Let z = 19 + i and w = 4 + 10i.
What is the first step in determining zw?
Replace i2 with –1.
Multiply z by the conjugate of w.
Apply the distributive property or FOIL.
Combine the corresponding real and imaginary parts.
EDGE
In the first step apply the distributive property or FOIL to find zw. Option C is correct.
Given that,
Let z = 19 + i and w = 4 + 10i.
The first step is to be determined.
The number that constitute of real and imaginary numbers are called a complex numbers. Complex number is represents as z = a + ib, where a = real number and bi = imaginary number
z = 19 + i and w = 4 + 10i
in order to find the product of complex numbers z and w following are the steps,
z.w = ( 19 + i )( 4 + 10i )
Step ⇒ 1
Applying distributive law,
z.w = 19 * ( 4 + 10i ) + i * ( 4 + 10i )
Step ⇒ 2
opening the parenthesis,
z.w = 19 * 4 + 19*10i + i * 4 + i * 10i
similarly, further steps are
z.w = 76 + 190i +4i + 10i²
since i² = -1
z.w = 76 + 194i - 10
z.w = 66 + 194i
Thus, in the first step apply the distributive property or FOIL to find zw. Option C is correct.
Learn more about complex numbers here: https://brainly.com/question/28007020
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Answer:
C
Step-by-step explanation:
Apply the distributive property of FOIL
A plane flies at a steady rate of 40 mph while a second plane flies at a steady rate of 100 mph. The planes are 200 miles apart and fly directly toward each other. In how many hours will they meet?
plz help
times almost up
Answer:
The time the two planes will meet is 1.43 hours
Step-by-step explanation:
Given;
speed of the first plane in positive direction, = 40 mph
speed of the second plane in negative direction(opposite direction) = -100 mph
distance between the two planes = 200 miles
Let the time the two planes will meet = t
the position of the first plane at this time "t" = 40t
the position of the second plane at this time "t" = -100t
(40t)>--------------------------------<(-100t), this space between them is 200 miles.
Thus, the difference in the distance they traveled before meeting should be equal to 200 miles.
40t - (-100t) = 200
40t + 100t = 200
140t = 200
t = 200 / 140
t = 1.43 hours
Therefore, the time the two planes will meet is 1.43 hours
are there instances that rational algebraic equation can be transformed into quadratic equation
Answer:
yeah
Step-by-step explanation:
hmm
Answer:
yes you can
Step-by-step explanation:
for example you have a second order algebraic equation, which have the general form ax^2 + bx + c = 0, for any constants a, b, and c, you can use the quadratic equation to find the values of x. However, sometimes it is easier to simply factor the expression into (fx+g)(hx+i) = 0, for any constants f, g, h, and i, and then solve the two resulting equations fx+g = 0 and hx+i=0 for the values of x.
i hope this helps
Please answer. Have to find what numbers make that equation true
Answer:
(x+8y)(x-8y)
Step-by-step explanation:
8 squared is 64 and so is y for y^2.
One positive and a negative turns into a negative, so that's why it's only one.
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Question Help
As part of a research project, the blood pressures of 2000 patients in a hospital are recorded. The systolic blood pressures (given in millimeters) have
an approximately normal distribution with mean y = 122 and standard deviation o = 15. Use the 68-95-99.7 rule to complete the following.
(a) Estimate the number of patients whose blood pressure was between 92 and 167 millimeters.
(b) Estimate the number of patients whose blood pressure was between 92 and 137 millimeters.
Question 3: On a recent math quiz, 20 of the 32 students who took the
quiz used a pen and the rest used a pencil. Which of the following is the
ratio of the students who used a pen to those who used a pencil? *
5 to 3
5 to 8
8 to 5
O 13 to 8
Answer:
5 to 8
Step-by-step explanation:
bc u divide the numerator and denominator by 4
3. (05.05)
Which of the following inequalities matches the graph? (1 point)
x<2
y>2
x<2
x>2
Answer:
The inequality x>2 matches the graph.
