rounding 0.0692494 to 3SF is 0.069
Let $z$ and $w$ be complex numbers satisfying $|z| = 5, |w| = 2,$ and $z\overline{w} = 6+8i.$ Then enter in the numbers \[|z+w|^2, |zw|^2, |z-w|^2, \left| \dfrac{z}{w} \right|^2 \]below, in the order listed above. If any of these cannot be uniquely determined from the information given, enter in a question mark. Don't even know where to start.
I got 49 for the first one, 100 for the second one, 9 for the 3rd one, and 6.25 for the 4th one. But it was wrong, so I don't know how to do this question.
Answer:
1st entry: 41
3rd entry: 17
Step-by-step explanation:
The 1st and 3rd entry are incorrect.
We will use the following for the 1st and 3rd:
[tex]|z+w|=|z|^2+|w|^2+2R(z\overline{w})[/tex]
[tex]|z-w|=|z|^2+|w|^2-2R(z\overline{w})[/tex]
where [tex]R(z\overline{w})[/tex] means 'real part of [tex]z\overline{w}[/tex]'.
Let's do part 1 now)
25+4+2(6)
29+12
41
Let's do part 3 now)
25+4-2(6)
29-12
17
Identify the least common multiple of:
(x + 1), (x - 1), & (x^2 - 1)
Given:
The expressions are [tex](x+1),\ (x-1)[/tex] and [tex](x^2-1)[/tex].
To find:
The least common multiple of given expressions.
Solution:
The expressions are [tex](x+1),\ (x-1)[/tex] and [tex](x^2-1)[/tex]. The factor forms of these expressions are:
[tex](x+1)=1\times (x+1)[/tex]
[tex](x-1)=1\times (x-1)[/tex]
[tex](x^2-1)=(x-1)(x+1)[/tex] [tex][\because a^2-b^2=(a-b)(a+b)][/tex]
The least common multiple is the product of all distinct factors with its highest degree. So,
[tex]L.C.M.=1\times (x+1)\times (x-1)[/tex]
[tex]L.C.M.=(x+1)(x-1)[/tex]
[tex]L.C.M.=x^2-1^2[/tex] [tex][\because a^2-b^2=(a-b)(a+b)][/tex]
[tex]L.C.M.=x^2-1[/tex]
Therefore, the least common multiple of given expressions is [tex]x^2-1[/tex].
I need the answers and it's due today, please help
Answer:
1. 3
2. 1
3. 2
4. 4
5. 5
Step-by-step explanation:
In the given figure alongside,prove that
Triangle ABC is simalar to Triangle SRT
Find the length of AC
Answer:
let's use Pythagoras theorem,
h²=b²+l²
so,
ad²=ac²+dc²
6²=ac²+3²
36-9=ac²=27
√27 can be written as 3√3,
hence ac= 3√3
Given that X = - 2 and y = 4 , Evaluate the expression. 5y – 4x
Answer: 28
Step-by-step explanation: 5(4)-4(-2) which is 20+8 and that is 28.
Use the figure below, If m
Answer:
m anglw ABD answers is 50 degree
A rectangle measures 15 cm by 10 cm is given, if the length of side is
increased by 20%, find the increase of area in percentage.
Answer:
20 % increase in Area
Step-by-step explanation:
1. Original Rectangle Area = 150cm ²
2. 20% of 15 is 3
3. Increased length is equal to 18
4. Increased Rectangle Area = 180cm ²
5. Ten percent of 150 = 15.
6. 15x2(ten percent) = 30. Which give us 150+30 equal to 180.
7. 2 ten percent equals 20%
8. Answer is 20%.
Put these numbers in order from least to greatest.
1/8,1/2,0.13, and 7/8
Answer: 1/8, 0.13, 1/2, 7/8
Step-by-step explanation: Mental Math
Step-by-step explanation:
0.13,1/2,1/8,and 7/8
hope it is helpful to you
What percent does a lender generally look for when considering the debt-to-income (DTI) ratio of a loan applicant?
a. less than or equal to 36%
b. less than or equal to 42%
c. less than or equal to 50%
d. less than or equal to 72%
Please select the best answer from the choices provided
A. B. C. D.
Answer:
A
Step-by-step explanation:
less than 36% seems fine
Answer:
A
Step-by-step explanation:
Math a challenging subject, sigh...
Name the polygon with seven sides_____
a polygon with seven sides is called a heptagon
Answer:
Hyptagon
Step-by-step explanation:
In geometry, a heptagon is a seven-sided polygon or 7-gon.
The heptagon is sometimes referred to as the septagon, using "sept-" (an elision of septua-, a Latin-derived numerical prefix, rather than hepta-, a Greek-derived numerical prefix; both are cognate) together with the Greek suffix "-agon" meaning angle.
