[tex]\large\underline{\sf{Solution-}}[/tex]
Given complex number is
[tex]\rm \longmapsto\:\dfrac{1}{ {(2 + i)}^{2} } [/tex]
[tex]\rm \: = \: \dfrac{1}{4 + {i}^{2} + 2 \times 2 \times i} [/tex]
[tex]\rm \: = \: \dfrac{1}{4 - 1 + 4i} [/tex]
[tex]\rm \: = \: \dfrac{1}{3+ 4i} [/tex]
[tex]\rm \: = \: \dfrac{1}{3+ 4i} \times \dfrac{3 - 4i}{3 - 4i} [/tex]
[tex]\rm \: = \: \dfrac{3 - 4i}{ {3}^{2} - {(4i)}^{2} } [/tex]
[tex]\rm \: = \: \dfrac{3 - 4i}{9 -16 {i}^{2} } [/tex]
We know,
[tex] \rm \longmapsto\:\tt{ {i}^{2} \: = \: - \: 1 \: } \\ [/tex]
So, using this, we get
[tex]\rm \: = \: \dfrac{3 - 4i}{9 -16( - 1)} [/tex]
[tex]\rm \: = \: \dfrac{3 - 4i}{9 + 16} [/tex]
[tex]\rm \: = \: \dfrac{3 - 4i}{25} [/tex]
[tex]\rm \: = \: \dfrac{3}{25} - \dfrac{4}{25}i[/tex]
Write an equation of the line passing through point P(2, 3) that is perpendicular to the line y-4=-2(x+3) .
Answer:
y - 3 = 1/2(x - 2)Step-by-step explanation:
The given line has a slope of -2.
The perpendicular line will have a negative-reciprocal slope:
m = 1/2Use same point-slope form and the point P(2, 3):
y - y₁ = m(x - x₁)y - 3 = 1/2(x - 2)[tex]\\ \sf\longmapsto y-4=-2(x+3)[/tex]
Here slope is -2
The perpendicular line have additive and multiplicative inverse slopem=1/2
Put co-ordinates of P in equation
[tex]\\ \sf\longmapsto y-3=\dfrac{1}{2}(x+2)[/tex]
The sum of the real numbers x and y is 11. Their difference is 5. What is the value of xy?
Answer:8
Step-by-step explanation:
Answer:
xy=24
Step-by-step explanation:
x+y=11
x-y=5
x=y+5
y+5+y=11
2y=6
y=3
x=8
xy=24
Sachin used synthetic division to divide a polynomial, p(x), by x + 5 and found that there was no remainder. What does this tell Sachin about how p(x) and x + 5 are related?
A. x + 5 is a factor of p(x)
B. p(x) divided by x + 5 is 0
C. x + 5 is not a factor of p(x)
D. x + 5 cannot be divided evenly into p(x)
Answer:
A
Step-by-step explanation:
The x + 5 is a factor of p(x) this represents that p(x) and x + 5 are related.
Given that,
Let us assume polynomial be p(x), and it is divided by x + 5.There is no remainder.Based on the above information, we can say that
x + 5 represent the factor of p(x).
Therefore we can conclude that the first option is correct.
Learn more: brainly.com/question/24169758
Which of the following represents the distance between x and y on a number line?
A. (x + y)
B. |y - x|
C. (y – x)
D. |x+y|
E. yx
Identify the factors of the terms of the expression.
6 + 2a + 15b the factors of the terms are?
Given :
6 + 2a + 15bTo find :-
The factors of the terms of the expression.Solution :-
First term :-
6 Factors = 1 , 2,3,6Second term :-
2a Factors = a , 1 , 2Third term :-
15bb,1,3,5,15Find the missing angle measure.
Answer:
83
Step-by-step explanation:
Find an equation in point-slope form for the line having the slope m= - 4 and containing the point (4,5).
The equation in point-slope form is
(Use integers or fractions for any numbers in the equation.)
Step-by-step explanation:
The point-slope form of a line is (y - y₁) = m(x - x₁)
Since we know the slope (m) is -4
And the point ( x₁, y₁ ) is (4, 5)
Then we can just plug these into the equation above:
⇒ y - 5 = - 4 (x - 4)
I often use Desmos to check my answer. As seen below, the equation does pass through the point (4, 5).
Q is a degree 5 polynomial that passes through the origin, has zeros i and 7 - i, and q(-1)= -520. find the equation for q
Using the factor theorem, the equation for q is:
[tex]q(x) = 4(x^5 - 14x^4 + 51x^3 - 14x^2 + 50x)[/tex]
The Factor Theorem states that a polynomial function with roots [tex]x_1, x_2, ..., x_n[/tex] is given by:
[tex]f(x) = a(x - x_1)(x - x_2)...(x - x_n)[/tex]
In which a is the leading coefficient.
In this problem:
Passes through the origin, so x = 0 is a zero, that is [tex]x_1 = 0[/tex].x = i is a zero, and thus, it's conjugate also is, that is, x = -i, hence [tex]x_2 = i, x_3 = -i[/tex]x = 7 - i is a zero, and thus, it's conjugate also is, that is, x = 7 + i, hence [tex]x_4 = 7 - i, x_3 = 7 + i[/tex]Then, the equation is:
[tex]q(x) = a(x - 0)(x - i)(x + i)(x - 7 + i)(x - 7 - i)[/tex]
[tex]q(x) = ax(x^2 - i^2)((x-7)^2 - i^2)[/tex]
Considering that [tex]i^2 = -1[/tex]
[tex]q(x) = ax(x^2 + 1)(x^2 - 14x + 50)[/tex]
[tex]q(x) = ax(x^4 - 14x^3 + 51x^2 - 14x + 50)[/tex]
[tex]q(x) = a(x^5 - 14x^4 + 51x^3 - 14x^2 + 50x)[/tex]
q(-1) = -520 means that when [tex]x = -1, q = -520[/tex], and this is used to find a.
[tex]q(x) = a(x^5 - 14x^4 + 51x^3 - 14x^2 + 50x)[/tex]
[tex]-520 = a(-1 - 14 - 51 - 14 - 50)[/tex]
[tex]130a = 520[/tex]
[tex]a = \frac{520}{130}[/tex]
[tex]a = 4[/tex]
Hence, the equation is:
[tex]q(x) = 4(x^5 - 14x^4 + 51x^3 - 14x^2 + 50x)[/tex]
A similar problem is given at https://brainly.com/question/24380382
Mable earns $180 in 18 hours. at this rate how many dollars will she earn in 30 hours
Step-by-step explanation:
18 hours = $180
1 hour = 180/18 = $10
so 30 hours = 30 × 10 = $300
please give me a brainliest answer
The length of a rectangle is 8 cm more then 4 times the with. If the perimeter of the rectangle is 46 cm, what are the dimensions
Answer:
15
Step-by-step explanation:
let the breadth be x
let the length be x+8
perimeter of rectangle=2 (length +breadth)
so, 2 (x+x+8)=44cm
=2 (2x+8)=44
=4x + 16=44
=4x= 44-16
=4x= 28
=x = 28÷4
=x= 7
therefore,
breadth is 7 (x)
length is 7+8 (x+8)
=15
Can someone answer this for me
A = {1, 3, 5, 7, 9}
B = {2, 4, 6, 8, 10}
C = {1, 5, 6, 7, 9}
A ∪ (B ∩ C) =
Answer:
Answer is (1,3,5,6,7,9)
can someone answer this
Answer:
b.d-6 that's the correct answer
Answer:
it is a
Step-by-step explanation:
how to graph the linear function:
g(x) = -4 + 7x
Answer:
Step-by-step explanation:
Slope: 7/1
y-intercept: (0,-4)
Start in the y-intercept (0,-4). Go up 7 and 1 to the right. You only need two points to trace a line.
p + 7 /8 = 18/ 12 what does p equal
Answer:
P = 5/8 or 15/24
Step-by-step explanation:
p = 18/12 - 7/8
p = 36/24 - 21/24
p = 15/24 ( Simplify )
p = 5/8
Answer:
Step-by-step explanation:
[tex]p+\dfrac{7}{8}=\dfrac{18}{12}\\\\p=\dfrac{18}{12}-\dfrac{7}{8}\\\\\\LCM \ of 8 \ and \ 12 \ is \ 24\\\\p=\dfrac{18*2}{12*2}-\dfrac{7*3}{8*3}\\\\p=\dfrac{36}{24}-\dfrac{21}{24}\\\\p=\dfrac{15}{24}[/tex]
[tex]p=\dfrac{5}{8}[/tex]
Suppose f(x) = 5x - 4. Describe how the graph of g compares with the graph of f.
g(x)=f(x) + 12
IDEE
Select the correct choice below, and fill in the answer box to complete your choice.
O A. g(x) has a scale factor of compared to f(x). Because it scales the horizontal direction, the graph is stretched horizontally.
OB. The graph of g(x) is translated unit(s) to the left compared to the graph of f(x).
OC. The graph of g(x) is translated unit(s) down compared to graph of f(x).
OD. g(x) has a scale factor of compared to f(x). Because it scales the vertical direction, the graph is stretched vertically.
O E. g(x) has a scale factor of compared to f(x). Because it scales the horizontal direction, the graph is compressed horizontally.
O F. g(x) has a scale factor of compared to f(x). Because it scales the vertical direction, the graph is compressed vertically.
O G. The graph of g(x) is translated unit(s) to the right compared to the graph of f(x).
O H. The graph of g(x) is translated unit(s) up compared to graph of f(x).
