Answer:
[tex] \frac{2 - 3i}{4 + 2i} = \frac{1 - 8i}{10} [/tex]
Step-by-step explanation:
To simplify an expression like this, we multiply top and ottom of the fraction (denominator and numerator) by the complex conjugate of the bottom (numerator). For a complex expression (a+bi), the complex conjugate is (a−bi). When we do the calculation, it will become clear why this works so well.
Note that (a−bi)/(a−bi) is just the same as 1, so when we do this multiplication the result is the same number we started with.
[tex] \frac{2 - 3i}{4 + 2i} = \frac{2 - 3i}{4 + 2i} \times \frac{4 - 2i}{4 - 2i } \\ = \frac{8 - 12i - 4i + 6 {i}^{2} }{16 + 8i - 8i - 4 {i}^{2} } \\ = \frac{8 - 16i + 6 {i}^{2} }{16 - 4 {i}^{2} } [/tex]
But
[tex] i = \sqrt{ - 1} \: so \: {i}^{2} = - 1 [/tex]
Using this and collecting like terms, we have:
[tex]\frac{8 - 16i + (6 \times - 1) }{16 - 4 ( - 1) } = \frac{2 - 16i}{20} = \frac{1 - 8i}{10} [/tex]
3. Yenny has (6m + 4) sweets. Maria has half as many sweets as Yenny.
Express the total number of sweets they have in its simplest form.
Ans:
Answer:
9m + 6
Step-by-step explanation:
Maria has half as many sweets as Yenny , that is
[tex]\frac{1}{2}[/tex] (6m + 4) ← multiply each term in the parenthesis by [tex]\frac{1}{2}[/tex]
= 3m + 2
Total sweets = 6m + 4 + 3m + 2 ← collect like terms
= 9m + 6
Write an equation of the line in fully simplified slope-intercept form.
Answer:
Equation is 4y = -3x + 12
Step-by-step explanation:
General equation of a line:
[tex]y = mx + c[/tex]
for the slope:
[tex]slope = \frac{y_{2} - y_{1} }{x _{2} - x_{1} } [/tex]
consider points: (4, 0) and (0, 3)
[tex]slope = \frac{3 - 0}{0 - 4} \\ \\ slope = - \frac{3}{4} [/tex]
for y-intercept, c :
[tex]y = mx + c[/tex]
consider point (0, 3):
[tex]3 = ( - \frac{3}{4} \times 0) + c \\ \\ c = 3 \\ c = 3[/tex]
Equation is:
[tex]y = - \frac{3}{4} x + 3 \\ \\ 4y = - 3x + 12[/tex]
pliss help me with this question
Answer:
1/32 people responded for Tampa.
Step-by-step explanation:
Find the value of x that will make A||B. Geometry
Answer:
x = 30
Step-by-step explanation:
These angles are supplementary which means they add up to 180:
2x + 50 + 5x - 80 = 180
7x - 30 = 180
7x = 180 + 30
7x = 210
x = 30
Help help help help help
Step-by-step explanation:
f(x) =14x+4
h(x)=7x
f(x)-h(x)=14x+4-7x
=7x+4
Note:if you need to ask any question please let me know.at soccer practice, each player must kick the ball to every other player present at least once. If there are 17 players at practice, what is the minimum number of kicks required?
====================================================
Explanation:
Player 1 has 16 people to kick the ball toPlayer 2 has 15 people to kick the ball to (since player 1 already is accounted for)Player 3 has 14 people to kick the ball toAnd so on.
We'll have this countdown: 16, 15, 14, ..., 3, 2, 1, 0. By the time we get to the 17th player, they won't have anyone to kick the ball to. This is because they've already been counted in the previous scenarios. This is to avoid double-counting.
So the problem simply boils down to us adding up the numbers 0,1,2,...14,15,16.
This is an arithmetic sequence with first term a = 0 and common difference d = 1. The sum of the first n = 17 terms is...
Sn = (n/2)*(a + d(n-1))
S17 = (17/2)*(0 + 1(17-1))
S17 = (17/2)*(16)
S17 = 17*8
S17 = 136 is the final answer
-----------------
An alternative method:
Consider we have two slots A and B
For slot A, we have 17 choices because we have 17 players.
Then for slot B, we have 17-1 = 16 choices since we don't want to reselect whoever goes in slot A.
If order mattered, then we'd have 17*16 = 272 different permutations.
However, order doesn't matter. A sequence like {player1,player4} is identical to {player4,player1}. All that matters is the overall group rather than the order of it. Both of those examples say the same thing: they connect player 1 to player 4.
In short, the value 272 is too large and it double-counts the true answer. We need to divide by 2 to correct for this.
272/2 = 136
We arrive at the same answer as before. There are 136 kicks required so that each player kicks the ball to every other player.
The minimum Number of kicks required in other to ensure that each player kicks the ball to every other atleast once is 136 kicks.
The Number of kicks could be related to the sum of the nth term of an arithmetic series
[tex]S_n = \frac{n}{2} (2a_1 + (n-1)d)[/tex]
n = number of terms = 17 players
First term,
[tex]a_1 = 0[/tex]
Common difference, d = 1
Inputting the Values into the equation :
[tex]S_n = \frac{17}{2} (2(0) + 16 \times 1)[/tex]
[tex]S_n = 8.5(0 + 16)[/tex]
[tex]S_n = 0 + 136[/tex]
[tex]S_n = 136[/tex]
Hence, the minimum number of kicks which would be taken by the players in other to ensure that each player kicks to ball to every other atleast once is 136 kicks.
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The sum of two number is 22 and difference is 8. Find the numbers.
Answer:
7 and 15
Step-by-step explanation:
Let the numbers be x and y
[tex]x + y = 22[/tex]
[tex]x - y = 8[/tex]
On adding both
[tex]x + y + x - y = 22 + 8[/tex]
[tex]2x = 30[/tex]
[tex]x = \dfrac{30}{2} [/tex]
[tex]x = 15[/tex]
From 1
[tex]15 + y = 22[/tex]
[tex]y = 22 - 15[/tex]
[tex]y = 7[/tex]
Answer:
[tex]take \: numbers \: xand \: y \\ given \: that \: x + y = 22 .....(1)\\ x - y = 8.....(2) \\ x = 8 + y \\ put \: this \: in \: (1) \\ 8 + y + y = 22 \\ 8 + 2y = 22 \\ 2y = 22 - 8 \\ 2y = 14 \\ y = \frac{14}{2} \\ y = 7 \\ pt \: y = 7in \: eqution \: (2) \\ then \: \\ x - 7 = 8 \\ x = 7 + 8 \\ x = 15 \\ therefore \: x = 15 \\ y = 7 \\ thank \: you[/tex]
The area of a rectangle is 0.8 square units. The length is 3.2 units and the width is x units.
What is the value of x?
x=0.25
x=2.4
x=2.56
x=4
Pls help meeeehhhh I will give brainliesttttt :D
the product of 2 and the second power of y
Answer:
[tex]2*y^{2}[/tex]
Step-by-step explanation:
The product of 2 is multiplication and the second power of y is just y squared
N The distance between Tanjung Malim and Sungai Petani is x km. A car was driven from Tanjung Malim to Sungai Petani at an average speed of 90 km/h. The return journey when the car was driven at an average speed of 105 km/h took 30 minutes, Calculate the value of x CHAPTER SUMMARY
Answer:
52.5 km
Step-by-step explanation:
the info about the trip from Malim to Petani is irrelevant and only there to confuse us.
but from the return trip info we get all we need.
for x km it took then 30 minutes at an average speed of 105 km/h.
to get km out of km/h, we need to multiply the speed number by the hours traveled. that removed the "h" and leaves us with km.
n km/h × a h = a×n km
so, now, in our example we have 105 km/h, and 30 minutes = 1/2 h.
so, we have
x = 105 km/h × 1/2 h = 105/2 km = 52.5 km
Lyndsey has 4 ½ cups of ice cream and wants to give each child at the shelter ½ cup of ice cream. How many children can she serve?
