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
when you apply combine like terms to the right side of the equation what do you end up with?
Answers
Since the first term and the last term, 6x and -5x are like terms you add them. 6 plus -5 is one. In this case it would be x.(it is not necessary to put 1 in front of the x). And 7 is positive and it is the only term left by itself.
A number n minus 3 is at least –5.
Answers
Answer:
n-3≥-5
If you need the equation solved...
n-3≥-5
+3 +3
n≥-2
Hope this helped!! Have a great day c:
I need help with 9and 10 pleas
Answers
10 is either a or b
Write the equation in vertex form using the following information: vertex (4, -6) and a=1.
Submit
Answers
Answer:
y = (x - 4)² - 6Step-by-step explanation:
An equation of a quadratic function in a vertex form is y=a(x-h)²+k, where vertex is (h, k)
vertex (4, -6) means h = 4 and k = - 6
So:
y = 1(x - 4)² + (-6)
y = (x - 4)² - 6
Select each set of points that are colinear.
Answers
Answer:
friend, a points are collinear
Answer:
points K and R are colinear
Step-by-step explanation:
help asap please click the image to find the question
Answers
Answer:33
Step-by-step explanation: You do what's inside the parenthesis first then you divide the number by 6 and lastly you add 5squared which is 25 to the quotient.
Solve the inequality below.
4(x + 3) < 6x – 2
Answers
Answer:
X > 7
Step-by-step explanation:
4(x + 3) < 6x – 2
4x + 12 < 6x -2
-6x -6x
-2x + 12 < -2
-12 -12
-2x < -14
----- -----
-2 -2
x > 7
The < change because it was divided by a negative number
8. PLS ANSWER!!!!
and show work
Answers
Answer:
The equation of the parallel line is y = 5x + 11
Step-by-step explanation:
→ Parallel lines have same slopes and different y-intercepts
→ The slope-intercept form of the linear equation is y = m x + b, where
m is the slopeb is the y-interceptIn our question
∵ The equation of the given line is y = 5x + 2
→ Compare it with the form above to find its slope
∴ m = 5
∵ The two lines are parallel
∴ Their slopes are equal
∴ The slope of the parallel line is 5
→ Substitute it in the form of the equation above
∴ y = 5x + b
→ To find the value of b substitute x and y in the equation by the
coordinates of any point on the line
∵ The line passes through point (-2, 1)
∴ x = -2 and y = 1
∵ 1 = 5(-2) + b
∴ 1 = -10 + b
→ Add 10 to both sides
∴ 1 + 10 = -10 + 10 + b
∴ 11 = b
→ Substitute value of b in the equation
∴ y = 5x + 11
∴ The equation of the parallel line is y = 5x + 11
If a system of linear equations has the unique solution (2, -3), then its graph consists of what?
•parallel lines
•lines that intersect at a single point
•identical lines
•a y-intercept at -3
Answers
Answer: B - lines that intersect at a single point
Step-by-step explanation: Just took a test
Mandy makes cupcakes, she uses 8 3/4 cups of flour for 12 cupcakes. How many cups of flour are needed to make 1 cupcake? Explain how you found each amount.
Answers
Answer:
Step-by-step explanation:
.75=3/4
8.75 cups divided by 12 cupcakes = .73 (rounded up) cups of flour per cupcake
please help! i would appreciate it!
Answers
Answer:
(Answer
Step-by-step explanation:
deleted)
Write an equation in slope-intercept form of the line that passes through the given point and is perpendicular to the graph of the given equation.
(-5,8); y=1/5x-3
Answers
Answer:
y = –5x – 17
Step-by-step explanation:
First, we shall determine the slope of the equation y = 1/5x – 3.
The slope of the equation y = 1/5x – 3 can be obtained by comparing the equation with y = mx + c.
This is illustrated below:
y = 1/5x – 3
y = mx + c
Thus, the slope (m) of equation
y = 1/5x – 3 is 1/5
Next, we shall determine the slope of the line perpendicular to the equation as follow:
For perpendicular lines, their slope (m1 and m2) are related as follow:
m1 × m2 = –1
m1 = 1/5
1/5 × m2 = –1
m2/5 = –1
Cross multiply
m2 = 5 × –1
m2 = –5
Therefore, the slope of the line is –5.
Finally, we shall determine the equation of the line as follow:
Coordinate = (–5, 8)
x1 coordinate = –5
y1 coordinate = 8
Slope (m) = –5
y – y1 = m(x –x1)
y – 8 = –5(x – (–5))
y – 8 = –5(x + 5)
y – 8 = –5x – 25
Rearrange
y = –5x – 25 + 8
y = –5x – 17
Therefore, the equation is y = –5x – 17.
Is Mr. Martin a hero? xplain why or why not.
Answers
Answer:
mr martin was a hero in my eyes he saved many lives and was one of the strongest people to ever live (who is mr martin?)
Step-by-step explanation:
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.
Which pair of quantities form a proportional relationship? Select all that apply
Answers
Answer:
The 4th and 6th
Step-by-step explanation:
Which table represents a linear function?
answers are in the picture plz help im timed
Answers
Answer: first table
Step-by-step explanation: go with the first one
Ignore a and b but can you help with c and d? Plz I’ll mark you as a brainiest
Answers
140+2x=180
2x=40
x=20
C: 2x+20=60
2x=40
x=20
D: 3x+10=100
3x=90
x=30
1.What is the standard form of a linear equation?
