Answer:
a) |z+w|² cannot be uniquely determined from the information provided.
b) |zw|² = [|z| × |w|]² = (4×2)² = 64.
c) |z+w|² cannot be uniquely determined from the information provided.
d) |z/w|² = [|z|/|w|]² = (4/2)² = 4
Step-by-step explanation:
z & w are complex numbers with magnitudes
|z| = 4
|w| = 2
We are the told to find
|z + w|²
|zw|²
|z - w|²
|z/w|²
Let the complex numbers be
z = x + iy
w = a + ib
|z| = √(x² + y²) = 4
|w| = √(a² + b²) = 2
|z|² = x² + y² = 16
|w|² = a² + b² = 4
z+w = (x + iy) + (a + ib) = (x + a) + i(y + b)
|z+w|² = (x + a)² + (y + b)² = x² + 2ax + a² + y² + 2by + b²
= (a² + b²) + (x² + y²) + 2ax + 2by
= |w|² + |z|² + 2ax + 2by
= 4 + 16 + 2ax + 2by
= 20 + 2(ax + by)
This cannot be determined from the information provided.
zw = (x + iy)(a + ib) = ax + i(bx + ay) - by
= (ax - by) + i(bx + ay)
|zw|² = a²x² + b²y² - 2abxy + b²x² + a²y² + 2abxy
= a²x² + b²y² + b²x² + a²y²
= a²(x² + y²) + b²(x² + y²)
= (a² + b²)(x² + y²)
= |w|² × |z|²
= 4×16
= 64
c) z-w = (x + iy) - (a + ib) = (x - a) + i(y - b)
|z-w|² = (x - a)² + (y - b)²
= x² - 2ax + a² + y² - 2by + b²
= (a² + b²) + (x² + y²) - 2ax - 2by
= |w|² + |z|² - 2ax - 2by
= 4 + 16 - 2ax - 2by
= 20 + 2(ax + by)
This cannot be determined from the information provided.
d) z/w = (x + iy)/(a + ib)
Rationalizing by multiplying numerator and denominator by (a - ib)
(z/w)= [(x + iy)(a - ib)/(a + ib)/(a - ib)]
= [ax - by + i(ay - bx)]/(a² + b²)
|z/w|² = [(ax + by)² + (ay - bx)²]/(a² + b²)²
= [a²x² + b²y² + 2abxy + b²x² + a²y² - 2abxy]/(a⁴ + b⁴ + 2a²b²)
= [a²x² + b²y² + b²x² + a²y²]/[(a² + b²)² - 2a²b² + 2a²b²]
= [(a² + b²)(x² + y²)]/[(a² + b²)²]
= [(x² + y²)/(a² + b²)]
= |z|²/|w|²
= (4/2)²
= 4
Hope this Helps!!!
Does anyone know the answer ?
Answer:
Using Piragorean Theorem:
[tex]x=\sqrt{7^2+10^2}=\sqrt{100+49}=\sqrt{149}[/tex]
Answer:
[tex]\sqrt{149[/tex]
Step-by-step explanation:
7² + 10² = 12.21²
49 + 100 = 149
Select the expression that represents the multiplicative inverse of -4. A. -(-4) B. C. 4 D. -4
Answer:
-1/4
Step-by-step explanation:
Multiplicative inverse is another word for reciprocal
It is the number you multiply by to get 1
-4 * x = 1
Divide each side by -4
x = 1/-4
x = -1/4
Answer:
- 1/4
Step-by-step explanation:
- 4 * x = 1
= - 1/4
Hope this helps!
yo pleaseee help me w these!! marking brainiest!!!
LAT QUESTION AND LAST TRY!!! WILL GIVE BRANLIEST!!!! AT LEAST TAKE A LOOK, SHARE YO SMARTNESSS!!!!!!!! PLS
12. ___________________ lines cross at a right angle.
A) Parallel
B) Slanted
C) Intersecting
Answer:
The answer is A, parallel.
Step-by-step explanation:
Answer:
A
Step-by-step explanation:
took the test
Pamela and her friend Nicole are each baking apple pies and tarts for a bake sale, using the same recipes. Pamela baked 5 apple pies and 7 apple tarts, using a total of 68 apples. Nicole made 5 apple pies and 9 apple tarts, which used 76 apples. How many apples does each dessert require?
Answer:
Each apple pie requires 8 apples, and each apple tart requires 4 apples.
Step-by-step explanation:
We see that both Pamela and Nicole bake the same amount of apple pies, but different amounts of apple tarts. Because of this, we can subtract the two to try to figure out the amount of apples for each apple tart. We subtract 68 from 76, giving us 8. Nicole baked 9 apple tarts, while Pamela baked 7, and 9-7=2. So we can bake two apple tarts with 8 apples, so one apple tart requires 4 apples (we divide by 2). Now that we know the amount of apples per each apple tart, we multiply 7 apple tarts that Pamela made by 4 apples, giving us 28. We subtract that from the total amount of apples Pamela used, which was 68, giving us 40. From this we can deduct that 5 apple pies need 40 apples, and we divide by 5, giving us 1 apple pie requires 8 apples.
How do I solve this?
A=bh/2
A=2/3ft*3/5ft/2
A=2/3×5/5*3/5×3/3/2
A=10/15*9/15/2
A=90÷15/2
A=6ft^2
Answer:
The area of triangle is 1/5 feet².
Step-by-step explanation:
You have to use area of triangle formula, A = 1/2×height×base. Then substitute the following values into the formula :
[tex]area = \frac{1}{2} \times height \times base[/tex]
Let height = 3/5,
Let base = 2/3,
[tex]area = \frac{1}{2} \times \frac{3}{5} \times \frac{2}{3} [/tex]
[tex]area = \frac{1}{2} \times \frac{1}{5} \times \frac{2}{1} [/tex]
[tex]area = \frac{1}{2} \times \frac{2}{5} [/tex]
[tex]area = \frac{1}{5} {feet}^{2} [/tex]
NOT TO SURE!! LAT QUESTION AND LAST TRY!!! WILL GIVE BRANLIEST!!!! AT LEAST TAKE A LOOK, SHARE YO SMARTNESSS!!!!!!!! PLS
12. ___________________ lines cross at a right angle.
A) Parallel
B) Slanted
C) Intersecting
Answer:
C) Intersecting
Step-by-step explanation:
happy to help ya:)
Answer:
Is thier an answer that you can put as Perpindicular because that should be the right answer
Step-by-step explanation:
Perpendicular lines are two lines that intersect and form right angles
Help please! if you answer correctly i will give brainliest
Answer:
lesser x =1
greater x = 3
Step-by-step explanation:
x^2 -4x+3 =0
Factor
What two numbers multiply to -3 and add to -4
-3*-1 = 3
-1+-1 = -4
(x-3)(x-1) =0
Using the zero product property
x-3 =0 x-1 =0
x=3 x=1
Answer:
lesser x = 1
greater x = 3
Step-by-step explanation:
x^2 - 3x - x + 3 = 0
x(x - 3) - 1(x - 3) = 0
= (x - 3)(x - 1) =0
= x = 3, 1
Hope this helps!
A bag has the following 10 colored stones in it. There are 2 red, 2 blue, 1 orange, 2 purple and 3 green stones. What is the probability of a green stone?
Answer:
30%
Step-by-step explanation:
Think of the 10 as 100%. 2 as 20% and so on. The green makes up 30%.
A healthy human body is approximately 18% carbon by weight. Determine how many pounds of carbon a body weighing 200 lbs contains. How many kilograms would that be? Use 0.454 kg equals 1 lb in your conversion. A. 440 lb. Of carbon; 16 kg of carbon b. 36 lb. Of carbon; 79 kg of carbon c. 36 lb. Of carbon; 16 kg of carbon d. 440 lb. Of carbon; 79 kg of carbon
Answer:
c. 36 lb. Of carbon; 16 kg of carbon
Step-by-step explanation:
An healthy body is approximately 18% carbon by weight. To determine how many pounds of carbon a body weighing 200Ibs contain can be gotten below.
