have a daughter in sports, which option would you vote for and why?
Answer:
The answer is "0.052 and 0.056".
Step-by-step explanation:
For option 1:
Your daughter's opportunity (in sport) (when a person only wins once)
[tex]\to \frac{1}{39}+\frac{1}{38}\\\\ \to \frac{38+39}{1,482} \\\\\to \frac{38+39}{1,482} \\\\\to 0.052[/tex]
For option 2:
Your daughter would win a chance (in sport) [tex]= \frac{1}{18} = 0.056[/tex]
So a little better, the second option. The rationale is that there are fewer girls than boys so if a lottery in a smaller group is awarded you are more likely to win.
This graph shows the cost of a small cheese pizza at 3 different restaurants. a) explain how the size of the bars gives a false impression about the cost of the pizza at different restaurants.
I would answer, but I don’t see the graph. If you add the graph I could help (if you want of course, not trying to be rude. Sorry!)
Which of the following is geometric sequence
A. 1,1/2,1/4,1/8
B.2,4,6,8
C.1,1,2,3,5
D.7,4,1,-2
Answer:
A
Step-by-step explanation:
...................
Answer:
here's the whole unit test
Step-by-step explanation:
ur welcomeeeee ;)
What combination of variables could you analyze using correlation?
religious identification & life satisfaction
IQ score and annual income
ethnic identification & average # of children
preferred genre of music & age
Answer:
YOu have to add them i think
Step-by-step explanation:
First add the 3-4 and then finish it
Which drawing wouldn’t be useful to find the area of this trapezoid? and why ?
Answer:
C
Step-by-step explanation:
Though you may think that u can change that piece to there, but the possibility is very less
Solve tan(x+π2)+tan(x−π2)=2 for 0≤x<2π
In the interval 0≤x <π, the solution is
Answer:
[tex]x = \pi \div 4 [/tex]
Which expression is equivalent to 14x^8y^10
Answer:
The answer for this problem is 2xy^6 * 7x^7y^4 (C).
An electronics firm claims that the proportion of defective units of a certain process is 5%. A buyer has a standard procedure of inspecting 15 units selected randomly from a large lot. On a particular occasion, the bury found 5 items defective. a) What is the probability of this occurrence, given that the claim of 5% defective is correct
Answer:
0.0006 = 0.06% probability of this occurrence
Step-by-step explanation:
For each unit, there are only two possible outcomes. Either it is defective, or it is not. The probability of an unit being defective is independent of any other unit, which means that the binomial probability distribution is used to solve this question.
Binomial probability distribution
The binomial probability is the probability of exactly x successes on n repeated trials, and X can only have two outcomes.
[tex]P(X = x) = C_{n,x}.p^{x}.(1-p)^{n-x}[/tex]
In which [tex]C_{n,x}[/tex] is the number of different combinations of x objects from a set of n elements, given by the following formula.
[tex]C_{n,x} = \frac{n!}{x!(n-x)!}[/tex]
And p is the probability of X happening.
An electronics firm claims that the proportion of defective units of a certain process is 5%.
This means that [tex]p = 0.05[/tex]
A buyer has a standard procedure of inspecting 15 units selected randomly from a large lot.
This means that [tex]n = 15[/tex]
a) What is the probability of this occurrence?
Probability of 5 defective items, whch is P(X = 5). So
[tex]P(X = x) = C_{n,x}.p^{x}.(1-p)^{n-x}[/tex]
[tex]P(X = 5) = C_{15,5}.(0.05)^{5}.(0.95)^{10} = 0.0006[/tex]
0.0006 = 0.06% probability of this occurrence
5c + 40 + 2 and 5c + 2(2c + 1)
Answer:
5c + 42 and 9c + 2
Step-by-step explanation:
if a number has a variable next to it then it cannot be combined with a number that is alone.. Therefore there is no exact answer unless the variable has a number that you can replace it with. So basically numbers with the same number can be added together and numbers alone can be added together. If you do the math right then you should get the answer.
For vectors u = i + 6j, v = 5i – 3j, and w = 9i – 2j, determine u • w + v • w.
27
18
90
48
Answer:
This is the explanation you can find answer by rolling it.This morning, the cafe served 8 coffees in all, 75% of which were regular. How many regular coffees did the cafe serve?
Answer:
6 regular coffees. Thank it if its helpful, thank you!
Step-by-step explanation:
75% of 8 is 6
Reasoning:
75/100*8/1=600/100
600/100=6!
Answer:
Regular coffee served by cafe = 75%* 8
= 75/100*8 = 6 coffees
Step-by-step explanation:
