The value of a is equal to 3 and the value of b is equal to 4.
Complex Number
A Complex Number is represented by z=a+bi, where:
a= real part
bi= imaginary number
b= imaginary part
i= [tex]\sqrt{-1}[/tex], therefore i²= -1
For solving this question, you should solve the product (-11 + 5i) * (1 – i). After that, you should compare the previous results with the result for expression ( (a + bi)* (2 + 3i) )-i. From this comparison, using the linear system you will find the variables a and b.
Step 1 - Solve the product (-11 + 5i) * (1 – i)(-11 + 5i) * (1 – i)=
-11 +11i +5i -5i²
-11 +16i -5i², as i²= -1 you can rewrite
-11 +16i -5(-1)
-11 +16i +5
-6+16i
Then,
(-11 + 5i) * (1 – i)= -6+16i
Step 2 - Simplify the expression ( (a + bi)* (2 + 3i) )-i( (a + bi)* (2 + 3i) )-i
(2a+3ai +2bi +3bi²) -i, as i²= -1 you can rewrite
(2a+3ai +2bi +3b(-1)) -i
(2a+3ai +2bi -3b) -i
( (2a-3b) + i(3a +2b) ) -i ,
For adding complex numbers, you must add or subtract the corresponding real and imaginary parts. Thus, you will have:
(2a-3b) + i(3a +2b-1)
Then,
( (a + bi)* (2 + 3i) )-i= (2a-3b) + i(3a +2b-1)
Step 3 - Identify real and imaginary parts for previous results
For (-11 + 5i) * (1 – i)= -6+16i
real part = -6
imaginary part = 16
For ( (a + bi)* (2 + 3i) )-i= (2a-3b) + i(3a +2b-1)
real part = 2a-3b
imaginary part = 3a +2b-1
Step 4 - Construct a linear system from real and imaginary parts2a-3b= -6
3a +2b-1=16, you can rewrite as 3a +2b=17.
Thus the system will be:
[tex]\begin{bmatrix}2a-3b=-6\\ 3a+2b=17\end{bmatrix}[/tex]
Step 5 - Solving the linear system
2a-3b=-6 (1)
3a+2b=17 (2)
Multiplying equation 1 by 2 and equation 2 by 3, you can rewrite as:
4a-6b= -12
9a+6b=51
Sum the equations
4a-6b+9a+6b= -12 +51
13a= 39
a=39/13=3
Replacing the value of a=3 in equation 1, you can find b.
2a-3b=-6 (1)
2*3-3b= -6
6 -3b = -6
-3b = -6 -6
-3b= -12
b= -12/-3 = 4
Read more about complex numbers here:
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if x+y = -10 and x-y = 2 what is the value of x
Answer:
x = -4
Step-by-step explanation:
The solution to a "sum and difference" system of equations can be found by adding the equations together.
(x +y) +(x -y) = (-10) +(2)
2x = -8 . . . . . . simplify
x = -4 . . . . . . . divide by 2
_____
Additional comment
y = -6, though this question did not ask that value.
Find the value of x. X+5 4 2x A x = [?] Enter
Answer:
x = 3
Step-by-step explanation:
In [tex]\triangle ABC,\: DE||AC[/tex]
[tex]\implies [/tex]By Basic Proportionality Theorem:
[tex]\frac{BD}{DA}=\frac{BE}{EC} \\ \\ \implies \: \frac{x + 5}{2x} = \frac{4}{3} \\ \\ \implies \: 3(x + 5) = 4(2x)\\ \\ \implies \: 3x +15 = 8x \\ \\ \implies \: 3x - 8x = - 15 \\ \\ \implies \: - 5x = - 15 \\ \\ \implies \: x = \frac{ - 15}{ - 5} \\ \\ \implies \: x = 3[/tex]
A shop charges `\$1.95` for a small `3`-ounce soft serve.
What is the cost per ounce of soft serve?
PLEASE HELP!!!
