Answer:
[tex]4-i[/tex]
Step-by-step explanation:
Use the formula for the distance of a complex number from the origin on the complex plane.
[tex]\sqrt{a^2+b^2}[/tex]
[tex]a+bi[/tex]
[tex]4-i[/tex]
[tex]\sqrt{4^2-i^2}[/tex]
[tex]\sqrt{4^2+(-1)^2}=\sqrt{16+1}=\sqrt{17}[/tex]
The complex number that has a distance of [tex]\sqrt{17}[/tex] is [tex]4-i[/tex].
By Pythagorean theorem the complex number 4 - i has a distance from the origin to its location of [tex]\sqrt{17}[/tex] units on the complex plane. (Correct choice: D)
How to determine the distance of a complex numberComplex numbers are a generalization from real numbers, whose expression are of the form a + i b, where a and b are the components of the real and imaginary components, respectively. The magnitude of complex numbers is determined by Pythagorean theorem, this is, the distance from the origin to the location of the number on the complex plane:
[tex]r = \sqrt{a^{2}+b^{2}}[/tex]
If we know that a = 4 and b = -1, then the magnitude of the complex number is:
[tex]r = \sqrt{4^{2}+(-1)^{2}}[/tex]
[tex]r = \sqrt{17}[/tex]
By Pythagorean theorem the complex number 4 - i has a distance from the origin to its location of [tex]\sqrt{17}[/tex] units on the complex plane. (Correct choice: D)
RemarkThe statement presents several typing mistakes, correct form is shown below:
Which complex number has a distance of [tex]\sqrt{17}[/tex] from the origin on the complex plane?
A. 2 + i 15
B. 17 + i
C. 20 - i 3
D. 4 - i
To learn more on complex numbers, we kindly invite to check this verified question: https://brainly.com/question/10251853 #SPJ5
Mrs. Schroeder, a school principal, drove her own car for a class trip, taking a different route. The principal’s car can travel 32 miles per gallon of gas, and it used 12 gallons for the trip. How many miles did the principal drive? ____miles
Answer: 384 miles
Step-by-step explanation:
From the question, Mrs. Schroeder, a school principal, drove her own car for a class trip, by taking a different route and we are told that the principal’s car can travel 32 miles per gallon of gas, and it used 12 gallons for the trip.
Since it used 1 gallon of gas for 32 miles, 12 gallons will be for:
= 32miles × 12
= 384 miles
The principal drove for 384 miles.
Help me please........
Answer:
A
Step-by-step explanation:
By the Pythagorean Theorem, you know that:
[tex]2^2+5^2=c^2[/tex]
Therefore, the correct answer is choice A. Hope this helps!
Answer: choice A
Step-by-step explanation:
Based on the pythagorean theorem which states
[tex]a^{2} +b^{2} =c^{2}[/tex]
c being the hypotenuse
so 2^2+5^2=c^2
and c would equal [tex]\sqrt{29}[/tex]
climate scientists use computer models to predict the likely change in global average temperature under various assumptions about CO2 production. What type of data source is this?
Answer:
[tex]\fbox{\begin{minipage}{10em}Option A: Simulation \end{minipage}}[/tex]
Step-by-step explanation:
The data is not collected from the world outside, but a computer.
=> The data can be generated under assumption from simulation only.
=> Option A is correct.
Hope this helps!
:)
Answer:
a. Simulation
Step-by-step explanation:
A computer model is generally a simulation of the real world. Certainly, a model of Earth's climate is a simulation.
__
In some cases, the data of interest is the performance of the computer itself (as opposed to some system outside the computer). In those cases, the running of the computer under different scenarios might be considered an experiment.
Jonathan bought a table and some chairs and a furniture store. The equation that models the situation is Y equals 25X +80, where why is the amount of money he spends and X is the number of chairs he bought. What does the Y intercept mean in the situation?
Answer:
Step-by-step explanation:
The equation modeling the situation is ;
y = 25x + 80
We want to know what the y-intercept mean in this question
Mathematically, the equation of a straight line is ;
y = mx + c
where c is the y intercept and m is the slope
What we should understand is that at the y intercept which is 80 here, the value of x is 0
Now since y means the amount of money spent and x is number of chairs bought, the value 80 means that the amount spent when he bought 0 number of chairs is 80
Now going by the question, since he bought 0 chairs here and we still have some cost, definitely he spent the money on other things which of course might be the amount spent in purchasing some tables
Find the distance between (-3, 3) and (-3, -3).
Answer:
6
Step-by-step explanation:
Since the x coordinate is the same, we only have to look at the y coordinate
3 - -3 = 3 +3 = 6
The distance is 6
Answer:
6
Step-by-step explanation:
Notice that x does not change. We do go from y = -3 to y = 3, so the distance between these two y-values is 3 - (-3) = 6
You are playing a game in which each player wins, loses, or draws (ties) at each turn. For each turn won, you are awarded 5 points. If you lose the turn, you lose 5 points. If it is a draw, you get 0 points. For the first dozen rounds, you had the following results: win, win, draw, win, lose, lose, win, lose, draw, lose, lose, lose. What was your point total for the rounds?
Answer:
-10 because you lost twice more than you won.
Hope this helps!
the straight line L has the equation 4y=5x+3. Point A has the coordinates (3,-2) Find the equation of the line straight line that is perpendicular to L and passes through A. Write your answer in the form y-mx+c where m and c are decimals or fractions {3 marks}
Answer:
y = - [tex]\frac{4}{5}[/tex] x + [tex]\frac{2}{5}[/tex]
Step-by-step explanation:
The equation of a line in slope- intercept form is
y = mx + c ( m is the slope and c the y- intercept )
Rearrange 4y = 5x + 3 into this form by dividing the 3 terms by 4
y = [tex]\frac{5}{4}[/tex] x + [tex]\frac{3}{4}[/tex] ← in slope- intercept form
with slope m = [tex]\frac{5}{4}[/tex]
Given a line with slope m then the slope of a line perpendicular to it is
[tex]m_{perpendicular}[/tex] = - [tex]\frac{1}{m}[/tex] = - [tex]\frac{1}{\frac{5}{4} }[/tex] = - [tex]\frac{4}{5}[/tex] , thus
y = - [tex]\frac{4}{5}[/tex] x + c ← is the partial equation
To find c substitute (3, - 2) into the partial equation
- 2 = - [tex]\frac{12}{5}[/tex] + c ⇒ c = - 2 + [tex]\frac{12}{5}[/tex] = [tex]\frac{2}{5}[/tex]
y = - [tex]\frac{4}{5}[/tex] x + [tex]\frac{2}{5}[/tex] ← equation of perpendicular line
What is the completely factored form of x3 – 64x?
Answer:
x( x-8)(x+8)
Step-by-step explanation:
x^3 - 64x
Factor out an x
x( x^2 -64)
This is the difference of squares x^2 -8^2 which is a^2 - b^2 = (a-b)(a+b)
x( x-8)(x+8)
Answer:
[tex]x(x - 8)(x + 8)[/tex]
Step-by-step explanation:
[tex] {x}^{3} - 64x \\ x( {x}^{2} - 64) \\ x( {x}^{2} - {8}^{2} ) \\ = x(x - 8)(x + 8)[/tex]
hope this helps
brainliest appreciated
good luck! have a nice day!
If f(x) = x³ - 2, find f(3).
Answer:
25
Step-by-step explanation:
[tex]f(x)=x^3-2 \\\\f(3)=(3)^3-2= \\\\27-2= \\\\25[/tex]
Hope this helps!
Answer: 25
Explanation: Notice that f is a function of x. So we want to find f(3).
We find f(3) by plugging 3 in for x everywhere
that x appears in the function.
So we have (3)³ - 2.
(3)³ is equal to 3 × 3 × 3 or 27.
So we have 27 - 2 which is 25.
So f(3) is equal to 25.
What is 2x^2-13x+15?
Answer:
Step-by-step explanation:
Answer:
[tex] (2x - 3)(x - 5) \\ [/tex]
Step-by-step explanation:
[tex]2 {x}^{2} - 13x + 15 \\ 2 {x}^{2} - 10x - 3x + 15 \\ 2x(x - 5) - 3(x - 5) \\ (2x - 3)(x - 5)[/tex]
hope this helps you.
brainliest appreciated
good luck! have a nice day!
Solve -2/3x > 8 or -2/3x -12 or x -6} 3. {x | -12 < x < -6}
The Wild Dogs and the Rattlers also have membership programs for their fans. The Wild Dogs program has an initial fee of $20 and a discounted single-game ticket price of $1.50. The Rattlers program has an initial fee of $14 and a discounted ticket price of $2.25 per game. Which linear equation represents the Wild Dogs program? Let x represent the number of games and y the total c
Answer:
b y=1.5x+20
Step-by-step explanation:
JUST DID IT ON ENDGE 2021
The equation for Wild Dogs program is y = 20 + 1.5x.