Which formula gives the coordinates of the midpoint of the segment connecting points (u, v) and (s, 6,t),
Answer:
[tex](\frac{u+s}{2} , \frac{v+t}{2} )[/tex] (the first option)
Step-by-step explanation:
The midpoint of a segment connecting two points [tex](x_1, y_1)[/tex] and [tex](x_2,y_2)[/tex] can be described by the following formula: [tex]\frac{x_1 + x_2}{2} = x_{mid}[/tex] and [tex]\frac{y_1 + y_2}{2} = y_{mid}[/tex]. As you can see, the formula essentially takes the average of the x- and y-coordinates to find the point in the middle.
With points (u, v) and (s, t), the midpoint becomes [tex](\frac{u+s}{2} , \frac{v+t}{2} )[/tex] (the first option).
Will give branliest
Find l.
l= [?] in
Find angle C!!!!! See the image below! I need this answer fast
Answer:
55
Angle C is a inscribed angle of the of Arc Ba.
CA is the diameter so that means Arc BA equal 110 becuase
110+70=180.
Angle C is half of Arc BA so Angle C is
[tex]55[/tex]
Help ASAP please thank u
Answer:
(A). F(x) = (x+1)^2
Step-by-step explanation:
If you replace x with the values of the axis, you get all the coordinates of the graph.
If this helps you, please give brainliest!
Suppose the hypotenuse of a right triangle is 13 cm and one of the legs is 10 cm. Use the Pythagorean Theorem to find the measure of the triangle’s other leg.
Answer:
3
Step-by-step explanation:
Pythagorean rule
[tex]hyp = opp + adj \\ therefore. \\ opp = hyp - adj \\ and \\ adj = hyp - opp[/tex]
opp=13-10
opp=3
Which of these is the lowest unit price for apples? $8.00 per 10-pound bag $21.40 per 3-pound bag $4.10 per 5-pound bag $.79 per pound Click on the correct answer.
Answer:
.79 cents a pound is the lowest unit price for apples
Step-by-step explanation:
Jodi has two bank accounts. Her parents started Account A for her. It currently has $100 in it, and Jodi deposits $20 into it each month. Jodi's grandparents started Account B for her. It currently has $300 in it, and her grandparents deposit $40 into it each month.
Answer:
(f+g)(x) = 60x + 400
Step-by-step explanation:
Given :
Amount in account A:
f(x) = 20x + 100
Amount in account B :
g(x) = 40x + 300
Total amount in Account A and B:
f(x) + g(x) = (20x + 100) + (40x + 300)
(f+g)(x) = (20x + 40x) + (100 + 300)
(f+g)(x) = 60x + 400
A side of the triangle below has been extended to form an exterior angle of 129°. Find the value of x.
129° + x = 180°. [Linear pair]
=> x = 180° - 129°
=> x = 51°
Emily has pledged to start a healthy lifestyle and so she started walking to keep fit. On Monday, she walked 2/4 of a mile, and on Tuesday she walked 5/6 of a mile. How far did she walk in her first two days of exercise?
Quickkkkkk
Answer:
1 [tex]\frac{1}{3}[/tex] miles.
Step-by-step explanation:
2/4 + 5/6 = ?
We must convert these fractions to the same denominator so we can add fractions. Least common multiple of 4 and 6 is 12.
2/4 = 6/12
5/6 = 10/12
6/12 + 10/12 = 16/12
16/12 = 4/3
4/3 = 1 [tex]\frac{1}{3}[/tex]
If a triangle has one interior angle measuring 102°, what is a possible pair of measurements for the other two
interior angles
it edmentum guided notes so it has to be a writing answer
Answer:
a2+a3=78
a2 and a3 must both be positive numbers that add up to 78
so a2 = a3 = 39
a1=102, a2=39, a3=39
Step-by-step explanation:
a1=102
a1+ a2 + a3=180 (all interrior angles of a triangle add up to 180)
a2+a3=78
a2 and a3 must both be positive numbers that add up to 78
The two triangles are similar. What is the value of x? Enter your answer in the box. x = Two right triangles, one smaller than the other, back to back, so that their right angles form a straight angle. The two acute angles along the straight angle are congruent to each other. The overlapping part of the legs is labeled 12. The part of the overlapping side that extends above the smaller triangle is labeled 3. The leg of the smaller triangle that is a ray of the straight angle is labeled 3 x plus 1. The leg of the larger angle that is a ray of the straight angle is labeled 4 x.
Answer:
The two triangles are similar.
What is the value of x?
Enter your answer in the box.
x=
The value of x is 7 units.
What is Similarity of Triangles?Two triangles are said to be comparable if their two sides are in the same ratio as the two sides of another triangle and their two sides' angles inscribed in both triangles are equal.
Given :
AD = 6 units , BD = 8 units, m∠ABC = m∠DBE = 90° and
∠DEB ≅ ∠ACB
Now, AB = AD + BD
= 8 + 6 = 14 units
Now, In ΔABC and ΔDBE,
∠DBE = ∠ABC ( Each of 90° )
∠DEB = ∠ACB ( given )
So, By using AA postulate of similarity of triangles , ΔABC ~ ΔDBE
Now, proportion of the corresponding sides will be equal.
