Which values of x and y would make the following expression represent a real number? (4+5i)(x+ yi)
Ox=4,y= 5
Ox=-4, y = 0
Ox=4, y=-5
Ox=0, y= 5
Answers
Answer:
C
Step-by-step explanation:
We have the expression [tex](4+5i)(x+yi)[/tex] and we want to find the values of [tex]x[/tex] and [tex]y[/tex] such that the expression will evaluate to a real number.
So, let's first expand the expression. Distribute:
[tex]=4(x+yi)+5i(x+yi)[/tex]
Distribute:
[tex]=4x+4yi+5xi+5yi^2[/tex]
Simplify:
[tex]=(4x-5y)+(4yi+5xi)[/tex]
So, we want to make the second part within the real numbers.
Notice that we only have two ways of doing this: 1) Either both [tex]x[/tex] and [tex]y[/tex] are imaginary numbers themselves canceling out the [tex]i[/tex], or 2), the entire expression equals 0.
Since our answer choices consists of only real numbers, this means that the imaginary part must be equal to 0. So:
[tex]4yi+5xi=0[/tex]
We can divide everything by [tex]i[/tex]:
[tex]4y+5x=0[/tex]
Now, we can use our answer choices.
Running down the list, we can see that the choice that works is C. If we substitute the values of C into the equation, we get:
[tex]4(-5)+5(4)=0\\\Rightarrow -20+20=0\stackrel{\checkmark}{=}0[/tex]
Therefore, our answer is C.
Answer:
c
Step-by-step explanation:
Related Questions
In January Mr Patel's electricity meter reading is 36 517. During the next three months he uses 1 084 units of electricity. a) What is the reading on his meter at the end of these three months? b) In Janurary Mr Patel'a gas meter reading is 51 314. Three months later it is 51 809. How many units of gas has he used? c) Electricity costs 12 pence per unit. Gas costs 8.6 pence per unit. Work out the total cost of Mr Patel's gas and electricity for these three months. Give your answer in pounds.
Answers
Answer: 172.65 pound
Step-by-step explanation:
a. What is the reading on his meter at the end of these three months?
January's electricity meter reading = 36,517.
Electricity used for next three months = 1 084 units
Meter reading at the end of the three months will be:
= 36517 + 1084
= 37601
b. In Janurary Mr Patel'a gas meter reading is 51 314. Three months later it is 51 809. How many units of gas has he used?
This will be:
= 51,809 - 51,314
= 495 units
c. Electricity costs 12 pence per unit. Gas costs 8.6 pence per unit. Work out the total cost of Mr Patel's gas and electricity for these three months.
Electricity used for next three months = 1 084 units
Gas used for next three months
= 495 units
Cost = (1084 × 12pence) + (495 × 8.6 pence)
= 13008 pence + 4257 pence
= 17265 pence = 172.65 pound
misty is driving on a scenic road trip, and the graph shows the number of hours traveled compared to the number of miles of the trip remaining. Use the graph below to the answer.
Write an equation of the graph in slope-intercept form.
A. y=-100/3x+450
B. y=100/3x-450
C. y=450x+100/3
Answers
Answer:
omg im finding the answer too i go to bcms i see the travid isd thing on ur tabs
Step-by-step explanation:
Answer:
Option A. y=-100/3x+450 is correct.
Step-by-step explanation:
PLEASE HELP. Select the two roots of (3x+7)(2x-5)=0
Answers
Answer:
-7/3 & 5/2
Step-by-step explanation:
3x +7 = 0
3x = -7
x = -7/3
2x-5=0
2x = 5
X = 5/2
find three points that solve the equation then plot on the graph -x-2y=8
Answers
i gotchu: (-8,0) (0,-4) (4,-6)
Answer:
(-8,0) (0,-4) (4,-6)
Step-by-step explanation:
Is this a function? Explain
Answers
Answer:
Yes
Step-by-step explanation:
The only reason a graph will not be a function is if it doesn't pass the vertical line test. In other words, if you draw a vertical line at any point, it will never pass through more than 1 point.
In that case, that is true, so it must be a function.
m= -(4+ m) + 2
m=
what’s m?
Answers
Answer:
m = -1
Step-by-step explanation:
m= -(4+ m) + 2
Distribute
m = -4-m+2
m = -2-m
Add m to each side
m+m = -2-m+m
2m = -2
2m/2 = -2/2
m = -1
need help!! 40 points !!
The triangles shown below must be congruent.
Answers
Answer:
The question asks if they must be congruent, so the answer is false
Step-by-step explanation:
All the angles are equal
47 = 47
62=62
71=71
The side between the 62 and 71 equals 7 on the left, we are not given the side between the 62 and the 71 on the right so we do not know if the triangles are congruent. We need to have one of the sides be equal for the triangles to be congruent.