A. 4
B. 5
C. 8
D. 9
Someone help and explain please.
Answer:
k = 5/6
Step-by-step explanation:
The √ can be rewrite as a power, and this power is 1/2
So √a = a^1/2, and it is multiplying a, so we add the powers: a¹•a^1/2 = a^(1+1/2) = a^3/2
And the ³√ can be rewrite as the power 1/3, but the a inside the ³√ is to the power of 2, so we can rewrite it like this: (a²)^1/3
And to evaluate this we have to multiply the powers, so we will have: a^2/3
Now we have this fraction:
[tex] \frac{ {a}^{ \frac{3}{2} } }{ {a}^{ \frac{2}{3} } } [/tex]
A fraction with powers in the same base can be rewrite like a subtraction of the powers, so let's do that:
[tex] \frac{ {a}^{ \frac{3}{2} } }{ {a}^{ \frac{2}{3} } } = {a}^{ \frac{3}{2} - \frac{2}{3} } = {a}^{ \frac{5}{6} } [/tex]
help
Given h(x) = 2x – 1, find h(-1).
Answer:
Answer:
-3
Step-by-step explanation:
What this tells you is that where you see an x on the right hand side of the equation, you put -1.
h(-1) = 2(-1) - 1
h(-1) = -2 - 1
h(-1) = - 3
The slope and a point on a line are given. Use the information to locate three additional points on the line.
Slope = -4; Point (-2,1)
Determine three points on the line with slope -4 and passing through (-2,1).
A. (5,-3),(-3,-1),(-7,0).
B. (2,0),(-6,2),(-10,3).
C. (-3,5),(-1,-3),(0,-7).
D. (0,2),(2,-6),(3,-10).
Please help me solve this question.
Answer:
C
Step-by-step explanation:
the typical form of line equation is
y = ax + b
a = the slope of the line (expressed as y/x ratio telling us how many units y changes when x changes a certain number of units).
b = the intercept on the y-axis (when x = 0).
we know, a = -4
and we use the point (x = -2, y = 1) to get b
y = -4x + b
1 = -4×-2 + b = 8 + b
b = -7
=>
y = -4x - 7
only the points of option C are all fulfilling this equation.
e.g. x = 0, y = -7
-7 = -4×0 - 7 = -7, true, -7 = -7
and so on.
Help me pleaseee!!
Would appreciate ^^
**BRAINLIST, thanks and points***
Answer:
See below
Step-by-step explanation:
22. 30 = 2 * 3 * 5
23. 126 = 2 * 3 * 3 * 7
24. 4900 = 2 * 2 * 5 * 5 * 7 * 7
25. 39204 = 2 * 2 * 3 * 3 * 3 * 3 * 11 * 11
26. There's no square number
27. The highest common factor are
30 is 5
126 is 7
4900 is 7
39204 is 11
28. The lowest common factor are
30 is 2
126 is 2
4900 is 2
39204 is 2
What about you? What did you get?
Petra invests $10 800. After 4 years she has earned $3240 in interest.
At what annual rate of interest did she invest her money?
. A bakery opened yesterday with its daily supply of 40 dozen rolls. Half of the rolls were sold by noon, and 80 percent of the remaining rolls were sold between noon and closing time. How many dozen rolls had not been sold when the bakery closed yesterday
16 dozen
Step-by-step explanation:
a dozen=12
x=(40×12)/2
=240 rolls : are sold by noon
y=240×(80/100)
=192 rolls after noon
192/12= 16 dozen left
Given h(x) = –2x – 4, solve for x when h(x)
6.
