Step-by-step explanation:
[tex]\large\underline{\sf{Solution-}}[/tex]
Consider,
[tex]\rm \longmapsto\:\dfrac{ \sqrt{7} + i \sqrt{3} }{ \sqrt{7} - i \sqrt{3}} + \dfrac{ \sqrt{7} - i \sqrt{3} }{ \sqrt{7} + i \sqrt{3} } [/tex]
On taking LCM, we get
[tex]\rm \: = \: \dfrac{ {( \sqrt{7} + i \sqrt{3})}^{2} + {( \sqrt{7} - i \sqrt{3})}^{2} }{( \sqrt{7} + i \sqrt{3})( \sqrt{7} - i \sqrt{3})} [/tex]
We know,
[tex] \purple{\rm \longmapsto\:\boxed{\tt{ {(x + y)}^{2} + {(x - y)}^{2} = 2( {x}^{2} + {y}^{2})}}} \\ [/tex]
and
[tex] \purple{\rm \longmapsto\:\boxed{\tt{ (x + y)(x - y) = {x}^{2} - {y}^{2} \: }}} \\ [/tex]
So, using these Identities, we get
[tex]\rm \: = \: \dfrac{2\bigg[ {( \sqrt{7})}^{2} + {(i \sqrt{3}) }^{2} \bigg]}{ {( \sqrt{7}) }^{2} - {(i \sqrt{3})}^{2} } [/tex]
[tex]\rm \: = \: \dfrac{2(7 + 3 {i}^{2})}{7 - {3i}^{2} } [/tex]
We know,
[tex] \purple{\rm \longmapsto\:\boxed{\tt{ {i}^{2} = - 1}}} \\ [/tex]
So, using this, we get
[tex]\rm \: = \: \dfrac{2(7 - 3)}{7 + 3} [/tex]
[tex]\rm \: = \: \dfrac{2 \times 4}{10} [/tex]
[tex]\rm \: = \: \dfrac{4}{5} [/tex]
Hence,
[tex] \red{\rm\implies \:\boxed{\sf{ \dfrac{ \sqrt{7} + i \sqrt{3} }{ \sqrt{7} - i \sqrt{3}} + \dfrac{ \sqrt{7} - i \sqrt{3} }{ \sqrt{7} + i \sqrt{3} } \: is \: purely \: real}}}[/tex]
=
The length of a rectangular room is 15 feet longer than the width. If the room's perimeter is 250 feet,
what are the room's dimensions?
Width = 70 ft; length = 280 ft
Width = 55 ft; length = 70 ft
Width = 70 ft; length = 35 ft
Width = 55 ft; length = 220 ft
Answer:
B. Width = 55ft; length = 70ft
Step-by-step explanation:
it is the only one in which the length is 15 ft longer than that of the width.
starts at 12 and ends at 6
Answer:
126
Step-by-step explanation:
i don't know if it's correct or not
Think about all the ways in which a circle and a parabola can intersect.
Select all of the number of ways in which a circle and parabola can intersect.
0
1
2
3
4
5
Answer:
3
Step-by-step explanation:
Answer:
0,1,2,3,4
Step-by-step explanation:
trustttttt meee
Brent went for a bicycle ride. The clocks show his start time and his
end time. How long did Brent ride his bicycle?
Answer:
He rode his bicycle for 40minutes
Hope it helps:)
Suppose that the average speed of cars on a busy section of a local highway was normally distributed with a mean of 65 mph and standard deviation of 4 mph. What is the probability that the speed of a random car in this data set was less than 53 mph?
0.025
0.0015
0.16
0.475
==================================================
Explanation:
mu = 65 = population meansigma = 4 = population standard deviationLet's convert x = 53 to its corresponding z score
z = (x-mu)/sigma
z = (53-65)/4
z = -12/4
z = -3
This indicates we're 3 standard deviations below the mean.
Recall that the Empirical Rule states that roughly 99.7% of the data items in a normal distribution are within 3 standard deviations of the mean. That leaves 100% - 99.7% = 0.3% outside this range. This small percentage is the combined percentage in both tails. Take half of this to find the amount in the left tail only.
(0.3%)/2 = 0.15%
This then converts to 0.0015 when we move the decimal point 2 spots to the left.
Are the triangles congruent?
-yes by SSS
-yes by SAS
-yes by ASA
-yes by AAS
-yes by HL
Answer:
yes by SAS
it is Side angle Side
do all number lines show only whole number
Answer:
no
Step-by-step explanation:
no because some numbers could be negative and most number lines also contain 0. whole numbers are positive, non decimal/fractional, real numbers
A train decreased its speed by 72 miles hour in 12 minutes. Find the average change in speed per minute.