The graph of g(x) and f(x) are related by the given equation g(x) = f(x) + 12,
therefore, the ordered pair of the graph of g(x) is (f(x) + 12, x).
The choice that correctly describes how the graph of g(x) compares with f(x)
is the option; H. The graph of g(x) is translated unit(s) up compared to graph
of f(x).
Reasons:
The given function is f(x) = 5·x - 4
The function g(x) = f(x) + 12
Required:
To select the correct choice from the given options
Solution:
The difference between f(x) and the required function, g(x), is the addition
of a constant positive value of 12 to the function f(x).
Therefore, each f(x) output value is further increased by 12 to obtain the
graph of g(x), which gives;
The graph of g(x) is translated 12 units up compared to the graph of f(x),
which corresponds with the option H.
Learn more here:
https://brainly.com/question/15938361
write an equation of the line that passes through the point P(2, 5 ) that is parallel to y=4x+1
If the heights of a population of men are approximately Normally distributed, and the middle 99.7% have heights between 5'0" and 7'0", what is the standard deviation of the heights of the population?
a. 1"
b. 12"
c. 6"
d. 4"
e. 3"
Answer:
4 inches
Step-by-step explanation:
the middle number is 6 and the distance from 99.7 from the middle is 3 standard deviations. 12/3 =4
The value of 99.7% is the closest to the percentage of these heights that is within 3 standard deviations of the mean. The correct option is e.
What is the empirical rule?If your distribution follows a normal distribution, the standard deviation and mean can tell you where the majority of the data are.
It is given that the heights of a large population of ostriches are normally distributed. The percentage of these heights is within 3 standard deviations of the mean.
As we know from the empirical rule:
It is the rule of 68-95-99.7.
From the data given in the question: The height of a large population of ostriches is normally distributed.
X ~ (u, б²)
Normal distribution.
P{u - 3б < X < u + 3б}
From the distribution table:
P{u - 3б < X < u + 3б} = 99.7%
Thus, the value of 99.7% is the closest to the percentage of these heights that is within 3 standard deviations of the mean.
Learn more about the empirical rule here:
brainly.com/question/5440679
#SPJ2
bindus choir class is performing a concert. she wants to buy as many tickets as she can afford. if tickets cost $3.25 each and she has $14.25 to spend, how many tickets can she buy?
Answer:
4 tickets
Step-by-step explanation:
1 ticket is $3.25
2 ticket is $6.5
3 ticket is $9.75
4 ticket is $13
5 tickets is over and makes $16.25
a new car increased in price from 78200 to 136850 what is the percentage increase
Answer:
The percentage increase is by 1.75
Step-by-step explanation:
78,200 x 1.75 = 136,850
Pls help will mark the brainiest
If you deposit $400 into an account that offers a 5% interest rate. How much interest will you earn after 1 year?
Answer: The answer is $20
Multiply 400 by .05 or 5%.
If you wanna know 6 years it would be 536 usd
Explanation:
This would be an compound interest. Meaning that your gain every year would increase exponentially.
The equation to calculate this would be: Kn = K0⋅
(1+p100)n Kn is your savings after the period nK0 is your starting deposit p is the percentage n is the period of interest for your example we would have.
Kn=400⋅
(1+5100)6
rewrite the equation in slope-intercept form y + 4 = -2 (x-5)
Answer:
y = -2x + 6
Step-by-step explanation:
Slope intercept form: y = mx +b
y + 4 = -2(x - 5)
y + 4 = -2x + 10
y = -2x + 10 - 4
y = -2x + 6
Which of these is not a factor of 4x2? x2 2.
Solve the system of equations using the substitution method.
x+y=6
x = 2y
Answer:
x=4, y=2
Step-by-step explanation:
if x=2y just put 2y into the spot where x is for x+y=6
x+y=6
(2y) + y = 6
3y = 6
y = 2
now that I know y I can then replace y with the number 2
x= 2y
x = 2(2)
x= 4
Ed is 7 years older than Ted. Ed's age is also 3/2 times Ted's age. How old areTed and Ed.
factor the following equation
1263 + 14b2 + 30b + 35
Answer:
Step-by-step explanation:
2 ( 7 b 2 + 15 b + 649 )
Answer:
1298+28b+30b
1298+58b
2(649+29b)
PLSSS HELP THIS IS HARD ANYONE
Answer:
Option D
Step-by-step explanation:
f(-1,3) = (3-2 , 2*(-1) = (1, -2)
f(-3,5) = (5-2 , 2*(-3) ) = (3, -6)
f(-1,0) = (0-2 , 2*(-1) = (-2, -2)
Question:What is the equations of this function?
Plz help will give brainiest
What is the slope of the line on the graph?
Enter your answer in the box.
No links Nothing unrelated
Answer:
6
Step-by-step explanation:
(y1-y2)/(x1-x2) = (-1-5)/(0-1) = -6/-1 = 6