Answer:
x = -16
Step-by-step explanation:
given:
[tex]h(x) = -2x - 4[/tex]
solve for x, when:
[tex]h(x) = 6[/tex]
~~~~~~~~~~~~
➡️ [tex] x = -2(6) - 4 [/tex]
➡️ [tex] x = -12 - 4[/tex]
➡️ [tex] x = -16 [/tex]
The solution of x when the function h ( x ) = 6 is x = -5
What is a function rule?The function rule is the relationship between the input or domain and the output or range. A relation is a function if and only if there exists one value in the range for every domain value.
A function is a relation from a set of inputs to a set of possible outputs where each input is related to exactly one output.
Given data ,
Let the function be represented as h ( x )
Now , the value of h ( x ) is given by
h ( x ) = -2x - 4 be equation (1)
On simplifying the function rule , we get
when h ( x ) = 6
Substitute the value of h ( x ) = 6 , we get
6 = -2x - 4
Adding 4 on both sides , we get
-2x = 10
Divide by -2 on both sides , we get
x = 10 / -2
x = -5
Therefore , the value of x is -5
Hence , the equation is x = -5
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Find the distance between the two points rounding to the nearest tenth (if necessary).
(0,-6) and (9,-1)
Hey there! I'm happy to help!
Imagine the line that is created when you connect the two points (the distance between the two points).
You can create a right triangle where this distance is the hypotenuse where the two legs are the change in x and y. So, if you take those changes in x and y, you can use the Pythagorean Theorem (a²+b²=c²) to find the distance between the two points, which is the hypotenuse.
Our change in x is 9 because 9-0 is 9.
We square it
9²=81
Our change in y is 5 as -1-(-6) or -1+6 is 5.
5²=25
We add these.
81+25=106
We square root and round to the nearest tenth.
√106≈10.3
So, our distance is 10.3.
This Pythagorean Theorem method actually gives us a formula called the distance formula that you can use to find the distance between points.
[tex]\sqrt{(x_{2} -x_{1})^2+(y_{2}-y_{1})^2}[/tex]
Have a wonderful day and keep on learning! :D
A triangle has a perimeter of 11.5 feet. The side lengths are x feet, 2x – 2 feet, and 3x + 1.5 feet. What is the value of x?
Answer:
x = 2 feetStep-by-step explanation:
We know that the perimeter is the sum of side lengths.
P = a + b + cSubstitute the values and solve for x:
x + 2x - 2 + 3x + 1.5 = 11.56x - 0.5 = 11.56x = 12x = 12/6x = 2Answer:
[tex]perimeter = h + l + b \\ = x + 2x - 2 + 3x + 1.5 = 11.5 \\ x \: terms \: togather \\ x + 2x + 3 x- 2 + 1.5 = 11.5 \\ 6x - .5 = 11.5 \\ 6x = 11.5 + .5 \\ 6x = 12 \\ x = \frac{12}{6} \\ x = 2 \\ thank \: you[/tex]
One number is 8 more than the other number. Twice the smaller number is 7 more than the larger number. Write the equation to represent this scenario.
a=15
b=23
Step-by-step explanation:
a+8=b
2a=b+7
2a=(a+8)+7
2a=a+15
a=15
Hakim and Aziz had some savings in the ratio 3 : 5. Hakim saved another $82 and Aziz spent $110. Both have the same amount of money now. How much do each of them have now?
===========================================================
Explanation:
Hakim and Aziz have savings in the ratio 3:5. This means that Hakim has 3x dollars while Aziz has 5x dollars. The x is some positive real number.
We're then told that Hakim saved another $82, which means it goes from 3x to 3x+82
At the same time, Aziz spent $110 which means the 5x decreases to 5x-110
At this point, the two people have the same amount of money. Set the expressions we found equal to one another and solve for x.
3x+82 = 5x-110
3x-5x = -110-82
-2x = -192
x = -192/(-2)
x = 96
Then use this x value to compute each expression like so
3x+82 = 3*96+82 = 3705x-110 = 5*96-110 = 370Both have $370 after Hakim saved that additional $82 and after Aziz spent that $110.