A.x+y=0
B.y= MX+b
C. m=rise/run
D. ax +By=C
2.Which term could be used to describe the graph of a line on a coordinate plane?
A. independent variable
B. test points
C. set of all solutions
D. dependent variable
3.Explain whether the points (−13,4), (−7,3), (−1,2), (5,1), (11,0), (17,−1) represent the set of all the solutions for the equation y=−1/6x+11/6.
A.Yes, because all the solutions of y=−1/6x+11/6 need to be integer values for x and y.
B.No, because the point (17,−1) is not on the line that represents the equation y=−1/6x+11/6.
C.No, because the set of all solutions of y=−1/6x+11/6 is represented by the line of the equation.
D. Yes, because all of the points that are listed are on the line y=−1/6x+11/6.
Answer them all in one answer please and thank you.
Answers
Answer:
1. D
sorry I know only first one
Solve the following equation
5(3x+5)=3(5x+1)
Answers
Answer:
No solutions
Step-by-step explanation:
Let's solve your equation step-by-step.
5(3x+5)=3(5x+1)
Step 1: Simplify both sides of the equation.
5(3x+5)=3(5x+1)
(5)(3x)+(5)(5)=(3)(5x)+(3)(1)(Distribute)
15x+25=15x+3
Step 2: Subtract 15x from both sides.
15x+25−15x=15x+3−15x
25=3
Step 3: Subtract 25 from both sides.
25−25=3−25
0=−22
Answer:
There are no solutions.
Hmmmmmmmmmmmmmmm?????????
Answers
Answer:whats the question?????
Step-by-step explanation:
√12
A. 2√5
B. 2√3
Which one?
Answers
Answer:
B. [tex]2\sqrt{3}[/tex]
Hope this helps!
Answer:
B.2√3
Explanation:
√2^2×√3
√2^2√3
2√3
Please help I’m not sure what it is don’t make fun I’m not good at math
Answers
Answer:
3.75 or 3[tex]\frac{3}{4}[/tex]
Step-by-step explanation:
The first thing we can find is the scale factor of the two triangles. You can see that the corresponding sides AB and A'B' are 2 and 8 respectively, and since the two triangles are similar, you can say that triangle ABC is shrunk by a factor of 2/8 or 1/4.
Next, we need to figure out what side B'C' is and we can do this using the Pythagorean theorem [tex]a^{2}[/tex]+[tex]b^{2}[/tex] = [tex]c^{2}[/tex]. Using this, we know that [tex]8^{2}[/tex]+
Now, since ABC is shrunk by 1/4 and the corresponding side of BC is equal to 15, we need to multiply 15 by 1/4 and you would find that BC is 3.75 or 3[tex]\frac{3}{4}[/tex].
A car travels 43 km in 56 minutes.
What is its average speed in km/h?
Give your answer rounded to 1 decimal place.
Answers
Answer:
[tex]\displaystyle v=46.07\ Km/h[/tex]
Step-by-step explanation:
Speed
The speed is the ratio between the distance x traveled by an object and the time t taken.
[tex]\displaystyle v=\frac{x}{t}[/tex]
The car travels x=43 Km in t=56 minutes. We are required to express the speed in Km/h. The time needs to be expressed in hours:
[tex]t = 56 / 60 = 0.933\ h[/tex]
Now apply the formula:
[tex]\boxed{\displaystyle v=\frac{43}{0.933}=46.07\ Km/h}[/tex]
Classify the system of equations.
2x = 5 - y
-3+y = -2x + 3
Click on the correct answer.
coincident
intersecting
parallel
Answers
Answer:
Parallel
Step-by-step explanation:
What is the length of c on the graph below?
6
10
8
14
Answers
Answer:
10 is the answer to the question
How many lines of symmetry, does this quadrilateral have
Answers
Answer:
im going to say 4 hope it helps
Step-by-step explanation:
Please answerrr!!! (don’t answer if you don’t know it) will give brainliest
Answers
evaluate = (√5+2√6) + (√8-√2√15)
Answers
Answer: 2√2 + 3√8 = 2√2 + 6√2 = 8√2 , because we simplified √8 = √(4 * 2)
Answer:
[tex]\sqrt{5}+2\sqrt{6} + 2\sqrt{2} - \sqrt{30} \approx 4.5[/tex]
Step-by-step explanation:
[tex](\sqrt{5}+2\sqrt{6} ) + (\sqrt{8} - \sqrt{2} \cdot \sqrt{15} )[/tex]
[tex](\sqrt{5}+2\sqrt{6} ) + (\sqrt{8} - \sqrt{30} )[/tex]
[tex](\sqrt{5}+2\sqrt{6} ) + (2\sqrt{2} - \sqrt{30} )[/tex]
[tex]\sqrt{5}+2\sqrt{6} + 2\sqrt{2} - \sqrt{30} \approx 4.5[/tex]
Simplify this equation (3√2)²
Answers
Answer:
18
Step-by-step explanation:
simplify the following
Answers
Answer:
D. 64 z^ 2
Step-by-step explanation:
Simplify the expression.