A healthy person has approximately 18% carbon by weight. Therefore, the number of pounds of carbon for a person weighing 200 Ibs is
pounds of carbon = 18/100 × 200
pounds of carbon = 36 Ibs
According to the question the weight should be in kg.Therefore, we have to convert using the conversion rate you highlighted.
1 Ib = 0.454 kg
36 Ibs = ? kg
cross multiply
weight of carbon in kg = 0.454 × 36
weight of carbon in kg = 16.344 kg
weight of carbon in kg ≈ 16 kg
Which statements are true? Check all that apply. Magnitude is never a negative value. The magnitude of –1.9 is |–1.9| which is 1.9. The absolute value of a number is greater than its magnitude. The numbers –4 and 4 have the same magnitude. The magnitude of Negative two-thirds is less than the magnitude of Two-thirds.
Answer:
A, B, D
Step-by-step explanation:
The options are:
A. Magnitude is never a negative value
This is true because the magnitude is only a representation of the numerical value of a number. It is the distance of the number from the 0 point on the number line. It is the absolute value of a number.
Hence, the polarity of the number is not necessary.
B. The magnitude of –1.9 is |–1.9| which is 1.9
This is true because they have the same numerical value.
C. The absolute value of a number is greater than its magnitude
This is false because absolute value and magnitude of a number are the same.
D. The numbers –4 and 4 have the same magnitude
This is true. They have the same absolute value, hence, they have the same magnitude.
E. The magnitude of -2/3 is less than the magnitude of 2/3
This is false as already explained in C above.
Answer:
a b d
Step-by-step explanation:
Can someone please help me
Answer:
1) D
2) B
3) A
4) D
Step-by-step Explanation:
1) 1,300,000
= 1.3 × 10⁶
2) 0.052
= 5.2 × 10⁻²
3) 4,500
= 4.5 × 10³
4) 0.00061
= 6.1 × 10⁻⁴
On a particular day in July, there is a 20% probability of rain in Vancouver, a 65% probability of rain in Calgary, and a 75% probability of rain in Saskatoon. What is the probability that it will rain in all 3 cities on that day?
Answer:
The probability that it will rain in all 3 cities on that day
P(V∪ C∪S) = 0.93 = 93%
Step-by-step explanation:
Let 'V' be the event of rain in Vancouver
Given that the probability of rain in Vancouver
P( V) = 20% = 0.20
P( V⁻) = 1- P( V) = 1 - 0.20 =0.80
Let 'C' be the event of rain in Calgary
Given that the probability of rain in Calgary
P( C) = 65% = 0.65
P( C⁻) = 1- P( C) = 1 - 0.65 =0.35
Let 'S' be the event of rain in Saskatoon
Given that the probability of rain in Saskatoon
P( S) = 75% = 0.75
P( S⁻) = 1- P( S) = 1 - 0.75 =0.25
First we will prove that the probability that it will not rain in all 3 cities on that day
P( V⁻ ∩ C⁻ ∩ S⁻ ) = P( V⁻) P( C⁻) P(S⁻)
= 0.80 × 0.35 × 0.25
= 0.07
The probability that it will rain in all 3 cities on that day
P(V∪ C∪S) = 1-(P( V⁻ ∩ C⁻ ∩ S⁻ )
= 1 - 0.07
= 0.93
Which function is graphed on the right?
There is no picture ; - ;
Answer:
its C
Step-by-step explanation:
What is the equation of the translated function, g(x), if
f(x) = x??
Answer:
There is not enough information to solve. We need some more information to solve this question. The best we can do is
g(x) = g(f(x))
I need help with this question please
Answer:
The exact length of the third side would be 9.
Step-by-step explanation:
To find the length of the triangle, just add the height (6) and the base (3) which equals 9.
Please answer !!!!!!!!!! Will mark brainliest !!!!!!!!!!!!!