Answer:
6 mph
Step-by-step explanation:
The average rate of change of the speed of the train will be 6 miles per hour.
What is speed?Speed is defined as the ratio of the time distance travelled by the body to the time taken by the body to cover the distance. Speed is the ratio of the distance travelled by time. The unit of speed in miles per hour.
Given that a train decreased its speed by 72 miles per hour in 12 minutes.
As the train is reducing its speed by 72 miles per hour in 12 minutes the average rate of change of the speed will be calculated by dividing the change by the time.
Rate of change = 72 / 12
Rate of change = 6 miles per hour
Therefore, the average rate of change in the speed of the train will be 6 miles per hour.
To know more about Speed follow
brainly.com/question/6504879
#SPJ1
Can anyone help me with this question?
Answer:
13
Step-by-step explanation:
Since this is a right triangle, you can use the Pythagorean Theorem.
The side y would be the hypotenuse.
[tex]a^{2} + b^{2} = c^{2}[/tex]
Plug it in:
[tex]5^{2} + 12^{2} = y^{2}[/tex]
Isolate y:
y = [tex]\sqrt{ 5^{2} + 12^{2} }[/tex]
Solve:
y = 13
A reason improper use of netiquette can be risky is that users can
O become vulnerable to online harassment.
O access inappropriate websites.
O have their private information stolen.
O receive unwanted spam.
The answer is A, Sorry I am late but for the future people i hope this helps them :))
- Have a nice day.
The improper use of netiquette can be risky as the user can become vulnerable to online harassment.
What is cybersecurity?Protecting the online data from the digital attacks initiated by a hacker is called cybersecurity. Cybersecurity is necessary to protect the various systems, networks and programs that may contain some confidential information about any person.
Given is to identify the reason why the improper use of netiquette can be risky.
The improper use of netiquette can be risky as the user can become vulnerable to online harassment.
Therefore, the improper use of netiquette can be risky as the user can become vulnerable to online harassment.
To solve more questions on cybersecurity, visit the link-
https://brainly.com/question/27560386
#SPJ7
Todd is buying material to fence his new garden. He buys 2 strands of barbed wire and a post for every 3m of fence. Each post costs 300 dollars and barbed wire costs 20 dollars per meter. What is the shape of the largest area Todd can enclose if he spends 3000 dollars on fence material? Show your work.
fence material 268 is your answer..
M<2 = 4x +6
What is the value of X?
Answer:
Step-by-step explanation: 10 but thanks green guy
Answer:
x = 10
Step-by-step explanation:
The triangle has 2 congruent sides and is therefore isosceles, then the 2 base angles are congruent, both 67°
The sum of the 3 angles is 180° , that is
4x + 6 + 67 + 67 = 180
4x + 140 = 180 ( subtract 140 from both sides )
4x = 40 ( divide both sides by 4 )
x = 10
Which property is illustrated by the equation below?
(7+6) +4= 7+ (6 + 4)
associative property
O commutative property
distributive property
O identity property
Answer:
We conclude that the question illustrates associative property.
Find the value of X.
Answer:
X=25
Step-by-step explanation:
The angle of (x+30) is the same as the angle of 55. Simply subtract 30 from 55.
Selesaikan persamaan linear serentak berikut.
2x + y = -5
3x - 4y = 9
Answer:
(-1;-3)
Step-by-step explanation:
[tex]\left \{ {{4(2x+y)=4*(-5)} \atop {3x-4y=9}} \right. \ => \ \left \{ {{8x+4y=-20} \atop {3x-4y=9}} \right. \ => \ \left \{ {{11x=-11} \atop {2x+y=-5}} \right. \ => \ \left \{ {{x=-1} \atop {y=-3}} \right.[/tex]
Solve for n.
n + 1 = 4(n – 8)
i will give a brainliest
n + 1 = 4(n - 8)
n + 1 = 4n - 32
n - 4n = -32 - 1
-3n = -33 / : (-3)
n = 11
cho hình thang ABCD vuông tại A và D cho biết AD=20 AC=52 và BC=29 Tính độ dài AB
Answer:
https://sooddan.zendesk.com
v = u + wz, make z the subject
please solve this fast
Step-by-step explanation:
shape BCD is an isosceles triangle meaning the base angles will be the same.
CA is a straight line meaning that it is 180
the sum of angles in a triangle always is 180
so
180-36= 144
to find x you need to half 144 as it is the sum of the base angles of the isosceles triangle.
144/2= 72
x=72
the angle just below y is also 72.
as CA is a straight line,
180-72= 108 giving you the answer for y
y= 108
so to make the answer clear
x= 72
y= 108
hope that helped! :)
if you would like to give me a brainliest feel free as im nearly to the end of my goal.
5*95 math question ...................