The question asks if they must be congruent, so the answer is false
Answer:
FALSE
Step-by-step explanation:
ap3x
does anyone know this
Answers
Answer:
A
Step-by-step explanation:
when you open the brackets you do 5 to the power of 5 and X to the power of 5
Can someone help me with this I really need help
Answers
Answer:
B.) x > -1 and x ≤ 4
Step-by-step explanation:
Hope this helps!
45 + 15(n − 1) for n = 6
Answers
Answer:
120
Step-by-step explanation:
Answer:
120
Step-by-step explanation:
Plug in what you know so: 45+15(6-1)
So, following the order of operations, you do the parentheses first so: 45+15(5)
Then, still following the order of operations, you'd multiply from left to right. So: 45+75
Then, you add from left to right, so you get 45+75=120
Your answer is 120.
In the picture lines AB and CD are parallel. Find the measures of ∠ECF.
Answers
Answer:
If the other angle measurment is 38° then angle EFC will be 142° ( 180-38= 142°)
Step-by-step explanation:
g(x) = -4(x + 3)(4x - 2)
Answers
which of the equation is graphed below
A.) y=1/4x+1
B.) y=-1/4x+1
C.) y=4x+1
D.) y=-4x+1
Answers
How many solutions does the equation 4x +2(x-5)=3(2x-4) have?
Answers
Answer:
no solutions
Step-by-step explanation:
Given
4x + 2(x - 5) = 3(2x - 4) ← distribute parenthesis on both sides
4x + 2x - 10 = 6x - 12
6x - 10 = 6x - 12 ( add 10 to both sides )
6x = 6x - 2 ( subtract 6x from both sides )
0 = - 2 ← not possible
This indicates the equation has no solution
I need your help with my hw!
Answers
Answer:
-4
Step-by-step explanation:
f(x) = 3(x) so....
3(-2) + 2
-6 + 2
-4
Nicole babysits on the weekends. She charges a flat fee of $10 and then $5 per hour. If she made $40 on Friday night, how many hours did she babysit?
Choose the equation to represent this situation.
Group of answer choices
Answers
L.B. Johnson Middle School held a track and field event during the school year. The chess club sold various drink and snack items for the participants and the audience. All together, they sold items 486that totaled .$2,673a.If the chess club sold each item for the same price, calculate the price of each item.
Answers
Answer:
$5.50
Step-by-step explanation:
L.B Johnson middle school held a track and field event
The chess club sold different drinks and snack item for both the audience and participants
They sold 486 items at a total of $2,673
Therefore the price of each item can be calculated as follows
= 2673/486
= 5.50
Hence the price of each item is $5.50
Differentiate the function.
h(x) = e^x^9+In(x)
Answers
Answer:
h'(x)= [tex]e^{x^{9}+In(x) } (9x^{8} +\frac{1}{x} )[/tex]
Step-by-step explanation:
h(x)=[tex]e^{x^{9} +In(x)}[/tex]
first, we will use the chain rule
step1: we divide the function into two parts So,
f(x)=[tex]e^{x^{9} +In(x)}[/tex] and g(x)=[tex]x^{9} +In(x)[/tex]
step2: rewrite [tex]x^{9} +In(x)[/tex] as u.
f(x)=[tex]e^{u}[/tex] and g(x)=u
step3: differentiate f(x) first.
f'(x)=[tex]e^{u}[/tex] (the formula is y=[tex]e^{x}[/tex] and y'=[tex]e^{x}[/tex] - the same)
step4: write the value of u for each function but now sub it in the differentiable form of f(x).
f'(x)=[tex]e^{x^{9}+In(x) }[/tex] and g(x)=[tex]x^{9}+In(x)[/tex]
step5: differentiate the function g(x).
g'(x)=[tex]9x^{8} +\frac{1}{x}[/tex]
(for [tex]x^{9}[/tex] the formula is y=[tex]x^{n}[/tex] and y'=[tex]nx^{n-1}[/tex] ) (for In(x) the formula is y=In(x) and y'=[tex]\frac{1}{x}[/tex] )
step6: use the chain rule to finish out So,
h'(x)=f'(x) × g'(x)
=[tex]e^{x^{9}+In(x) }[/tex] × [tex]9x^{8}+\frac{1}{x}[/tex]
step7: simplify.
h'(x)= [tex]e^{x^{9} +In(x)}(9x^{8}+\frac{1}{x})[/tex]
What is the range of a set of data. A. The middle number. B. The average of the data. C. The difference in the largest value from the smallest value. D. The largest value of the data
Answers
Answer:c
Step-by-step explanation:the difference between the largest and smallest is the range ...all the possible answers would be included in the range
Approximate the value of the positive square root of 110 to the nearest hundredth
Answers
i need help on this.