------------------
Extra info:
If we rewind things a bit, Hakim would have 3*x = 3*96 = 288 dollars while Aziz would have 5x = 5*96 = 480 dollars. This is before any additional saving or spending.
Then note how the ratio 288:480 fully reduces to 3:5 after dividing both parts by the GCF 96.
60x + 153 =9x + 51 , need help from every step
The answer you are looking for is x=-2.
Solution/Explanation:
60x+153=9x+51
Subtract 9x from both sides,
60x-9x+153=51
Simplifying this part of the equation,
51x+153=51
Now, subtracting 153 from both sides,
51x+153-153=51-153
Simplifying this part of the equation,
51x=-102
Finally, dividing 51 from both sides,
So, therefore, the final answer is x=-2. I hope this helped answer your question for you. Enjoy your day, and take care!
x = -2 is the solution to the equation 60x + 153 = 9x + 51.
Here, we have,
To solve the equation 60x + 153 = 9x + 51,
follow these steps:
Step 1:
Start with the given equation: 60x + 153 = 9x + 51.
Step 2:
Simplify the equation by combining like terms.
To do this, subtract 9x from both sides of the equation:
60x + 153 - 9x = 9x + 51 - 9x.
Simplifying further:
51x + 153 = 51.
Step 3:
Subtract 153 from both sides of the equation to isolate the variable term:
51x + 153 - 153 = 51 - 153.
Simplifying further:
51x = -102.
Step 4:
Divide both sides of the equation by the coefficient of x, which is 51, to solve for x:
51x / 51 = -102 / 51.
Simplifying further:
x = -2.
Step 5:
Check the solution by substituting x = -2 back into the original equation:
60(-2) + 153 = 9(-2) + 51.
Simplifying:
-120 + 153 = -18 + 51.
33 = 33.
Since the left side of the equation equals the right side after substituting x = -2,
we can conclude that x = -2 is the solution to the equation 60x + 153 = 9x + 51.
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Name the intersection of AD and DF
Answer:
i dont know
Step-by-step explanation:
Answer:
ADF
Step-by-step explanation:
AD and DF intersect at Angle ADF. It's in the picture.
solve using substitution
y = 3x - 4
3x + y = -4
y= 3x –4
3x + y = –4
3x + (3x –4) = –4
3x+3x – 4 = – 4
6x = – 4 +4
6x=0 —> x= 0/6 —> x=0
x = 0y = 3x – 4 —> y = 3(0) – 4 = – 4
y = – 4So; (x , y) —> (0 , – 4 )I hope I helped you^_^
Answer:
(0,-4)
Step-by-step explanation:
3x + y = -4
3x + (3x - 4) = -4
3x + 3x - 4 = -4
6x = 0
x = 0
y = 3(0) - 4
y = -4
When using the metric system, conversions which require division can be made by moving the decimal to the _____.
Answer:
left
Step-by-step explanation:
In the diagram below BD is parellel to XY what is the value of y ?
Answer:
C
Step-by-step explanation:
y and 67 are alternate exterior angles and are congruent , then
y = 67° → C
3 attempts remaining.
150 moths lived in a lab. Each week, some moths died, and about 1/5 survived . How many moths were still alive after 2 weeks?
What is 61.12÷3.2 uses to expressions.
Answer:
answer is 19.1
Step-by-step explanation:
answer is 19.1
It's geometry please help.
Answer:
BC = 22
Step-by-step explanation:
BD = 67
Bc = 3x - 2
CD = 4x + 13
BC + CD = BD (Given)
3x - 2 + 4x + 13 = 67
3x + 4x -2 + 13 = 67
7x + 11 = 67
7x = 67 - 11
7x = 56
x = 56 ÷ 7
x = 8
now instead of x put 8
Bc = 3x - 2
BC = 3(8) -2
BC = 24 -2
BC = 22