Write an expression using fractions to show how to determine the amount that each person will pay?Then calculate each person's contributions showing all steps in long division.
my chart:
jazzy: 35.7$
emily:48.9$
sarah:48.9$
layla:19.3$
total amount: 327$
________________________________________________________
SolveTo solve this problem, we must add each price together for the total.
[tex]4.26 + 9.76 + 6.33 + 14 = 34.35\[/tex]
To calculate our total store profits while finding the four contributions, we could divide by percent. For this case, 6%, also equal to 0.06
[tex]\frac{(estimate)34}{6\%(0.06)} = 573(estimate)[/tex]
Now that we have 573 as our estimate, subtract 573 by 34
[tex]573 - 34 = 539[/tex]
Therefore, the store's total profits were 573 dollars, and the four contributions from Jane, John, Zoey, and Hailey contributed to 34 dollars of it.
________________________________________________________
SolvedWe made 573$ total! That is a lot.Note that using percent and division was actually to calculate the store's total profits followed by the four contributions listed earlier. If any of this confuses you, please feel free to ask a question.________________________________________________________
Questions?Ask in the comments box.
Using proportions to solve for missing sides.
DGH~DEF
Find the value of x.
Answer:
25
Step-by-step explanation:
If ΔDGH ~ ΔDEF , then [tex]\frac{DG}{DE}[/tex] = [tex]\frac{GH}{EF}[/tex]
[tex]\frac{x+3}{2x-1}[/tex] = [tex]\frac{52}{91}[/tex]
After cross-multiplication: 52(2x - 1) = 91(x + 3)
104x - 52 = 91x + 273
13x = 325
x = 25
Answer:
x = 25Step-by-step explanation:
DGH~DEF ⇒ their corresponding sides are proportional
then
[tex]\frac{DG}{DE} =\frac{GH}{EF}[/tex]
then
[tex]\frac{52}{91} =\frac{x+3}{2x-1}[/tex]
then
[tex]\frac{4}{7} =\frac{x+3}{2x-1}[/tex]
then
4(2x-1) = 7(x+3) [cross multiply]
then
8x - 4 = 7x + 21
then
8x - 7x = 21 + 4
then
x = 25
If the circumstances of the circle below is 72, what is the length of AB (the minor arc)?
Answer:
12
Step-by-step explanation:
In the given circle circumference of the circle is = 72.
Since circumference of the circle = 2πr
[tex]2\pi r=72[/tex]
[tex]\frac{2*22}{7*r}=72[/tex]
[tex]r=\frac{72*7}{44}=\frac{504}{44}=\frac{252}{22}=\frac{126}{11}=11.45[/tex]
[tex]=\pi r \;theta /180=\frac{22}{7*11.45}*\frac{60}{180}[/tex]
[tex]11.99=12(About)[/tex]
Thus, Answer = 12
~lenvy~
Express in the form 1 : n , give n as a demical : 20 : 15
Answer:
1 : 0.75.
Step-by-step explanation:
15/20 = 0.75
So its 1 : 0.75
Answer:
1 : 0.75
Step-by-step explanation:
20÷20=1
15÷20=0.75
n=0.75
1. Mlla's cranbenyulce recipe uses 3 cups of water and 1 cup of cranberry concentrate.
Enter the percentage of the cranberry Juice recipe that is water.
126
Answer:
¾. because 3 out of 4 are water cups
Answer:
75%
Step-by-step explanation:
3 cups of water to 1 cup of cranberry concentrate.
So, 4 cups of ingredients.
The percentage of the cranberry juice that is water:
3 cups of water/4 cups of ingredients= 3/4.
To express 3/4 in percent, we multiply the fraction by 100%(percent).
[tex]\frac{3}{4}[/tex] * 100% = 75%
Hope this helps!
Please mark as brainliest!
x − 6 = -4 what is the solution
Step-by-step explanation:
[tex]x - 6 = - 4 \\ \\ \implies \: x = - 4 + 6 \\ \\ \implies \: x = 2[/tex]
Answer:
2
Step-by-step explanation:
because if you substitute 2-6 you will get negative 4
need help with this math hw
For the given equation, the center will be (1, -3) and the radius will be 3.