Answers
The TCMS Mustangs played the GCF Grizzlies. On the opening kickoff the ball traveled 35 yds. The running back ran for 17 yards on the next play. The quarterback was sacked for a loss of 5 yds. The next 3 plays had a gain of 4 yards per play. What was the total change in the position of the ball on the field?
Answers
Answer: The total change in the position of the ball on the field =24 yards
Step-by-step explanation:
According to integers, every loss is represented by negative integers and every gain is represented by positive integers.
As per given total run = 35+17-5+3(4)
= 59 yards
Change in position = 59 yards - 35 yards
= 24 yards
Hence, the total change in the position of the ball on the field =24 yards
What is the solution of 8 + a = 13? Justify each step. A. The steps are: (1) 8 + a = 13 (2) 8 + 8 + a = 13 + 8 (3) a = 21 The reasons are: (1) original equation (2) Addition Property of Equality (3) Simplify. B. The steps are: (1) 8 + a = 13 (2) 8 − 8 + a = 13 (3) a = 13 The reasons are: (1) original equation (2) Subtraction Property of Equality (3) Simplify. C. The steps are: (1) 8 + a = 13 (2) 8 − 8 + a = 13 − 8 (3) a = 5 The reasons are: (1) original equation (2) Subtraction Property of Equality (3) Simplify. D. The steps are: (1) 8 + a = 13 (2) 88+a=138 (3) a = 1.63 The reasons are: (1) original equation (2) Division Property of Equality (3) Simplify.
Answers
Answer:
C. The steps are: (1) 8 + a = 13 (2) 8 − 8 + a = 13 − 8 (3) a = 5 The reasons are: (1) original equation (2) Subtraction Property of Equality (3) Simplify.
Step-by-step explanation:
8 + a = 13 (original Equation)
Subtract 8 from both sides
8 + a - 8 = 13 - 8 ( subtraction property of equality
a = 5 (Simplify)
The correct answer is option C
C. The steps are: (1) 8 + a = 13 (2) 8 − 8 + a = 13 − 8 (3) a = 5 The reasons are: (1) original equation (2) Subtraction Property of Equality (3) Simplify.
the temperatue dropped 4C every hour for 8 hours what was the total number of degrees the temperature changed in 8 hours
Answers
Mrs. Sing invest $12,876 for her business at an annual interest rate of 7 percent for 3 years. Which number will mrs. sing substitute for r in the simple interest formula?
Answers
Answer:
The number that she will substitute is 7
Step-by-step explanation:
Mathematically, simple interest can be calculated using the formula ;
S.I = PRT/100
where P is the principal which is the amount invested = $12,876
T is the time which is 3 years
and R is the rate which is 7%
Answer:
Answer:
The number that she will substitute is 7
Step-by-step explanation:
i just took he test
Whoever can help me 1st I will mark the brain liest
Answers
A is 163 and C is 143
Joe is making a recipe that calls for 4 teaspoon of cinnamon. His only measuring spoon only holds 8 teaspoon. How many times will he need to fill his
measuring spoon to get enough cinnamon for the recipe?
Answers
Answer:
1/2
Step-by-step explanation:
because he will need to fill the 8 teaspoon half way
The parallel lines have ---------------- slope.
A. negative reciprocal
B. complementary
C. equivalent
D. opposite
Answers
Answer:
equivalent
Step-by-step explanation:
equivalent because they have to be the same and not intersecting with eachother♡ Hope it helps ;)
х+5y = 3
3х - 2y = -8
Answers
Subtract 5y from both sides: x=3−5y
Substitute
x=3−5y into 3x−2y=−8
Start with the original equation: 3x−2y=−8
Let x=3−5y: 3(3−5y)−2y=−8
Simplify: 9−17y=−8
Solve for y in 9−17y=−8: y=1
Substitute y=1 into , x=3−5y : x=-2
X=-2
Y=1
A 34-year-old woman has a maximum heart rate of 175 bpm. She plans an exercise program so that her heart rate will be between 80% and 90% of her maximum heart rate for at least 30 minutes a day, 3 days a week. Calculate the desired range of heart beats per minute for this exercise program
Answers
Answer:
The desired range is from 141 bpm to 157 bpm
Step-by-step explanation:
Given that the maximum heart rate = 175 bpm.
She plans an exercise program to reach the desired heart rate which is in the range of 80% and 90% of the maximum heart rate.
So, the lower limit of the desired heart rate = 80% of the maximum heart rate
=\frac{80}{100}\times 175= 140 bpm
and the upper limit of the desired heart rate = 90% of the maximum heart rate
=\frac{90}{100}\times 175= 157.5 bpm
So, mathematically, the desired range is between 140 bpm and 157.5 bpm.
The heart-beats per minute should be a counting number, so, round the upper limit to the lower integral value to be within the range.
Hence, the desired range is from 141 bpm to 157 bpm.