What are Linear Equations in Two Variables?The equations with one, zero, or an infinite number of solutions are known as linear equations with two variables. Each of the two variables in these equations has the largest exponent order of 1. A two-variable linear equation has the conventional form axe + by + c = 0, where x and y are the two variables. The answers can also be expressed as ordered pairs, such as (x, y). Two straight lines, which could be intersecting, parallel, or coincident, are included in the graphic representation of the system of linear equations in two variables.
Given membership program for Wild Dogs and the Rattlers,
for Wild Dogs,
initial fee = $20
ticket price per game = $1.50
for Rattlers
initial fee = $14
ticket price per game = $2.25
linear equation for Wild Dogs program,
Let x represent the number of games and y the total
y = 20 + 1.5x
for Rattlers
y = 14 + 2.25x
Hence the equation for Wild Dogs program, is y = 20 + 1.5x.
Learn more about Linear Equations in Two Variables;
https://brainly.com/question/24085666
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Which equation is equivalent to 4 x = t + 2
Answer:
Its supposed to be x = s
like its in the picture
So we divide both sides by 4
we get t+2 / 4
That means the answer is C
Answer:
the correct answer for this question is c. s= t+2/4
source. edge.
I need help,please as fast as possible
Evaluate and Solve 6x + 4 > 7
Answer:
x>1/2
Step-by-step explanation:
6x>3
x>1/2
Answer:
X>1/2
Step-by-step explanation:
6x + 4> 7
-4 on each side
6x > 3
Divide 6 on each side
X>1/2
Hope this helps plz mark brainliest!
500 / 500 equals what 97 points and brainliest answer ASAP if possible
Answer:
1
Step-by-step explanation:
500/500=1
x / x = 1
Answer:
The answer is 1.Step-by-step explanation:
This is because when you divide a number with each other then they cancel out to equal 1. This can happen with the letter x. So, x/x = 1.
Going back to the question 500/500 can cancel out to become 1.
Simplify
4a x 6a
8a?
Answer:
[tex]=24a^2[/tex]
Step-by-step explanation:
[tex]4a\cdot \:6a=24a^2\\\mathrm{Multiply\:the\:numbers:}\:4\cdot \:6=24\\=24aa\\\mathrm{Apply\:exponent\:rule}:\quad \:a^b\cdot \:a^c=a^{b+c}\\aa=\:a^{1+1}\\=24a^{1+1}\\=24a^2[/tex]
Answer:
Simply multiply across.
since they both have the same base(a),add the powers ie.(1+1)=2.
Hence 4a×6a=24a²
What steps should be taken to complete the conversion? StartFraction 8 miles Over 1 EndFraction times StartFraction 1.61 kilometers Over 1 mile EndFraction times StartFraction 1000 meters Over 1 kilometer EndFraction = blank
Answer:
See Explanation Below
Step-by-step explanation:
Given
[tex]\frac{8\ miles}{1} * \frac{1.61\ kilometres}{1\ mile} * \frac{1000\ metres}{1\ kilometer} =[/tex]
Required
What steps should be taken to complete the conversion?
The first step is to cancel out equal units;
Kilometre(s) will cancel out Kilometre(s)
Mile(s) will cancel out Miles
And we'll be left with metres
This is shown below
[tex]\frac{8\ miles}{1} * \frac{1.61\ kilometres}{1\ mile} * \frac{1000\ metres}{1\ kilometer} =[/tex]
[tex]\frac{8\ miles}{1\ mile} * \frac{1.61\ kilometres}{1\ kilometre} * \frac{1000\ metres}{1} =[/tex]
[tex]\frac{8}{1} * \frac{1.61}{1} * \frac{1000\ metres}{1} =[/tex]
The next step is to perform all multiplications
[tex]\frac{8 * 1.61 *1000\ metres}{1 * 1 * 1} =[/tex]
[tex]\frac{12,880\ metres}{1} =[/tex]
[tex]12,880\ metres[/tex]
Answer:
10 inches
Step-by-step explanation:
Find the area of the following trapezium:
26 cm
21 cm
33 cm
Write appropriate units with your answer.
