If a, b are real numbers and 7a + i(3a - b) = 14 - 6i , then find the values of a and b.
If a, b are real numbers and 7a + i(3a - b) = 14 - 6i, then find the values of a and b. Therefore, the value of a = 2 and the value of b = 12. 3.
The value of the variables 'a' and 'b' of the complex equation will be 2 and 12, respectively.
What is a complex number?The complex number is the combination of the real part and the imaginary part. Then the complex number is given as a+bi where the value of i is √(-1) and the value of i² is -1.
The equation is given below.
7a + (3a - b)i = 14 - 6i
Compare the real part of the equation, then we have
7a = 14
a = 14 / 7
a = 2
Compare the imaginary part of the equation, then we have
3a - b = - 6
3 x 2 - b = -6
6 - b = - 6
b = 6 + 6
b = 12
The value of the variables 'a' and 'b' of the complex equation will be 2 and 12, respectively.
More about the complex number link is given below.
https://brainly.com/question/10251853
#SPJ2
Chris paid $9.18 for a necklace. This amount includes a sales tax of 8%. What was the cost of the necklace before tax?
Answer:
8.5 or 8.50
Step-by-step explanation:
None for now
"Not putting it here"
The cost of the necklace before tax, for which Chris paid $9.18 including the sales tax of 8% is $8.5.
What is percentage increase ?Percentage increase is the amount added to the initial value in the percentage part.
Chris paid $9.18 for a necklace. This amount includes a sales tax of 8%.
Let the cost of the necklace before tax is x dollars. Now, the 108% of the x is $9.18. Thus,
[tex]x\times\dfrac{100+8}{100}=9.18\\x=\dfrac{9.18\times100}{108}\\x=8.5[/tex]
Hence, the cost of the necklace before tax, for which Chris paid $9.18 including the sales tax of 8% is $8.5.
Learn more about the percentage increase here;
https://brainly.com/question/2085058
What is the vertex of the graph of the function below?
y= x2 - 10x + 21
O A. (5,-4)
B. (3,0)
O C. (5,0)
OD. (3,-4)
Answer:
Step-by-step explanation:
A. (5,-4)
The vertex of the graph of the function is (5,-4).
The answer is option A.
What is a function?A function has an input and an output.
A function can be one-to-one or onto one.
It simply indicated the relationships between the input and the output.
Example:
f(x) = 2x + 1
f(1) = 2 + 1 = 3
f(2) = 2 x 2 + 1 = 4 + 1 = 5
The outputs of the functions are 3 and 5
The inputs of the function are 1 and 2.
We have,
To find the vertex of the function y = x² - 10x + 21,
We can use the formula:
x = -b/2a
where a is the coefficient of the x² term, b is the coefficient of the x term, and x is the x-coordinate of the vertex.
In this case,
a = 1 and b = -10, so:
x = -(-10)/(2 x 1) = 5
To find the y-coordinate of the vertex, we can substitute x = 5 into the function:
y = (5)² - 10(5) + 21 = -4
Therefore,
The vertex of the graph of the function is (5,-4).
Learn more about functions here:
https://brainly.com/question/28533782
#SPJ7
Which of the following is a true statement concerning the use of a placebo?
A.
B.
C.
D.
Answer:
its B
Step-by-step explanation:
What is the percent of increase from 900,000 to 1,000,000?
Round your answer to the nearest tenth of a percent and include a percent sign (%),
Answer:
1000000/900000= 10/9= 1.1111111111*100=11.11%
Examine the system of equations.
y = negative one-fourth x minus 2
x = 4
What is the solution to the system?
(–3, –2)
(4, –3)
(4, –2)
(4, –1)
The answer is 4,-3
Irfcdxsaacd d
Answer:
4,-3
Step-by-step explanation:
Consider a collection of envelopes consisting of 3 red , 3 blue , 1 green , and 2yellow . If three envelopes are selected at random, without replacement, determine the probability that at least one envelope is a red envelope.
Answer:
The probability is 31/35
Step-by-step explanation: