[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]
Please answer ASAP
The price of a dozen exercise book is 72 dollars find the cost of 18 exercise books
Answer:
$108Step-by-step explanation:
Dozen = 12
Use the ratio:
12 ⇒ 7218 ⇒ xFind x:
x = 72*18/12 = 108Graph f(x) = -3/4x - 4.
Answer:
PLS HELP ME 7
Step-by-step explanation:
A company’s stock was selling at $20 a share. A month later, it was selling at $26 a share. What is the percent gain
Answer:
The percent gain would be 77952515`0%
Mrs. James needs to have her Jeep repaired but does not want to spend more than $375 for the repairs. The mechanic says that the part needed for the repair will cost $100 and the labor will cost an additional $40 per hour. Which inequality represents the greatest number of hours the mechanic can work without exceeding Mrs. James' budget?
Answer:
375 = 40x + 100
Step-by-step explanation:
HELP PLZ!!!!!!!!!!! WILL GIVE BRAIN!!!!!!!
Answer: 1 go to 1 the 2 go to 5 the 3 go to 3 the 4 go to 2 the 5 go to 4
Step-by-step explanation: i hop this helps if not sorry :(
PLEASE help!! I’ll give brainliest!!
The graph shows the number of gallons in a pool being drained and
represents a linear function.
Which statement about this function is correct?
A. The y-intercept is (0, 8500), and the 8500 represents the number
of gallons before draining the pool.
B. The y-intercept is (0, 8500), and the 8500 represents the number of
gallons drained per hour.
C. The y-intercept is (8500, 0) and represents the number of hours it
takes to drain the pool.
D. The y-intercept is (8500,0) and represents the number of gallons
drained per hour.
Answer:A. The y-intercept is (0, 8500), and the 8500 represents the number
of gallons before draining the pool.
Step-by-step explanation:
The y-intercept is (8500,0) and -540 represents the number of gallons drained per hour. Then the correct option is D.
What is a linear equation?A connection between a number of variables results in a linear model when a graph is displayed. The variable will have a degree of one.
The linear equation is given as,
y = mx + c
Where m is the slope of the line and c is the y-intercept of the line.
The graph shows the number of gallons in a pool being drained and represents a linear function.
Let 'x' be the number of hours and 'y' be the volume. And the points are (4, 6340) and (6, 5260). Then the equation of the line is given as,
(y - 6340) = [(6340 - 5260) / (4 - 6)] (x - 4)
y - 6340 = - 540x + 2160
y = - 540x + 8500
The y-intercept is (8500,0) and -540 represents the number of gallons drained per hour. Then the correct option is D.
More about the linear equation link is given below.
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please help me to solve problems
Step-by-step explanation:
ajhai ans Pani chaiyo ki sabai ko ans pathau
Firstly, a key fact to keep in mind is Angles in a triangle equals 180⁰.
a. x+60⁰+30⁰=180⁰
x+90⁰=180⁰
x=180⁰-90⁰
x=90⁰
b. x+3x+40⁰=180⁰
collect like terms
4x+40⁰=180⁰
4x=180⁰-40⁰
4x=140⁰
Divide both sides by 4
x=35⁰
c. x+(x+7)+(x+5)=180⁰
3x+12=180⁰
3x=180⁰-12
3x=168⁰
x=168⁰÷3
x=56⁰
d. 52+x+y=180⁰
keeping in mind, two sides of this triangle are equal...
180⁰-52⁰=128⁰
128⁰÷2=64⁰
x=64⁰
x=64⁰ y=64⁰
e. b+a+90⁰=180⁰
right angled triangle
180⁰-90⁰=90⁰
90⁰÷2=45⁰
b=45⁰
b=45⁰ a=45⁰
f. Angles on a straight line equals 180⁰
180⁰-130⁰=50⁰
x=50⁰
Back to the triangle, in which two are equal,
50⁰+x+y=180⁰
180⁰-50⁰=110⁰
110⁰÷2=55⁰
y=55⁰
y=55⁰ z=55⁰
To be honest, I don't know how to solve the last two questions, hope I was helpful, if you wish, please mark BRAINLIEST.