Answer:
619.5cm2
Step-by-step explanation:
Based on what you defined as the parallel sides been 26cm and 33cm and the height been 21cm.
Hence the are of trapezium is half sum of the parallel sides × height.
Expressed mathematically we have:
1/2( 26 +33) × 21 = 1/2 ( 59) × 21 = (59×21)/2= 619.5cm2
HLPPPPPPPP MEEEEEEEEEEEEE PLZZZZZZZZZZZZ if d is the circumference of abc what is the measure of aex
Answer:
∠AEX = 70°
Step-by-step explanation:
From the diagram
AX ≅ BX
BY ≅ CY
AZ ≅ CZ
∠XAE = 20°
A circumcenter has equal distant from vertices of the triangle since radii of circles are congruent.
For the given figure, the midpoints is at Z, X, Y
And the perpendiculars also occur at Z, X, Y
∠Z = 90°
∠X = 90°
∠Y = 90°
∠XAE ∠AXE +∠AEX= 180° (sum of angles in a triangle)
∠AXE = ∠X = 90°
20° + 90° +∠AEX= 180°
110° +∠AEX= 180°
∠AEX = 180°-110°
∠AEX = 70°
I’ll mark you brainliest help!!! Which function is increasing?
Answer:
the answer is D. have a nice day :)
What is the remainder when (3x4 + 2x3 − x2 + 2x − 19) ÷ (x + 2)? (1 point) Select one: a. 0 b. 5 c. 10 d. 15
Answer: C. / 10
Step-by-step explanation:
Answer:
B
Step-by-step explanation:
Given a polynomial divided by a factor (x + h) then the remainder is f(- h)
Given
f(x) = 3[tex]x^{4}[/tex] + 2x³ - x² + 2x - 19 divided by (x + 2)
To find remainder evaluate f(- 2)
f(- 2) = 3[tex](-2)^{4}[/tex] + 2(- 2)³ - (- 2)² + 2(- 2) - 19
= 3(16) + 2(- 8) - 4 - 4 - 19
= 48 - 16 - 4 - 4 - 19
= 5 → B
Find the slope of the line that passes through (5, 9) and (2, 2).
Simplify your answer and write it as a proper fraction, improper fraction, or integer.
Answer:
bdudbrksowodndiwnsonsuendumdjdndoamslals
The right answer is 7/3
hope it helps
Good luck on your assignment
An angle measures 32° less than the measure of its supplementary angle. What is the
measure of each angle?
Answer:
Step-by-step explanation:
x+x-32=180
2x-32=180
2x=180+32
2x=212
x=106
x-32=>106-32=74
what is the meaning of the word 'coplanar'
Answer:
It means in the same plane
need help!!!!!!!!!!!!!!!!!!!!!!!
Answer:
3/5
Step-by-step explanation:
The sine of an angle is the length of the opposite side divided by the length of the hypotenuse. In this case, that is 6/10, which can be simplified to 3/5. Hope this helps!
6/10, or 3/5. (sine is opposite/hypotenuse)
Find the y-intercept of the following equation. Simplify your answer.
y = 4x + 4
y-intercept
Answer:
The slope is 4 and the y intercept is 4
(0,4)
Step-by-step explanation:
The equation is in the form
y = mx+b where m is the slope and b is the y intercept
y = 4x+4
The slope is 4 and the y intercept is 4
(0,4)
Can someone please help me :(
Answer:
Step-by-step explanation:
ok its AAS because if you see the most aperent thing on the trangle is that
Answer:
AAS
Step-by-step explanation:
The two triangles are congruent because they have two equal angles and one side
Pls help me. I need this done ASAP thank you :)
Answer:
[tex]\frac{5}{7}[/tex]
Step-by-step explanation:
So she has 14 shirts in all. There are 10 colored shirts.
[tex]\frac{10}{14} =\frac{5}{7}[/tex]
answer 5 /7
hi there are fourteen shirts and the more shirts the less of a possiblility
Step-by-step explanation:
if you want a percentage its 7.14 %
i hope i helped if you need help with any thing else please tell me :)
please mark as brainliest
Can anyone help solve this
Answer:
Step-by-step explanation:
The solution or solutions to a system are where the 2 graphs intersect each other. Our graph goes up by 2 units. The point of intersection on the left is at (-6, 8) and the point of intersection on the right is at (2, 0).
