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]
Solve for b in the literal equation a+ b+ c= 180
Answer:
b = 180 - a - c
Step-by-step explanation:
To solve for b given the literal equation, a + b + c = 180:
Subtract a and c from both sides:
a + b + c = 180
a - a + b + c - c = 180 - a - c
b = 180 - a - c
What is cos(45°)?
45°
1
Cos (459) = VI?
[]
COS
=
Hint: Remember to rationalize the denominator.
Answer:
[tex]\rm \dfrac{\sqrt2}{2}[/tex]
Step-by-step explanation:
A right angled ∆ is given to us and we need to find out the value of cos 45° ( with rationalized denominator ) . As we know that in a right angle ∆ , the value of cosine is ,
[tex]\rm\implies cos\theta =\dfrac{base}{hypotenuse} [/tex]
In the given triangle ,
Value of base = 1 Value of hypotenuse = √2On substituting the respective values ,
[tex]\rm\implies cos45^\circ =\dfrac{1}{\sqrt2} [/tex]
For rationalizing the denominator , multiply numerator and denominator by √2 , we have,
[tex]\rm\implies cos45^\circ=\dfrac{1(\sqrt2)}{(\sqrt2)(\sqrt2)} [/tex]
Simplify ,
[tex]\rm\implies \boxed{\pink{\frak{ cos45^\circ=\dfrac{\sqrt2}{2} }}}[/tex]
3 (n+1) - 5 = 3n - 1
I need help with this question
Answer:
There are no solutions.
Step-by-step explanation:
3(n+1) = 3n+3.
3n+3-5 = 3n-2.
3n-2 doesn't equal 3n-1, so there are no solutions.
Dilations of a triangle are congruent to the original triangle. true or false
Answer true
Step-by-step explanation:
true
Please help, I’ll mark your answer as brainliest!
Hooke’s Law for an elastic spring states that the distance a spring stretches varies directly as the force applied. If a force of 180 newtons stretches a spring 5 cm, how much will a force of 270 newtons stretch the same spring?
Will give Brainliest :)
Answer:
7.5m
:) hoped this helped!
Step-by-step explanation:
Find the slope of the line passing through each of the following pairs of points and draw the graph of the line. (-2,3), (5, 5)
There isn't any graph example but I need help!!! i will award 10 brainiest
Answer:
Slope: 2/7
Step-by-step explanation:
y2 - y1/ x2 - x1 = 2/7
Help please ill mark brainliest!
The polygon is 5 units in length and not 4
so using the given formula P = 2l + 2w
(2 x 5) + (2 x 3)
10 + 6
= 16 units
Jaylo bought a television priced at $349. She received a 20% discount and paid a 7% sales tax. What is the total price of the television? A. $74.69 B. $298.74 C. $348.87 D. $448.12
Answer:
B
Step-by-step explanation:
349 ---100%
x ------ 20%
x= (349×20)÷100
x=69.8
349-69.8=279.2
279.2 ---100%
x-----7%
x=(279.2×7)÷100
x=19.54
Final result
279.2+19.54=298.74
And final result is B
The total price of the television is B. $297.74
Given that,
Jaylo bought a television priced at $349. She received a 20% discount and paid a 7% sales tax.Based on the above information, the calculation is as follows:
[tex]= (\$349 \times (1- 0.20) + \$349 \times (1- 0.20) \times 0.07)\\\\= \$279.20 + \$19.544[/tex]
= $297.74
Learn more: brainly.com/question/17429689
If 35 cycles were produced in 5 days by a company then how many cycles will be produced in 21 days.
Answer:
126
Step-by-step explanation:
35/5 = 6.
6 is the number in 1 day
6x21=126
126 is the number in 21 days
Hope that helps
If someone could help me I would mean a lot man.
Use the equation for the constant of proportionality, k =y/x, to determine each unknown value.
a. k = and y = 15
b.k = 1 and y = 5
Answer:
a k= and y=15
B . k=1 and y=5
I went to the movies and bought 4 tickets. It cost me 23 dollars for the tickets after I applied my 5 dollar Tuesday discount. Create an equation for this situation where x is cost of each ticket. How much did each ticket cost? (answer asap pls)
Answer:
x= 5.75$
Step-by-step explanation:
23 divided by 4 = 5.75$ (without the discount it is 10.75$)
Answer:
each ticket=$7.
x=7
Step-by-step explanation:
The total price of your tickets AFTER applying your $5 discount was 23.