Correct option is (3)
What is a circle?A circle is a closed, two-dimensional object where every point in the plane is equally spaced from a central point. The line of reflection symmetry is formed by all lines that traverse the circle. Moreover, every angle has rotational symmetry around the center.
As per the given data:
Equation of the circle is [tex](x - 1)^2 + (y + 3)^2 = 9[/tex].
For a circle with equation [tex](x - a)^2 + (y - b)^2 = r^2[/tex]
The center is given by (a, b) and the radius is given by r.
Similarly comparing with the equation [tex](x - 1)^2 + (y - (-3))^2 = 3^2[/tex].
The center will be (1, -3) and the radius will be 3
Hence, For the given equation the center will be (1, -3) and the radius will be 3.
To learn more about circle, click:
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20 60 100 140 180 120 What percent of the time did Main Street have 100 or more cars per hour?
The distribution of the cars is an illustration of percentages
The main street has 100 or more cars per hour for 66.7% of the time
How to determine the time percentage?The dataset is given as:
20 60 100 140 180 120
From the above dataset, we have:
100 or more cars = 4Total distribution of cars = 6The percentage is then calculated as:
Percentage= 4/6 * 100%
Evaluate the product
Percentage= 66.7%
Hence, the main street has 100 or more cars per hour for 66.7% of the time
Read more about percentages at:
https://brainly.com/question/11360390
what is the 5th grade meaning of congruent
2x+3y=8 find the solution using addition elimination method
Answer:
X equals 1, and Y equals 2
First, find the value of 2x, we have to assign one to make the problem work.[tex]2x = 2 * 1[/tex]
Now, find y.[tex]3y = 3 * 2[/tex]
Find the results of the multiplication. Remember that anything times 1 is always the same number, the base number.[tex]2 * 1 = 2[/tex]
[tex]3 * 2 = 6[/tex]
Now, add.[tex]6 + 2 = 8[/tex]
________________________________________________________
Now, we go over what we learned.
________________________________________________________
What have we learned?We learned how to make inequalities true by assigning values to substitutions.
Questions related to this topic? Ask me in the comments box.
What must be a factor on the polynomial Function F(x) graphed on the coordinate plane below?
X-3
X-1
X+1
X+2
Answer:
x - 1
Step-by-step explanation:
The graph touches the x-axis at x = 1, its factor would be (x - 1)
Idc about this question, someone answer the question before this plsss, but here, math problem for fun:
Graph this and simplify it >:):
4x - 8x + 6x^2 - 28x + 7y + (y - 4)^2 - 20y = (y + 5 - x)^2
Answer:
Step-by-step explanation:
.
Fill in the blanks to find the difference in the expressions.
-2x+5
8
A
A x2+
С
X
B x +
11
x +4
X +3
x2 + 7x +
D
[tex]\dfrac{-2x+5}{x+4} - \dfrac{8}{x+3}\\ \\= \dfrac{(-2x+5)(x+3)-8(x+4)}{(x+4)(x+3)}\\\\=\dfrac{-2x^2-6x+5x+15 -8x -32}{x^2+3x+4x+12}\\\\=\dfrac{-2x^2-9x-17}{x^2+7x+12}\\\\\\=\dfrac{-2x^2+(-9)x +(-17)}{x^2+7x+12}\\\\\text{Hence, }~ A=-2,~ B=-9, ~C=-17, ~D=12[/tex]
Fill in the blanks below with the correct units. (a) Jessica's pet dog has a mass of 6 ? . (b) The soccer field at Jessica's school is 110 ? long. (c) Joe squeezed an orange and got about 60 ? of juice.
Answer:
a. 6 kg.
b. 110 m long.
c. 60 ml of juice.
what is 10/9 in a fraction
This kinds of fractions called improper fractions
The rule is
p/q is a rational number and p>qWe can turn it into mixed fraction
10/91-1/9Luke bought a pair of shoes online for $78. He used a coupon code to get a 40% discount. The website also applied a 20% processing fee to the price after the discount. How much was the processing fee? Round to the nearest cent.
