Answer:
[tex]b = 3[/tex]
Step-by-step explanation:
We are given that:
[tex](2 + bi)(3+2i) = 13i[/tex]
And we want to determine the value of b.
First, expand:
[tex]\displaystyle \begin{aligned} (2+bi)(3+2i)&=2(3+2i)+bi(3+2i) \\ &= (6+4i)+(3bi+2bi^2) \\ &= (6+2b(-1))+(4i+3bi) \\ &= (6-2b) + (4+3b)i\end{aligned}[/tex]
Therefore, we can write that:
[tex](6-2b) + (4+3b)i = 0+ 13i[/tex]
If two complex numbers are equivalent, their real and imaginary parts must be equivalent. Hence:
[tex]6-2b = 0 \text{ and } 4+3b = 13[/tex]
Solve for each case:
[tex]b=3 \text{ and } b=3[/tex]
The two solutions are equivalent, hence such a number b exists.
In conclusion, b = 3.
7x -3x = 20?
I do not know what this is…
7x-3x = 20
Simplify by subtracting:
4x = 20
Divide both sides by 4:
X = 5
Answer:
7x-2x=20
6x=20
6x÷6=20÷6
x=16.67
More math for the experts!
If some one could figure out the x and y are
The problem is
3x+4y=50
-2x=y
Answer:
x = -10
y = 20
Step-by-step explanation:
y = -2x
so
substituting the value in equation ii
3x + 4y = 50
or, 3x + 4(-2x) = 50
or, 3x + (-8x) = 50
or, 3x-8x = 50
or, -5x = 50
so, x = -10
so
y = -2x
or, y = -2*(-10)
so, y = 20
What is 463,954 rounded to the nearest ten thousand?
400,000
460,000
463,000
463,900
Find the measure of the given angle.
Answer:
132
Step-by-step explanation:
A roof repairer works out that he will need to work with a colleage charges $20 per hour. In the end, they took 6 hours to fix the roof.
a. Write an expression with parentheses to describe how much the homeowner ownes for labor.
b. Evaluate your expression to calculate the cost of the labor.
a) 20(x)=y
b) $120
Let x= number of hours
Let y= Cost of labor
20 will remain constant, what matters is how many hours are being worked. If it's $20 per hour then it's safe to assume 1 hour is 20 dollars worth of labor. Due to it being per hour you have to multiply the rate by however many hours worked to get your final cost.
A store donates 3% of total sales to a charity. Mr. Winn bought 4 jackets at the store. Each jacket had a price $150. how much did the store donate to charity because of the jackets Mr. Winn bout?
Answer:
$18
Step-by-step explanation:
3%=0.03
$150*0.03=$4.50
$4.50*4=$18
,
20. In the figure, O is the centre of the concentric circles of radii 17 cm
and 10 cm respectively. Chord AD of the larger circle cuts the smaller
circle at B and C such that AB = 9 cm. Find
(a) the distance of AD from the centre,
Answer:
I confirm my answer : 8(cm)
Step-by-step explanation:
In the triangle OAB, BO²=AB²+AO²-2*AB*AO*cos( BAC)
cos (BAC)=9²+17²-10²/(2*9*17)=15/17
AC/AO=cos(BAC) ==> AC=17*15/17=15
OC²=AO²-AC²=17²-15²=64
OC=8 (cm)
If y=3x + 5 what is the value of y when x= 12?
The difference between 7 and -14.
Numerical expression
Answer:
7-(-14)
7+14=21
Step-by-step explanation:
- and - = +
Hello!
Im beginning year 11 this year and I recently did really bad in my Mocks! I really need some help and advice for all of my subjects because I truly dont know how to revise effectively and because I keep Procrastinating!
Any advice would be appreciated or if u have links to videos and helpful websites I would appreciate it
Here are my results :
Maths : 4
Eng Language : 4
Eng Lit : 4
Chemistry : 4
Physics : 3
Biology : 3
RE: 4
Health and Social care : Level 2 Pass
History : 4
Food Tech : 4
Spanish : 4
Thank u!