Therefore, the price of 4 tickets would be 23+5, aka 28.
We can first begin with,
4x-5=23
4x=23+5
4x=28
x=7.
First one to answer will be marked brainliest
Answer:
the ans is..... 10.75 km......
5. The two figures are scaled copies of each other.
a. What is the
scale factor that
takes Figure 1
to Figure 2?
e
P
ס
R
С
A
A
b. What is the
scale factor that
takes Figure 2.
to Figure 1?
D
Figure 1
Figure 2
S
The quadrilaterals are similar and are related by a scale factor, taken from
a specific location, that maps the points on one figure to the other.
a. The scale factor that takes Figure 1 to Figure 2, is 3
b. The scale factor that takes Figure 2 to Figure 1 is [tex]\dfrac{1}{3}[/tex]
Reasons:
From the question, we have that Figure 1 is a scaled copy of Figure 2, therefore;
Let ABCD represent Figure 1, we have;
ABCD ~ PQRS
Length of [tex]\overline{AD}[/tex] = √(2² + 3²) = √(13)
Length of [tex]\overline{PS}[/tex] = √(6² + 9²) = √(117) = √(9 × 13) = 3·√(13)
Therefore;
a. The scale factor that takes Figure 1 to Figure 2, SF₁₂, is therefore;
[tex]SF_{12} = \mathbf{\dfrac{\overline{PS}}{\overline{AD}}}[/tex]
Which gives;
[tex]SF_{12} = \dfrac{3 \cdot \sqrt{13} }{\sqrt{13} } = 3[/tex]
The scale factor that takes Figure 1 to Figure 2, SF₁₂ = 3
(3 times the lengths of Figure 1 gives the lengths on Figure 2)
b. The scale factor that takes Figure 2 to Figure 1, SF₂₁, is given as follows;
[tex]SF_{21} = \mathbf{\dfrac{\overline{AD}}{\overline{PS}}}[/tex]
Which give;
[tex]SF_{21} = \dfrac{\sqrt{13} }{3 \cdot \sqrt{13} } = \mathbf{\dfrac{1}{3}}[/tex]
The scale factor that takes Figure 2 to Figure 1, SF₂₁ is [tex]\underline{\dfrac{1}{3}}[/tex]
Learn more here:
https://brainly.com/question/17207164
What is the value of x
Can you use the perpendicular bisector theorem to solve for RS?
a)yes
b)no
two complementary angles are in a ration of 2 3 find the measure of each angle
A complementary angle is 90 degrees. The ratio is 2:3 so the equation would be:
2x+3x=90
5x=90
x=18
One of the angles would be 2(18) or 36 degrees and the other angle would be 3(18) or 54 degrees.
36+54 is equal to 90 degrees so it checks out.
which sentence from this introduction paragraph is most clearly providing background
Answer:
sentence 2?
Step-by-step explanation:
sentence 1 provides background for the question, sentence 2 provides background for the graph, and sentence 3 is the question.
If you wanted the answer to the question:
8:4 = 2:1
x ft
x ft
Bedroom
5 ft
Closet
5 ft
6 ft
Bathroom
Answer:
bedroom is 12ft which is equal to 6ft on left of bathroom if we add 6 +6=12 because it is rectangle and bathroom is square and square have 4 equal sides so both sides are 12ft
*Will Give Brainliest Answer Please Help*
Find a quadratic equation that models the situation, and use it to solve the problem. Show your work..
Two square shaped swimming pools need to be constructed by the local civic body for athletes training. The difference between the perimeters of the two pools is 16 ft. If the sum of the areas of the two pools is 730ft^2 , find the side length of the smaller pool.
Answ
tep-by-step explanation:
2. What is the value of the pass after 15 rides?
# of Rides Bus Pass Value Rule
0 $100.00
1 $98.25
2 $96.50
3 $96.75
15 ??? $73.75 ??? Is my answer 73.75 right? If not does anyone know the correct answer
!plz help!