cot 10° . cot 20°. cot 70°. cot 80°. cot 45° = 1
Answer:
steps below
Step-by-step explanation:
cot 10° * cot 20° * cot 70° * cot 80° * cot 45°
= (cos 10°/sin 10°)*(cos 20°/sin 20°)*(cos 70°/sin 70°)*(cos 80°/sin 80°)* (1)
= (cos 10°*cos 80°)(cos 20°*cos 70°) / (sin 10°*sin 80°)(sin 20°*sin 70°)
= (1/2*(cos60°+cos90°)*1/2(cos50°+cos90°))/(1/2*(cos60°-cos90°)*1/2(cos50°-cos90°)) ... cos90° = 0 cos60° = 1/2
= (1/8*cos50°) / (1/8*cos50°)
= 1
PLEASE HELP WILL MARK BRAINLIEST NO FAKE ANSWERS
Arrange it in descending order and give the degree of the polynomial.
Answer:
the degree is 5
they are in decending order
Step-by-step explanation:
PLEASE HELP ASAP I WILL GIVE U A LOT OF POINTS AND BRAINLIEST :D
Multiply to get the answer:
4×10⁷ * 3.65×10² = (4*3.65)×10⁷⁺² = 14.6×10⁹ = 1.46×10¹⁰ krill#2Convert to scientific notation and find the ratio of the second number by the first:
26000000000 = 2.6×10¹⁰Divide:
4.94×10¹³ ÷ 2.6×10¹⁰ = (4.94/2.6)×10¹³⁻¹⁰ = 1.9×10³ = 1900 timesA game spinner has 8 sections, 3 red, 1 blue, 2 yellow, and 2 green. What is the probability that you will spin a yellow?
Answer:
1/4 Percent
Step-by-step explanation:
add all them up and youll get 8 the see the yellow takes up 1/4 percent of the numbers.
A copy machine makes 32 copies per minute how long does it take to make 152 copies?
Answer:
It should take about 4.75 min.
Step-by-step explanation:
Hope this helps and could you mark me as the brainliest
Only answer please please
Answer: D
Step-by-step explanation:
Answer:$22.50
Step-by-step explanation:
The three friends already paid the entrance fee. The question asks how much MORE will they pay for 5 MORE rides (8-3 rides). Since tickets are $1.50 each, and we have 3 people:
($1.50/ticket)*(5 tickets/person)*(3 persons) = $22.50 more.
[Note how the units cancel, leaving just $]
Which answer choice shows that the commutative property does NOT hold for matrix multiplication?
Answer:
D.
Step-by-step explanation:
AB is NOT equal to BA in matrix multiplication.
It is not commutative.
PLS HELP ME
PLS HELP ME
Answer:
A x=-8 or x=-2
B x=-4 or x=-3
C x=-1 or x=-12
What percent represents the part of the model shaded green. A.60% B.62.5%. C.66.7% D.75%
Answer:
60%
Step-by-step explanation:
3/5 = 6/10 = 60%
Answer:
A. 60%
Step-by-step explanation:
3/5 =30/50=60/100
i dentify the given condition anf the unknown
Answer:
Is there a picture i could go by to answer your question or is this is?
On the grid below, which point is located in the quadrant where the x-coordinate is a negative number and the y-coordinate is a positive number? ASAP!!
Group of answer choices
A
B
C
D
Is it B?
Answer:
B
Step-by-step explanation:
B is on the upper half of the plane meaning its y-value is positive, however it is on the left side of the plane meaning its x-value is negative.
A would be (+,+)
C would be (-,-)
D would be (+,-)
ASAP PLS!!
-GIVING OUT BRAINLIEST
Answer:
The answer is (C)
Step-by-step explanation:
guys pls help me!!!!!!
Answer:
X = 126
Step-by-step explanation:
180 - 54 = 126
54+x=180
How much is 9396 divided by 18? Use partial quotients to answer.
Answer:
9396/18 is 522
plzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzz
Answer:
Its A
Step-by-step explanation:
took the test a while ago
Algebra 2 11th grade
4. If x = y + 3, then in the second equation you can write
-3 (y + 3) + 3y = 6
Expanding and simplifying gives
-3y - 9 + 3y = 6
-9 = 6
but this is clearly not true, so this system as no solution.