AD/ DB= BC/ BE
14/8 = 3x/ 2x-2
4x= 28
x= 7
Hence, the value of x is 7 units.
Learn more about similarity of Triangle here:
https://brainly.com/question/11923416
#SPJ6
CAN SOMEONE PLEASE ANSWER THESE TWO QUESTIONS?! I NEED HELP!
Answer:
B ; A
Step-by-step explanation:
1) The first operation that we have to do is the division
2) we have to added up the the fishes
plz answer fast i need the answers thank u
Answer:
Step-by-step explanation:
(-5 , 2) here -5 is x coordinate and 2 is y coordinate since x coordinate is negative and y coordinate is positive it lies in II quadrant.
(2 , -5) here 2 is x coordinate whereas -5 is y coordinate and siince x coordiante is positive and y coordinate is negative it lies in IV quadrant.
(x^3 - 2)(x^2 + 11)
to find the degree of polynomial first u need to factor this out
x^3(x^2 + 11) -2(x^2 + 11)
x^3 * x^2 + x^3 * 11 - 2 * x^2 - 2 * 11
x^3+2 + 11x^3 - 2x^2 - 22
x^5 + 11x^3 - 2x^2 - 22
since the highest degree is 5 the degree of the polynomial is also 5.
Step-by-step explanation:
MARK ME BRAINLIEST THANKS MY ANSWER PLEASE
Which segments have equal
lengths?
The segment that has equal length are known as congruent segment
Answer: corresponding segments
Step-by-step explanation:
Solve for b in the literal equation y = 12x + 12b.
b=
Answer:
[tex]b = \frac{y-12x}{12}[/tex]
Step-by-step explanation:
subtract 12x from both sides, then divide by twelve.
in isosceles Triangle RST below what is the value of y
Answer:
second option
Step-by-step explanation:
y + y + 38 = 180 degree ( sum of interior angle of a triangle is 180 degree)
2y = 180 - 38
y = 142/2
y = 71 degree
Answer:
71 degrees
Step-by-step explanation:
Hi there!
All the interior angles of a triangle add up to 180 degrees.
Knowing this, we can construct the following equation:
[tex]180=y+y+38\\180=2y+38[/tex]
Subtract 38 from both sides
[tex]180-38=2y+38-38\\142=2y\\71=y[/tex]
I hope this helps!
A bungee jumper leaps off a cliff 122 meters from the ground. Her cord, when fully stretched, is 72 meters long, and it takes 6 seconds after the jump for it to extend fully. The distance between e jumper and the ground as a function of time can be modeled as a quadratic function. Which equation represents her distance from the ground as a function of time?
Answer:
Answer is B.
Step-by-step explanation:
You can solve this by recognizing the vertex and the y-intercept of the quadratic equation based on the information provided.
The vertex occurs 6 seconds into the jump, when the cord is fully stretched to 72m, before it starts to contract again. This is when the jumper is closest to the ground, 122-72 = 50m above the ground. Notice the jumper never reaches the ground because the cord is only 72m long - it can't make it the full 122m - so there will not be an x-intercept (or t-intercept in this case). Anyway - the vertex is (6,50) using this information.
The y-intercept is the point at which t=0, the beginning of the jump. At the beginning of the jump, the jump is still on top of the cliff, 122m up. So the coordinates of the y-intercept are (0,122).
Now plug these values into the vertex form of the quadratic formula and solve for a:
[tex]f(t) = a(t-h)^2+k\\122=a(0-6)^2+50\\72 = 36a\\a=2[/tex]
This means our general equation (in vertex form) for this scenario is:
[tex]f(t)=2(t-6)^2+50[/tex]
Our answer options are in standard form, so just expand the vertex form of the equation to finish:
[tex]f(t)=2(t-6)^2+50\\f(t)=2(t^2-12t+36)+50\\f(t)=2t^2-24t+72+50\\f(t)=2t^2-24t+122[/tex]
the pythagorean theorem equation
Answer:
(Altitude)^2+(Base)^2=(Hypotenuse)^2
write a linear equation in one variable for each of the following situations:
Answer:
i. y = 4
ii. p = 45
iii. m = 5
Step-by-step explanation:
(a) In triangle PQR, PQ = QR. So that,
Perimeter = PQ + PR + QR
40 = (2y + 3) + (5y - 2) + (2y + 3)
= 2y + 3 + 5y - 2 + 2y + 3
40 = 9y + 4
40 - 4 = 9y
36 = 9y
y = [tex]\frac{36}{9}[/tex]
y = 4
(b) The age of Rahim's father is p years. Since he is 29 years older than Rahim, we have;
p = 16 + 29
p = 45
Rahim's father is 45 years old.
(c) Cost of a chair = RM 5.90
Cost of m chairs = RM 5.90 x m
= RM 5.90m
Amount paid = RM 50 - RM 20.50
= RM 29.50
Thus,
RM 5.90m = RM 29.50
5.90m = 29.50
m = [tex]\frac{29.50}{5.90}[/tex]
= 5
m = 5
The number of units of chairs bought is 5.