GIVING BRAINLIEST
Answer:
$9.36Step-by-step explanation:
Te processing fee was applied to the discounted price.
The discounted price is
78 - 40% = 78*(100 - 40)/100 = 78*0.6 = 46.8Amount of fee is
20% of 46.8 = 0.2*46.8 = 9.36NO LINKS!! Explain your answers (show the support by showing the changes in x and y on your table). If the relationship is linear, inverse, or exponential, write the equation.
#5 and #6
Answer:
Linear relationship: increasing or decreasing one variable will cause a corresponding increase or decrease in the other variable.
Inverse relationship: the value of one variable decreases as the value of the other variable increases.
Exponential relationship: a constant change in the independent variable (x) gives the same proportional change in the dependent variable (y)
Question 5
As the x-value increases (by one unit), the y-value decreases.
Therefore, this is an inverse relationship.
The y-values are calculated by dividing 35 by the x-value.
[tex]\sf y=\dfrac{35}{x}[/tex]
**I believe there is a typing error in the table and that the y-value of x = 3 should be 11.67**
Question 6
As the x-value increases, the y-value increases. The y-value increases by a factor of 5 for each x-value increase of 1 unit.
Therefore, this is an exponential relationship.
[tex]\sf y=5^x[/tex]
Write the number in standard notation. 9 × 104
90,000
904
360
9,000
Answer:
90000
Step-by-step explanation:
because 10^4 = 10,000
then 9 x 10,000 = 90,000
Find the value by using logarithms
25.753
0.5341
Step-by-step explanation:
589292 is the correct answer:-)
please help me Find m
Answer: 70 degrees
Step-by-step explanation:
Hellp me please DDDDDDDDDDD:
Answer:
238 mm
Step-by-step explanation:
11x5 = 55
11x4=44
11x5=55
11x4=44
4x5=20
4x5=20
______(Add all up)
= 238 mm
Hope this helps :)
HELP ASAP.
39 BRAINLY POINTS PLUS BRAINLY USER
Answer:
1
Step-by-step explanation:
Given:
m = 12 n = 1/4Substitute the values into the expression:
1/2(m - 4) × n
⇒ 1/2(12 - 4) × 1/4
Simplify the expression:
⇒ 1/2(8) × 1/4
⇒ 4 × 1/4
⇒ 4 ÷ 4
⇒ 1 (Option B)
Answer:
D. 1
Step-by-step explanation:
Find the solutions to the equation below.
Check all that apply.
2x^2 + 7x + 3 = 0
A. x = 4
B. x = -1/2
C. x = 2
D. x = 7
E. x = 3
F. x = -3
Answer:
B and F.
Step-by-step explanation:
2x^2 + 7x + 3 = 0
2x^2 + 6x + x + 3 = 0
2x(x + 3) + 1(x + 3) = 0
(2x + 1)(x + 3) = 0
x = -1/2, -3.
Solve the following system of equations:
{−3x+4y=7, 7x−12y=−11
Provide your answer below:
What is cosK?
(25)/(7)
(25)/(24)
(7)/(25)
(24)/(25)
Step-by-step explanation:
7/25
we need to remember this triangle with 90° 7, 24, 25
Is 5/2 to the right of number 1 on number line?
Answer:
Yes;
Step-by-step explanation:
5/2 = 2 1/2
2 1/2 > 1
Yes, 5/2 is to the right of 1 on a number line.
write 82/10 as a mixed number in simplest terms brainly
A) 8 2/10
B) 10 1/4
C) 8 1/5
D) 2 4/5
Answer:
C) 8 1/5
Step-by-step explanation:
82/10= 8 2/10= 8 1/5
Answer:
A) 8 2/10
Step-by-step explanation:
10 goes into 82 8 times with a remainder of 2