Answer:
if you need help with some subjects you can come here in brainly it helps me a lot i just started grad 6 so yeah
like if you have a math question just go to ask question you and someone will help
and also explain so yeah hope i helped a little2a) what is the inverse of -134
2b) what is the inverse of 5/6
Answer:
2a ) 4/-13
2b) 6/5
What’s the answer to this? Please send help
Answer:
C
Step-by-step explanation:
PLEASE HELP PLEASE!!!!!
Answer:
60x^4y^6
Step-by-step explanation:
(5xy^2)×(12x^3y^4)
=60x^(1+3)y^(2+4)
=60x^4y^6
A triangle has three angles. The first angle measures 20 less than a number. The second triangle is three
times the number. The third is the number. What are the measurements of each of the three angles in this
triangle?
Answer:
first angle is 20, 2nd is 120, 3rd is 40.
Step-by-step explanation:
with these words, "20 less than a number, Three
times the number, is the number." We can set up the equation x-20+3x+x = 180. combine like terms and we get 5x-20=180. add 20 to both sides to get 5x=200 then divide 200 by 5x to get x = 40. We can then plug 40 into each of the expressions, x-20, 3x, x, to get our angles.
Which function describes the granh below?
Answer:
second one Step-by-step explanation:
Find the values of a and b that complete the mapping diagram
Answer:
A=0
B=1
Step-by-step explanation:
Just did it (:
Answer: A = 0, and B = 1.
Step-by-step explanation: I put 0, and 1, and it was the perfect answer.
The length of a rectangle is 2 ft longer than its width.
If the perimeter of the rectangle is 56 ft, find its length and width.
Hi! I'm happy to help!
To solve this, we first need to look at the perimeter equation:
P=2L+2W
We don't know our length, so we can represent it with x. Since our width is 2 feet shorter than x, we can represent it with x-2. Now, we plug these values into our equation:
56=2x+(2(x-2))
Let's simplify what the width is by multiplying:
56=2x+2x-4
Now, let's combine our 2xs
56=4x-4
Now, we just need to solve for x in order to find our length and width.
First, we need to isolate x on one side of the equation. We can do this by adding 4 to both sides:
56=4x-4
+4 +4
60=4x
Now, all we have to do is divide both sides by 4 and x will be fully isolated:
60=4x
÷4 ÷4
15=x
Now that we know x, let's plug this into our previous equations:
L=x=15
L=15
W=x-2=15-2=13
W=13
To verify our answers, we can plug this into our perimeter equation:
56=2(15)+2(13)
56=30+36
56=56
After double checking our answers, we know that our length is 15 and our width is 13.
I hope this was helpful, keep learning! :D
b) 20 labourers complete the construction of a building in 24 days. In how many days would 16 labourers complete the construction?
Answer:
16 labourers complete the construction
in 30 days
Step-by-step explanation:
mark me as a brainlist answer
Which expression is equivalent to
-9 - 9?
–9- (-9)
0-9 + (-9)
Submit Answer
0-9 +9
|-9- (-9)
-9 - 9 is the same that -9 + (-9)
Solve the fraction problems and reduce the answer to its lowest form:-
1)7/10×2/21
2)9/16×10/21
3)11/12×26/55
4)2/6×18/12×2/3
5)5/6×9/10
Answer:
1/1515/5613/301/33/4Step-by-step explanation:
1) 7/10 × 2/21
1/15
2) 9/16 × 10/21
90/336
15/56
3) 11/12 × 26/55
13/30
4) 2/6 × 18/12 × 2/3
72/216
1/3
5) ⅚ × 9/10
45/60
3/4
[tex]\frac{9}{20} + 2\frac{9}{10}[/tex]
Answer:
3 7/20
Step-by-step explanation:
9/20 + 2 9/10 = 9/20 + 2 18/20
= 2 + 27/20
= 2 + 1 7/20
= 3 7/20
Hello!