5. Solve the first equation for x :
x + 2y = 4 ===> x = -2y + 4
Substitute into the other equation:
2 (-2y + 4) - 3y = 1
-4y + 8 - 3y = 1
-7y = -7
y = 1
Solve for x :
x = -2•1 + 4
x = -2 + 4
x = 2
6. Solve the first equation for y :
2x - y = 6 ===> y = 2x - 6
Substitute into the other equation:
x + 2 (2x - 6) = -2
x + 4x - 12 = -2
5x = 10
x = 2
Solve for y :
y = 2•2 - 6
y = 4 - 6
y = -2
7. Solve either equation for x :
x + 4y = 10 ===> x = -4y + 10
Substitute into the other equation:
(-4y + 10) - 2y = -8
-6y = -18
y = 3
Solve for x :
x = -4•3 + 10
x = -12 + 10
x = -2
8. Solve the first equation for y :
-2x + y = 1 ===> y = 2x + 1
Substitute into the other equation:
4x - 2 (2x + 1) = 5
4x - 4x - 2 = 5
-2 = 5
This is false, so there is no solution.
9. Solve the second equation for x :
-x - 4y = -3 ===> x = -4y + 3
Substitute into the other equation:
2 (-4y + 3) + 8y = 6
-8y + 6 + 8y = 6
0 = 0
This means any value of x and y will satisfy these two equations, so there are infinitely many solutions.
How many solutions does this linear system have?
y = -6x+2
-12x - 2y = -4
one solution: (0,0)
O one solution: (1.4)
O no solution
O infinite number of solutions
Answer:
in finity
Step-by-step explanation:
Both provide ATP molecules, but only fermentation occurs when oxygen is present.
okokoo
The linear system have y = -6x+2 and -12x - 2y = -4 have infinite number of solutions.
What is Equation?Two or more expressions with an Equal sign is called as Equation.
The given system of linear equations are y = -6x+2 and -12x - 2y = -4
To solve this system, we can substitute the expression for y from the first equation into the second equation, as follows.
-12x - 2y = -4
substitute y = -6x + 2 from first equation
-12x - 2(-6x + 2) = -4
Distribute the negative sign
-12x + 12x - 4 = -4
0 = 0
The equation 0 = 0 is a true statement, which means that the system has infinitely many solutions.
Hence, the linear system have y = -6x+2 and -12x - 2y = -4 have infinite number of solutions.
To learn more on Equation:
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what fraction of an hour is 5 minutes in its simplest form
Answer:
1 / 12
Step-by-step explanation:
one hour = 60 minutes
so
5 / 60
= 1 / 12
Answer:
[tex]\frac{1}{12}[/tex]
Step-by-step explanation:
There are 60 minutes in 1 hour , then 5 minutes as a fraction of an hour is
[tex]\frac{5}{60}[/tex] = [tex]\frac{1}{12}[/tex] ← in simplest form
FIND THE FACTORS OF THE FOLLOWING POLYNOMIAL 3y²-2y-1
Answer:
y
[tex] y2 - 2y - 3[/tex]
[tex](y - 1)(y + 3) [/tex]
[tex](3y - 1)(3y + 3)[/tex]
Step-by-step explanation:
you multiple the 3 with the 1
then factor
then divide by 3 again but the denominator goes in front of the y.
Solve for X then find the measure of angle B
Answer:
Below in bold.
Step-by-step explanation:
The 2 angles are equal so
8x - 8 = 5x + 25
3x = 33
x = 11.
m < B = 8(11) - 8 = 80 degrees.
What is the slope of the following line?
A. 1/3
B. - 1/3
C. 3
D. - 3
Answer:
A
Step-by-step explanation:
Points of origin are (-3,0) and (0,1). Now we determine if it is a positive slope, it is as it goes up not down. It goes up 1 unit and over to the right 3 units, making the slope 1/3.
Triangle ABC is graphed in the coordinate plane.
Answer:
the answer is d
Step-by-step explanation:
just see the matching coordinates
How far did the cargo ship travel in one hour?
a
The ship travels 50 nautical miles in 1 hour.
b
The ship travels 25 nautical miles in 1 hour.
c
The ship travels 75 nautical miles in 1 hour.
d
The ship travels 100 nautical miles in 1 hour.
Answer:
needs a image not much information working with