Step-by-step explanation:
From the graph, it is clear that the shaded graph is heading towards the +ve infinity from the x > 2.
If the inequality includes < or >, we graph the equation as a dotted line.
From the graph, the dotted line indicates that x=2 is not included in the solution of the inequality.
so the interval of the domain of the inequality is: (2, ∞)
Therefore, the inequality x>2 matches the graph.
What is the answer to 5/8 + 1/2
Answer:
9/8 or 1 1/8
Step-by-step explanation:
Answer:
9/8 or 1 1/8
Step-by-step explanation:
find common denominator, its 8 for this problem so put [tex]\frac{1}{2} = \frac{4}{8}[/tex]
[tex]\frac{5}{8} +\frac{4}{8} = \frac{9}{8}[/tex]
(X+y)^16 what is the answer
Use the Binomial Theorem to expand.
I need help trying to find any fractions that are not in simplest form. (there should be a screenshot below. I dont know the hidden word that is supposed to go in the box... Reply if you understand..
Answer:
Denominator is the hidden word.
Step-by-step explanation:
8/18, 9/27, 42/48, 21/70, 14/35, 8/30, 15/39, 18/100, 8/64, 70/98, and 63/81 are all not in simplest form. Their letters (ENAMNIODOTR) unscramble to "denominator."
laura spent 2/5 of her money now she has $18 left how much money did she have origanily
Answer:
Money Laura had originally = $30
Step-by-step explanation:
Let the money Laura had = x
Money spent = 2/5 of x = [tex]\frac{2}{5}x[/tex]
Remaining money = $ 18
[tex]x - \frac{2}{5}x = 18\\\\\frac{x*5}{1*5}-\frac{2}{5}x = 18\\\\\frac{5x}{5} - \frac{2x}{5} = 18\\\\\frac{3x}{5}=18\\\\ 3x = 18*5\\\\3x = 90\\\\x = \frac{90}{3}\\\\x = 30[/tex]
Money Laura had originally = $30
e(x) = -x + -6
Find e(-2)
Answer:
I'm pretty sure it's -4
Step-by-step explanation:
If you substitute in -2, you get e(-2)= -(-2)+ -6
which is equal to 2-6
2-6=-4
Answer:
e(-2)=-4
Step-by-step explanation:
e(-2)=-(-2)+-6
=2-6
=-4
c) The first five terms of a sequence are shown below; 13, 9, 5, 1, -3 . Find the nth term of this sequence
Answer:
-7
Step-by-step explanation:
because they are going down by 4. So just subtract 4.
Which expression is
equivalent to 25x + 12 ?
Answer:
Step-by-step explanation:
What are the choices?
what does 900+900+900=
Answer:
2,700
Step-by-step explanation:
thx for da points tee hee
Answer:
2700
Step-by-step explanation:
HELP 50 POINTS
Could I get like an explanation so I know how to do this since its 50 points?
Answer: #2
Step-by-step explanation:
Answer:
c
Step-by-step explanation:
Some one please answer
Answer:
A and D
Step-by-step explanation:
0.45 - 0.23 = 0.22
0.45(8) = 3.60
89,235 written in expanded form? (2 points)
a
8 x 10,000 + 9 x 1,000 + 2 x 100 + 3 x 10 + 5 x 1
b
8 x 10,000 + 9 x 1,000 + 2 x 100 + 3 x 10 + 5 x 5
c
8 x 100,000 + 9 x 10,000 + 2 x 1,000 + 3 x 100 + 5 x 10
d
8 x 80,000 + 9 x 9,000 + 2 x 200 + 3 x 30 + 5 x 5
2. Select the solution for the system of linear equations y = 3x + 4 and y = x + 2.
A. (-1,1)
B. (1,-1
C. (-1,-1)
D. (1,1)
g One card is selected randomly from a standard 52-card deck. a. What is the probability of drawing a
Answer:
Probability [Getting a red card] = 1/2
Step-by-step explanation:
Given:
Total number of cards = 52
Find:
Probability [Getting a red card]
Computation:
Total number of red cards = 26
Probability [Getting a red card] = 26/52
Probability [Getting a red card] = 1/2
1. un numar se mareste cu 4 iar rezultatul se mareste de 4 ori. noul rezultat micsorat cu 4 se imparte la 4 si se obtine 4.aflati numarul
Răspuns:
1
Explicație pas cu pas:
Fie numărul = x
x + 4 = e - - (1)
e * 4 = f - - - (2)
Ecuația 2 - 4 împărțită la 4 = 4
(f - 4) / 4 = 4
Crucea se înmulțește
f - 4 = 16
f = 16 + 4
f = 20
Rezultatul 1 împărțit la 4 este egal cu 4
Prin urmare,
e = f / 4
f = 20
e = 20/4
e = 5
De la (1)
x + 4 = e
x + 4 = 5
x = 5 - 4
x = 1
Answer:
Step-by-step explanation:
[tex]\left[\begin{array}{ccc}1&2&3\\4&5&6\\7&8&9\end{array}\right][/tex]Subtract 8 from me. Then add 21. If you divide me by 4 and add 21 you get 29. What number am I?
Answer:
19
Step-by-step explanation:
x - 8 + 21 ÷ 4 + 21 = 29
x - 8 + 21 ÷ 4 = 29 - 21
= 8
x - 8 + 21 = 8 x 4
= 32
x - 8 = 32 - 21
= 11
x = 11 + 8
= 19
Therefore the number is 19. A bit confusing to me at first but I solved it :)
Evaluate this expression:
(5+5)-(5+5)
Answer:
0
Step-by-step explanation:
=(5+5)-(5+5) <-- Do what's inside the parenthesis first
=10 - 10 <-- Subtract
=0
50 POINTS!!!!Perpendicular Bisectors meet at the Circumcenter. What is the measure of BD?
20
15
25
24
Answer:20 degrees
Step-by-step explanation:
HELP ME PLEASE I NEED HELP I WILL GIVE BRAINLIST
Answer:
The second choice. About 1 cup.
Step-by-step explanation:
1/8 + 4/5 = 37/40
Thats around 1 full cup.
Answer:
♥B♥ about 1 cup!
Im pretty sure!
♥ お力になれて、嬉しいです！♥
The accompanying data represent the miles per gallon of a random sample of cars with a three-cylinder, 1.0 liter
engine.
32.7, 35.7, 38.0, 38.7, 40.1, 42.3, 34.3, 36.2, 38.1, 39.0, 40.6, 42.9, 34.5, 37.4, 38.3, 39.4, 41.4, 43.4, 35.3, 37.6, 38.5, 39.7, 41.7, 48.9
(a) Compute the z-score corresponding to the individual who obtained 38.1 miles per gallon. Interpret this result.
The z-score corresponding to the individual is __ and indicated the date value is __ standard decoration(s) __(below/above) the __(mean/median)
(b) Determine the quartiles.
(c) Compute and interpret the interquartile range, IQR.
(d) Determine the lower and upper fences. Are there any outliers?
Answer:
A) Z = -0.24
We can interpret this as the z-score corresponding to the individual who obtained 38. 1 miles per gallon is -0.24.