Answer & Step-by-step explanation:
[tex]\frac{1}{4}(x+5)^2-1=3[/tex]
Add 1 to both sides.
[tex]\frac{1}{4}(x+5)^2=4[/tex]
Multiply both sides by 4.
[tex](x+5)^2=16[/tex]
Take the square root of both sides.
[tex]\sqrt{(x+5)^2} =\sqrt{16}[/tex]
[tex]x+5=4[/tex]
Subtract 5 from both sides.
[tex]x=-1[/tex]
Please help me with this
Answer:
V of cylinder = V=πr^2h
V of rectangular prism = l*w*h
V of cylinder = 16 * 3.14 * 8
= 401.92
V of rectangular prism = 14 * 8 * 12
= 1344
Add = 401.92 + 1344
= 1,745.92
1,745.92 is the answer.Rounded the answer is Chelppppppppppppppppppppppppp!
Answer:
The difference is 22.5 km
Step-by-step explanation:
CD = 4.5 cm
DE = 8 cm
-----------
12 .5 cm
CE = 5 cm
The difference is
12.5 - 5 = 7.5 cm
Then multiply by the scale factor
7.5 cm * 3 km /1 cm =22.5 km
How many cubes eith side lengths of 1/4 cm does it take to fill the prism? Please help
Step-by-step explanation:
In order to find Volume for a rectangle use the formula: L * W * H
2 1/4 * 3/4 * 1 1/4 = 2 7/64
A cube with the side lengths of 1/4: 1/4 * 1/4 * 1/4 = 1/64
Divide 1/64, by the prisms volume, 2 7/64 to get 135.
I'm not sure if this is right, but I hope that helps! :)
Robin is a competitive archer. Her average arrow is within 6.5 cm of the center of the bullseye. John, Robin's trainer, keeps close records of each of Robin's shots so he can tell if she is improving. The graph below is John's record of Robin's last three arrows, where (0,0) is the center of the bullseye.
Answer:
Arrow C.
Step-by-step explanation:
Out of three arrows, nearest arrow from the origin will be the best arrow.
Ordered pair for arrow A → (-5, 4)
Distance between A and bullseye = [tex]\sqrt{(y_{2}-y_{1})^2+(x_{2}-x_{1})^2}[/tex]
= [tex]\sqrt{(0+5)^2+(0-4)^2}[/tex]
= [tex]\sqrt{41}[/tex]
= 6.40 units
Ordered pair for arrow B → (5, -5)
Distance between B and bullseye = [tex]\sqrt{(0-5)^2+(0+5)^2}[/tex]
= [tex]5\sqrt{2}[/tex]
= 7.1 units
Ordered pair for arrow C → (-2, -6)
Distance between C and the bullseye = [tex]\sqrt{(0+2)^2+(0+6)^2}[/tex]
= [tex]\sqrt{40}[/tex]
= 6.32 units
Distance between C and the bullseye is the shortest.
Therefore, arrow C will be the best arrow.
Answer:
6.3 cm
Step-by-step explanation:
Please help! Correct answer only! This assignment is due today.
Lester teaches a ceramics class on the weekends. In Sunday's class, the students created 19 clay objects, 12 of which were vases. After each class, Lester bakes the clay objects in a hot kiln to harden them. Students pick up their finished pieces later in the week.
If Lester randomly chose 16 clay objects to bake in the kiln Sunday night, what is the probability that exactly 11 of the chosen clay objects are vases?
Write your answer as a decimal rounded to four decimal places.
Answer: Lester gets about 400 k - 700k in casino hiest
Step-by-step explanation:
A certain pet store sells 6 times as many fish as kittens. It sells twice as many kittens as lizards. If the pet store sells 15 lizards a week, how many fish, kittens, and lizards does the pet store sell every week?
It sells twice as many kitten as lizards:
Kittens sold = 15 x 2 = 30 total kittens.
It sells 6 times the amount of fish:
Fish sold = 6 x 30 = 180 total fish.
