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]
hi pls help me thanksss
pls provide me with workings thankss :)
Step-by-step explanation:
(i)
Using cos(a - b) = cos a cos b + sin a sin b
[tex]\frac{4}{5}[/tex] = cos a cos b + [tex]\frac{1}{5}[/tex]
cos a cos b = [tex]\frac{4}{5} -\frac{1}{5} = \frac{3}{5}[/tex]
(ii)
Using cos(a + b) = cos a cos b - sin a sin b
cos(a + b) = [tex]\frac{3}{5}-\frac{1}{5}=\frac{2}{5}[/tex]
(iii)
Using cot a = [tex]\frac{cos a}{sin a}[/tex]
[tex]=(\frac{cos A}{sin A} )(\frac{cos B}{sin B} )[/tex]
[tex]=\frac{cos A cos B}{sin A sin B}[/tex]
[tex]=\frac{\frac{3}{5} }{\frac{1}{5} }[/tex] [tex]=\frac{3}{5}[/tex] × [tex]5[/tex]
= 3
please give me a brainliest answer
PLEASE HELP complete the construction a perpendicular line to segment AB through point P.
Answer:
.
Step-by-step explanation:
sorry i can't help
PLEASE HELP MEE!!! I WILL GIVE YOU THE BRAINLIEST
Answer:
Domain (-infinity, infinity) Range (-4, infinity)
Step-by-step explanation:
look at the x axis. the graph is going forever out, so infinity.
now look at the y axis. where does it stop? -4. you might need to use [ instead of ( when answering your problem (that just means including) hope this helps!
X+2x-5+6= 0 How would you picture model this to solve for x?
Hey there!
x + 2x - 5 + 6 = 0
1x + 2x - 5 + 6 = 0
3x + 1 = 0
SUBTRACT 1 to BOTH SIDES
3x + 1 - 1 = 0 - 1
CANCEL out: 1 - 1 because that gives you 0
KEEP: 0 - 1 because that helps solve for the x-value
0 - 1 = -1
NEW EQUATION: 3x = -1
DIVIDE 3 to BOTH SIDES
3x/3 = -1/3
CANCEL out: 3/3 because that gives you 1
KEEP: -1/3 because it gives you the value of x
SIMPLIFY IT
x = -1/3
Therefore, your answer is: x = - 1/3
Good luck on your assignment and enjoy your day!
~Amphitrite1040:)
PLEASE HELP!!
Josh works for MooMoo Milkshakes. The company wants to know what milkshake flavor is the most popular. Today, he surveyed
every third female customer on their favorite milkshake flavor. Eighteen customers
(out of 60 total) were surveyed, and 7 customers
prefer MooChooChocolate, 5 customers prefer VeryStrawberry, and 6 customers prefer BananaBoBanna.
What type of sampling is demonstrated in the situation above?
A. census
B. random sampling
C. negative sampling
D.convenience sampling
Answer: random sampling
Step-by-step explanation: Random sampling is where each member of the sample is randomly selected from the population. Since Josh chose every third female customer, he randomly chose the sample.
Answer: B random sampling .
Step-by-step explanation:
(95^5)(92^2) =
A)
9
B)
910
C)
187
D)
1810
Answer:
I think it is C it is guss A company makes a profit of $1.38 million. This is $2.54 million more than last year. What was the profit last year?
The answer also asks for us to fill in the blank; "The profit last year was $__ million, so I need help filling in the blank.
The "million" part is already taken care of by your teacher.
====================================================
Explanation:
x = profit last year (millions of dollars)
x+2.54 = profit this year, which is 2.54 million more than last year
x+2.54 = 1.38
x = 1.38-2.54
x = -1.16
The profit last year was -1.16 million dollars
This is the same as writing -1,160,000 dollars of profit.
A negative profit indicates that the company lost money. This is when the company is spending more than what they earn (i.e. they are in some kind of debt).
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
Two way tables!! Help!!!!
( only the bottom one )
Answer:
The answer is photo.
Step-by-step explanation:
So:
167 - 66 = 101
So the total of Spain is 101
Now what is Marc’s value for Spain?
33 + 40 = 73
101 - 73 = 28
Marc’s value is 28.
Elli’s value for Portugal is unknown. We know Elli’s total is 57 and her value for Spain is 40. So: 57 - 40 = 17.
Elli’s value for Portugal is 17.
Now what is Marc’s total?
We know Spain is 28 and Portugal is 24. So add them:
28 + 24 = 52
Marc’s total is 52.