✥ Answer ✥
9/20 + 2 9/10 = 67/20
❀ Step-by-step explanation: ❀
1. Calculate:
9/20 + 2 9/10
9/20 + 29/10 (We amplify by 2)
9/20 + 58/20
67/20
Good luck!
Diego started with this shape Diego moves the shape down, turns it 90 degrees clockwise then moves the shape to the right
Transformation involves changing the position and/or dimension of a shape, a line or a point.
I've added as an attachment, the result of the transformation.
From the question, the following transformations were performed by Diego.
Move downward ----- > Turn 90 degrees clockwise ----- > Move to the right
Move downward
When a shape is moved downward, the new position of the shape will be directly under its previous location
Turn 90 degrees clockwise
This means that the shape will be rotated, 90 degrees to the right. However, the position of the shape will remain unchanged.
Move rightward
When a shape is moved rightward, the new position of the shape will be directly to the right of its previous location
Refer to attachment for further explanation
Read more about transformations at:
https://brainly.com/question/11709244
solve by completing the square pls show work i will mark brainliest
Answer:
[tex]3(x-1)^2 +6[/tex]
Step-by-step explanation:
Write [tex]3x^2-6x+9[/tex] in the form: [tex]x^2 + 2ax + a^2[/tex].
Factor out 3.
[tex]3(x^2 -2x+3)[/tex]
Add and subtract [tex]\left(-1\right)^2\:[/tex].
[tex]3\left(x^2-2x+3+\left(-1\right)^2-\left(-1\right)^2\right)[/tex]
You dont have to write this section down but its for notes:
[tex]x^2+2ax+a^2=\left(x+a\right)^2[/tex]
[tex]x^2-2x+\left(-1\right)^2=\left(x-1\right)^2[/tex]
Continue writing this down to show work:
Complete the square
[tex]3\left(\left(x-1\right)^2+3-\left(-1\right)^2\right)[/tex]
Simplify
[tex]3\left(x-1\right)^2+6[/tex]
Find the difference of the two squares x2-49
Answer:
It is (x - 7)(x + 7)
Step-by-step explanation:
[tex] {x}^{2} - 49 \\ = {x}^{2} - {7}^{2} [/tex]
from the "difference of two squares"
[tex]( {a}^{2} - {b}^{2} ) = (a - b)(a + b)[/tex]
take;
a » x
b » 7
substitute:
[tex]( {x}^{2} - {7}^{2} ) = (x - 7)(x + 7)[/tex]
f(x) = 2x2 – 7x – 6. Find f(6)
Answer:
hello, your name similarty to my name
Step-by-step explanation:
put 6 from x and to find function
f(6)= 72-42-6=24
4/5 divided by 3 fraction.......
Answer:
4/15
Step-by-step explanation:
[tex]\frac{\frac{4}{5} }{3}=\frac{4}{5}(\frac{1}{3})=\frac{4}{15}[/tex]
I need help rounding numbers to the nearest tenth, hundredth and thousandth
Answer:
hey friend
what's your question
Mario is 68.5 inches tall. Tyler is 63.25 inches tall. How much taller is Mario than Tyler
Answer:
5.25inches
Step-by-step explanation:
difference in height = 68.5-63.25 =5.25
Height of Mario Hm = 68.5 inches
Height of Tyler Ht = 63.25 inches
Evidently, Hm > Ht
Now difference = Hm - Ht = 68.5 - 63.25
= 5.25 inches
Answer: Mario is 5.25 inches taller than Tyler.
Solve for x: 3x - 5 + 2x = 25 - 5x
Answer:
x=3
Step-by-step explanation:
Add 2x and 3x
5x-5=25-5x
move -5x to the other side by adding 5x on both sides:
10x-5=25
Add 5 on both sides:
10x=30
Divide 10 on both sides:
x=3
Hope this helps!
Answer:
Step-by-step explanation:
5x - 5 = 25 - 5x
10x - 5 = 25
10x = 30
x = 3