Answer:
im really confused. but its 2,75$ per pass?/ride? sorry i cant help much
Step-by-step explanation:
Answer choice B is incorrect
Answer:
i'd say C, reason being is because the origin is not directly on the point, so the dilation moves up 1.5
Step-by-step explanation:
Complete the square:
x2 - 6x + 9=-13+ blank
Answer:
to complete the square, you add (b/2)^2 on both side. in this case, b is -6, half of -6 is -3, -3 squared is 9, so:
x^2-6x+9=-13+9
(x-3)^2=-4
This quadratic equation have unreal solutions
Step-by-step explanation:
Answer:
Step-by-step explanation:
To complete the square, divide the coefficient of x by 2.
6 /2 = 3
Take square of 3 and add to both sides
3*3 = 9
x² - 6x + 9 = -13 + 9
x² - 6x + 9 = -4
(x - 3)² = -4
Which number line represents the solution set for the given inequality?
x + 1 ≤ -3 or -4x < -8
The solution to the system of equations is x≤ -4 and x > 2. Find the number line attached below:
Given the set of inequalities expressed as;
x + 1 ≤ -3 or -4x < -8
For the inequality expression x + 1 ≤ -3
x ≤ -3 - 1
x ≤ -4
For the inequality expression:
-4x < -8
Divide both sides by -4
-4x/-4 > -8/-4
x > 2
Hence the solution to the system of equations is x≤ -4 and x > 2. Find the number line attached below:
Learn more here: https://brainly.com/question/15816805
May I please receive help?
Parallel lines have the same slope, while perpendicular lines have an opposite reciprocal slope.
Line 1:
-5y = 3x + 7
y = -3/5x - 7/5
Line 2:
y = -5/3x + 8
Line 3:
6x - 10y = -4
-10y = -6x - 4
y = 3/5x + 2/5
Line 1 and Line 2 are neither perpendicular nor parallel. While their slopes are reciprocals of each other, the signs are not opposite (both are negative).
Line 1 and Line 3 are neither perpendicular nor parallel. While the slope itself is the same, the signs are different.
Line 2 and Line 3 are perpendicular. Their slopes are opposite reciprocals of each other.
Hope this helps!! :)
Please could I have some help with this question? Thanks
Answer: 270
Step-by-step explanation:
1) Find DE
1 : 6
17 : x
Cross multiply
x = 17 * 6
x = 102
DE = 102
2) Compare the two triangles
1st (ABC)
side = 45
base = 17
2nd (ADE)
side = x
base = 102
[tex]\frac{x}{45} = \frac{102}{17}[/tex]
Cross multiply
17x = 102 x 45
17x = 4590
x = 4590/17
x = 270
AD = 270
which technolgy is nasa devloping that will help astronaughts reach mars?
Answer:
The Mars 2020 rover mission has major new technologies that improve entry, descent, and landing: Range Trigger, Terrain-Relative Navigation, MEDLI2, and its EDL cameras and microphone.
Step-by-step explanation:
I hope this will help you
HELLOPPPPPPPPPPP PLEASEEE GEOMETRY
Answer:
the answer is low of contrapositive
Mary got a rectangular box. If the perimeter is 82cm and the length is 23cm, what is the
width of the box?
Answer:
w = 18cm
Step-by-step explanation:
Using the formula
P = 2 (l + w)
Solving for w
w = P
2﹣l = 82
2﹣23 = 18cm
please someone HELP I NEED TO GO TO BED SOON PLEASE GIVE ME ANSWER PLEASEE
a) Describe in words the pattern relationship.
b) Write a rule to describe the pattern shown.
c) If the table had an input of 7, what would be the output?
d) If the table had an output of 31, what would be the input?
Answer:
a. For every +1 input in x, y goes up 4 times plus 7.
b. y= 4x+7
c. 35
d. 6
Step-by-step explanation:
How to do c.
y=4x+7
y=4(7)+7
y=35
How to do d.
y=4x+7
31=4x+7
24=4x
x=6