Now, what is Raisa’s total. We everyone else’s total and we know it all adds up to 167 so:
57 + 52 = 109
167 - 109 = 58
Raisa’s total is 58.
What is her Portugal value?
58 - 33 = 25
Her Portugal value is 25.
(Factorials)
Solve 5!
_help please_
Answer:
5*4*3*2*1= 120
you multiply each number to it's previous one till you reach 1
I've tried everywhere to get this answerrrrr ill give brainliest for the correct answer mate!!
Answer:
list out some of the difference between Mendeleev periodic table modern periodic table plz give ans
Please
Helppp!!
Geometry
Answer:
m∠6 = 54°
Hope this helps!
Step-by-step explanation:
( 13x+9 ) and angle 4 are congruent meaning the same. That means angles 5 and 8 are also congruent to ( 13x + 9 ).
Angle 5 or angle 8 are Supplementary to angle ( 5x + 9 ) so a Supplementary angle is 180° and we need to find out x. ( 13x + 9 ) + ( 5x + 9 ) = 18x + 18.
Because Supplementary angles equal 180°, 18x + 18 = 180
18x = 162 x = 162/18 x = 9
Because ∠6 is congruent to angle ( 5x + 9 ), ∠6 = ( 5(9) + 9 )
∠6 = 45 + 9 ∠6 = 54
can someone please help me with this
Answer:
Perimeter = 18m
Area = 18m²
Step-by-step explanation:
On a rectangle, opposite sides have equal lengths. This means to find the perimeter you would do (3 × 2) + (6 × 2) which is 6 + 12 = 18
The perimeter is 18m
To find the area, you would do length × width. The length is 6 and the width is 3 so 6 × 3 is 18
The area is 18m²
Hope this helps!
PLEASE ANSWER I NEED HELP LOTS OF POINTS
Answer:
blank 1 = 4
blank 2 = -5
blank 3 = -1
Step-by-step explanation:
A salesperson earns a base salary of $400 per week plus 20%
commission on sales. He is offered double his base salary if he'll
accept half his original commission. Graph and label the original deal
and the new deal below. Next to the graph, find when the original deal
is a better choice. Explain your thinking.
Answer:
(Hope this helps can I pls have brainlist (crown)☺️)
Step-by-step explanation:
For how to graph this, best to look at the guidelines for graphing a break-even formula.
What we do want to know is where these two values equal each other.
So, set: 400 + 0.20X = 800 + 0.10X
Subtract 400 from both sides; also subtract 0.10X from both sides, to get:
0.10X = 400
To solve for "X", divide out both sides by: 0.10, to get:
X = 4,000
What can can glean from this, is that:
(1) The sales person is better off accepting the higher base salary, up to the point of sales being no more than $4,000;
(2) The sales person is better off accepting the lower base salary, if their sales are normally expected to exceed $4,000.
PLEASE HELP WE DON'T KNOW THE ANSWERS AND WE ARE ALL FAILING THIS CLASS PLS HELP//// I would like to thank you for helping us so much we greatly apricate this.
Answer:
leave unknown variables alone on one side. throw the numbers to the other side of the equation by changing sign
Confused ;-; please help me
Answer:
1)sss
2)asa
3)sas
Step-by-step explanation:
hope this helps
write the volume of a cylinder with a base radius 3 m and height 8 m in terms of pi
Show your work and leave your answer it terms of pi
Answer:
72π (in terms of pi)
Step-by-step explanation:
V = π·r²·h
Plug in the values.
V = π·3²·8
Solve.
V = 72π
To leave an equation in terms of pi, just square, multiply, and leave pi at the end.
3² = 9·8 = 72
72π
If you need the answer fully simplified, it is 226.19 (rounded up).
PLEASE HELP what is the next term what is A in the sequence and what is the common ratio for 2 4 8 16 32
Answer:
The next term is 64, a is 2, and the common ratio is 2.
Step-by-step explanation:
Look at what's happening from each number to the next. What do you need to do to get from 2 to 4, or 4 to 8? Multiply by 2. That's your common ratio. To get the next number in the sequence, multiply the last number by the common ratio of 2. 32 x 2 = 64, so the next number in the sequence is 64. "a" is just the very first term, meaning it's 2.
8 liters is the same as how many gallons? round anwer to the nearst tenth
Answer:
3.785, but rounded to the nearest tenth is 3.8
Step-by-step explanation:
Hope this helps!