B) Q1 = 36.8 and Q3 = 41
C)IQR = 4.2
This means that the distance between the first and third quartile is 4.2
D) LF = 30.5 and UF = 47.3
the only outlier is 48.9 which is more than UF
Step-by-step explanation:
We are given the data representing the miles per gallon of a random sample of cars with a three-cylinder as;
32.7, 35.7, 38.0, 38.7, 40.1, 42.3, 34.3, 36.2, 38.1, 39.0, 40.6, 42.9, 34.5, 37.4, 38.3, 39.4, 41.4, 43.4, 35.3, 37.6, 38.5, 39.7, 41.7, 48.9
Sum of data is;
ΣX = 32.7 + 35.7 + 38.0 + 38.7 + 40.1 + 42.3 + 34.3 + 36.2 + 38.1 + 39.0 + 40.6 + 42.9 + 34.5 + 37.4 + 38.3 + 39.4 + 41.4 + 43.4 + 35.3 + 37.6 + 38.5 + 39.7 + 41.7 + 48.9 = 934.7
Formula for mean is;
μ = ΣX/n
μ = 934.7/24
μ = 38.95
Formula for sample standard deviation of is;
s = √[(1/(n - 1))Σ(X - μ)²]
From online calculator, we have a value of;
s = 3.505
A) Formula for z-score is;
Z = (x - μ)/s
We are given x = 38.1
Thus;
Z = (38.1 - 38.95)/3.505
Z = -0.24
We can interpret this as the z-score corresponding to the individual who obtained 38. 1 miles per gallon is -0.24.
B) Arranging the set of given values in ascending order, we have;
32.7, 34.3, 34.5, 35.3, 35.7, 36.2, 37.4, 37.6, 38.0, 38.1, 38.3, 38.5, 38.7, 39.0, 39.4, 39.7, 40.1, 40.6, 41.4, 41.7, 42.3, 42.9, 43.4, 48.9
Number of data; n = 24
First quartile is;
Q1 = ((n + 1)/4)th = ((24 + 1)/4)th = 25/4 = 6.25th term
Thus, we will find the average of the 6th and 7th term;
Q1 = (36.2 + 37.4)/2
Q1 = 36.8
Similarly;
Q3 = ¾(n + 1)th = ¾(24 + 1)
Q3 = ¾ × 25 = 18.75th term
Thus, we will find the average of the 18th and 19th term.
Q3 = (40.6 + 41.4)/2
Q3 = 41
C) Formula for inter quartile range is;
IQR = Q3 - Q1
IQR = 41 - 36.8
IQR = 4.2
This means that the distance between the first and third quartile is 4.2
D) Formula for lower fence is;
LF = Q1 - (1.5 × IQR)
LF = 36.8 - (1.5 × 4.2)
LF = 30.5
Formula for upper fence is;
UF = Q3 + (1.5 × IQR)
UF = 41 + (1.5 × 4.2)
UF = 47.3
Now, an outlier will be any values in the given set less than LF or more than UF.
From the given set, the only outlier is 48.9 which is more than UF
The sum of two numbers is 47. The greater number is 9 more than the smaller number. Which equation can be used to solve for the smaller number? x + (x + 9) = 47 x − (x + 9) = 47 x(x + 9) = 47 x(x − 9) = 47
I believe the correct answer from the choices listed above is the first option. The equation that can be used to solve the problem would be x + (x + 9) = 47.
The sum of two numbers is 47. ---> x + y = 47 where x is the smaller number and y is the larger.
The greater number is 9 more than the smaller number. -----> y = x + 9
x + ( x + 9 ) = 47
Answer:
x + (x + 9) = 47
Step-by-step explanation:
This equation can be used to solve for
This equation can be used to solve forthe smaller number.
Here is a list of numbers 15 6 8 7 12 1 5 8 4 3 state the median
Answer:
The median is 6.5
The sum of three times a number (2) and -23 is 28.
Answer:
x = 17
Step-by-step explanation:
3x + -23 = 28
3x - 23 = 28
3x = 28 + 23
3x = 51
x = 51/3
x = 17
ANSWER ASAP GIVING BRAINLIEST!
A chemical reaction in a light stick causes it to give off a glowing green light. Explain why the reaction is endothermic or exothermic.
Answer:
The chemical reaction is due to chemical change in the chemicals within the light stick so it shows off color.
Step-by-step explanation:
The chemicals in the light stick interact with each other. This cause them to come together and give off a color of light.