Answer:
475
Step-by-step explanation:
the reason for this is because it just is
Marty says he would rather have –$5 than $0. Do you agree with Marty? Explain.
Answer:
No I don't agree with Marty because when or if I get more money I have to give it to the bank so lets say I earned 15 dollars I would have to give five to the bank because I owe the them but if Ii have 0 dollars I don't owe the bank money I get all the 15 dollars.
Step-by-step explanation:
Answer/Step-by-step explanation:
I disagree with Marty because If Marty would have -$5 it would mean he owns that person $5. If you don't have money you don't owe anything. If Marty would have -$5 it would mean he owns that person $5. If you don't have money you don't owe anything.
Which expression has a value between 0 and 1?
a. (1/2)^5 × (1/2)^10
b. (-3)^5
c. 4^-7 × 4^9
d. 2^2/2^-5
Answer:
a. (1/2)^5 × (1/2)^10
Step-by-step explanation:
HOPE IT HELPS YA
Solve the quadratic equation
d²-5d+6=0
Answer:
BBC
Step-by-step explanation:
Answer:
d = 6 d = -1
Step-by-step explanation:
Use displacement to factor
d²-5d+6=0
d²+d-6d-6=0
d(d+1)-6(d+1)=0
(d-6)(d+1)=0
d-6=0 or d+1=0
d = 6 d = -1
Type the missing numbers in this sequence:
-101, -105,
-109,
-117
Answer:
The answer is - 113 that is the correct answer skipping in three's and the first one is - 97
Answer:
-97, -101, -105, -109, -113, -117
Step-by-step explanation:
the order was add -4 each time
limθ→π/4 (cosθ−sinθ)/(θ– π/4)
Answer:
-√2
Step-by-step explanation:
For the typing purpose I replaced θ with n in the calculation
[tex]\lim_{n \to \frac{\pi }{4}} \frac{cos n-sin n}{\frac{\pi }{4} } ...limits L'Hopital's Rule\\= \lim_{n \to \frac{\pi }{4}} \frac{-sin n-cos n}{1 } ... plug. in . \frac{\pi }{4} \\= - sin \frac{\pi }{4} - cos \frac{\pi }{4}\\= - \frac{\sqrt{2} }{2} - \frac{\sqrt{2} }{2}\\= \frac{- 2\sqrt{2}}{2} \\= - \sqrt{2}[/tex]
10+10=? trả lời đi mà
10Answer:
10 + 10 =
Step-by-step explanation:
=20
Ted needs an average of at least 70 on his three day history tests. He has already scored 80 and 60 on two tests. What is the minimum grade Ted needs on his third.
Thank you for your assistance
Answer:
Step-by-step explanation:
To solve, we first need to know how to find the average of a group of numbers. To find the average of a group of numbers, you add all the numbers together and divide that answer by the number of numbers you have. For instance, to find the average of 1, 2, 3, 4 and 5, we would add all the numbers together, which would equal 15. We would then divide that number by 5, because there are 5 numbers total: 15/5 = 3. So the average is 3.
Now, to find the average in your problem, we need to look at what we know:
He received an 85 and 60 on two of the test scores
He needs an overall average of 70
Let's set this up in equation form:
%2885+%2B+60+%2B+x%29%2F3+%3E=+70
Now, let's get rid of our fraction on the left. We can do this by multiplying the entire equation by 3, giving us:
85 + 60 + x >= 210
Next, combine the numbers on the left, which will give us:
145 + x >= 210
Finally, subtract 145 from both sides, which will give us our answer:
145 + x - 145 >= 210 - 145 =
x >= 65
So, in order to average at least 70, he must score a 65 or higher on his third test.
What is 4 times 1 6/7. Write in the simplest form
Answer:
7 43/100
Step-by-step explanation:
4*1 6/7=4 24/7 which equals 7.43, or 7 43/100
Answer:
7 3/7
Step-by-step explanation:
4 * 1 6/7
1 = 7/7, so 1 6/7 = 7/7 + 6/7 = 13/7
4 * 13/7 = 52/7
7 can fit into 52 at most 7 times (because 7*7 is 49, and less than 52)
This leaves us with 3 left over
4 * 1 6/7 = 7 3/7
Find the slope of each line.
Answer:
Slope: - 5/2
Step-by-step explanation:
Gary had a 40% discount for car speakers. The sale price of the speakers was $96.25. What was the original price of the speakers? Round to the nearest cent.
Answer:
Step-by-step explanation:
If the price after the discount is subtracted is $96.25 then this is what you do
u times 0.40 x 96.25 which is 38.5 so since you are wanting to know what the price was before the discount you would add 38.5 to 96.25 and when you do that your answer is 134.75
but if you are just trying to get the discount from 96.25 you subtract 38.5 from 96.25