Answer 1,76211454 gallons
Step-by-step explanation: if you are in the UK , 1 gallon = 4,54 liters , in America is 3,78
Which graph represents the piecewise-defined function f(x) = { -x + 4, 0 ≤ X< 3
6,
X ≥ 3
9514 1404 393
Answer:
(d)
Step-by-step explanation:
The second line of the function is ...
f(x) = 6, x ≥ 3
This tells you that portion of the graph is the horizontal line y = 6, extending to the right from x = 3, and that there will be a solid dot at (3, 6).
This shows only on the attached graph.
Answer:
4th graph
Step-by-step explanation:
Robin earned $4,581 in 9 weeks. How much does he earn per week?
Answer:
$509 per weekStep-by-step explanation:
Well, in order to find the unit rate we simply do the following steps:
4,581 ÷ 9 = 509
So to answer the question, each week Robin earns $509.
Hope this helps! : )
Answer:
they earn 509 a week
Step-by-step explanation:4581 divided by 9
hi can anyone help with this question thx
first part of the question is in the pic
second part is here and it is:
York to London is a distance of 175miles
How many miles an hour faster was the first part of the journey?
Answer:
88 miles per hour
Step-by-step explanation:
12 + 122 = 134 minutes for the entire journey
The total distance was 197 miles.
The avarage speed is the total distance divided by the total time:
Convert the time from minutes to hours dividing it by 60:
134/60 = 2.24 hours
197/2.24 = 87.95 ≈ 88 miles per hour
please if you can i urgently need help thank you very much
Answer:
1/4
Step-by-step explanation:
2^7/2^9 = 1/2^2
Find the measures of a right triangle with one angle whose measure is 30
Answer:
The other measure is 60º
Step-by-step explanation:
a triangle= 180º total
a right triangle has one 90º angle
there is a 30º angle given
180-90=90
90-30=60
so 60º
PLS HELP WILL MARK BRAINLIEST
Represent the following algebraically
Answer:
width = (21 - 2n) ÷ 2 or 21/2 - n
Step-by-step explanation:
To find Width
let's say width is x
so 2x + 2n = 21
take away 2n from both sides
then 2x = 21 - 2n
Divide both sides by 2 to get x on its own
x = 21 - 2n /2
therefore the width of the rectangle is 21 - 2n /2
A diver descends at an average speed of 10.4 m/min. Use rational numbers to write her depth after 3.6 min.
Answer: it’s just 2.89 there’s nothing else to it
Marc solves the equation Latex: (\sqrt[4]{x})^3=5\textsf{.} His work is shown below. Step 1: Latex: (\sqrt[4]{x})^3=5 ( √ [ 4 ] x ) 3 = 5 Step 2: Latex: x^{\frac{3}{4} }=5 x 3 4 = 5 Step 3: Latex: x^{\frac{3}{4} \cdot \frac{4}{3} }=5^{\frac{4}{3} } x 3 4 ⋅ 4 3 = 5 4 3 Step 4: Latex: x=\sqrt[3]{5 \cdot 5 \cdot 5 \cdot 5} x = √ [ 3 ] 5 ⋅ 5 ⋅ 5 ⋅ 5 Step 5: Latex: x=5\sqrt[3]{\not{5} \cdot \not{5} \cdot\not {5} \cdot 5} x = 5 √ [ 3 ] ¬ 5 ⋅ ¬ 5 ⋅ ¬ 5 ⋅ 5 Step 6: Latex: x=5\sqrt[3]{5} x = 5 √ [ 3 ] 5 Explain what Marc did in steps 4 and 5. Why did he do this? Create your own radical equation and explain how to solve it. Is there an extraneous solution to your equation?
Based on the calculation, we can say that there is an extraneous solution to the equation
Given the equation solved by Marc expressed as:
[tex](\sqrt[4]{x})^3=5[/tex]
We are to check if the indices equation has an extraneous equation.
According to the law of indices [tex](\sqrt[n]{m} )^a=m^{\frac{a}{n} }[/tex], the expression becomes:
[tex](\sqrt[4]{x})^3=5\\x^\frac{3}{4}=5\\[/tex]
Raise both sides to the power of 4/3 as shown:
[tex](x^\frac{3}{4} )^\frac{4}{3} = 5^\frac{4}{3}\\x^1 = 5^\frac{4}{3}\\x = 5^\frac{4}{3}\\[/tex]
This shows that there is an extraneous solution to the equation
Learn more here: https://brainly.com/question/12232011
need help pls thx..........
Answer:
170 degree. is the answer
Find f(x) if it is known that f(x-2)=2x-4
Answer:
f=2
Step-by-step explanation:
f(x-2)=2x-4
divide x-2 to 2x-4
f=2
f(2-2)=4-4