Lizards = 15
Kittens = 30
Fish = 180
Answer:
They sell 225 pets each week.
Step-by-step explanation:
Let f be fish, k be kittens, and l be lizards.
[tex]f[/tex]÷6=[tex]k[/tex]
[tex]k[/tex]÷2=[tex]l[/tex]
If [tex]l=15[/tex], then:
[tex]k=30\\f=180[/tex]
180+30+15=225 pets
They sell 225 pets each week.
(I hope this isn't wrong but that answer seems wrong)
Hidaya runs each lap in 8 minutes. She will run less than 72 minutes today. What are the possible numbers of laps she will run today? Use n for the number of laps she will run today. Write your answer as an inequality solved for n.
Answer:
Step-by-step explanation:
n*8<72
:8 :8
n<72/8
n<9
n could be 1,2,3,4,5,6,7,8
Each 6 students reported the number of movies they saw in the past year 18,14,18,14,19,9
Answer:
Average: Add all and divide by 6
that gives us 92/6 = 15.333... or 15
Median: order it:
9, 14, 14, 18, 18, 19
median is 16
2 averages
Median: 16
Average: 15.33.. or 15
Outlier: 9
find the coordinates of the vertices of the triangle after a reflection across the line y= 3 and then across the line x = -1
Answer: A
Step-by-step explanation:
Reflection across y = 3
The simplest way to calculate the new coordinates is to draw y = 3, count how many units away the point is from y = 3, then count the same number of units from y = 3 in the OPPOSITE direction to find the reflection. (see attachment - blue color)
U = (-5, 4) is 1 unit above y = 3
U' = (-5, 2) is 1 unit below y = 3
T = (0, 5) is is 2 units above y = 3
T' = (0, 1) is 2 units below y = 3
S = (-4, 2) is 1 unit below y = 3
S' = (-4, 4) is 1 unit above y = 3
Reflection across x = -1
The simplest way to calculate the new coordinates is to draw x = -1, count how many units away the point is from x = -1, then count the same number of units from x = -1 in the OPPOSITE direction to find the reflection. (see attachment - red color)
U' = (-5, 2) is 4 units to the left of x = -1
U'' = (3, 2) is 4 units to the right of x = -1
T' = (0, 1) is 1 unit to the right of x = -1
T'' = (-2, 1) is 1 unit to the left of x = -1
S' = (-4, 4) is 3 units to the left of x = -1
S'' = (2, 4) is 3 units to the right of x = -1
4x + 3y - 8z
-5x + 7y + 10Z
(+) - 4x – 3y - 8z
Answer:
and 4x-5x-4x+3y+7y-3y-8z+10z-8z
-5x+7y-6z :this is the answer
what is the constant of proportionality for y=5/8x
Answer: 5/8
Step-by-step explanation:
Answer:
k = [tex]\frac{5}{8}[/tex]
Step-by-step explanation:
The standard form of an equation representing proportion is
y = kx ← k is the constant of proportionality
y = [tex]\frac{5}{8}[/tex] x ← is in this form
with k = [tex]\frac{5}{8}[/tex]
Someone please help ASAP
Answer:
5050
Step-by-step explanation:
To solve via calculator, go to the MATH menu, then the 0th option should say "summation" and insert it from there.
To solve algebraically, break the summation into 2 parts. Excuse the strange formatting, I can't find a way to do it normally.
4([tex]\frac{50}{1}[/tex]∑n) -
= 4( [tex]\frac{50(50+1)}{2}[/tex]) - 50(1)
= 5100 - 50
= 5050
A jar contains 4 red marbles, 6 blue marbles, 3 yellow marbles, and 5 green marbles. If one marble is randomly selected, what is the probability that it is red or green?
Answer:
1/2
Step-by-step explanation:
4 red marbles, 6 blue marbles, 3 yellow marbles, and 5 green = 18 marbles
P( red or green) = red or green / total
= (4+5) / 18
= 9/18
=1/2
Answer:
50%
Step-by-step explanation:
4 red + 5 green = 9 marbles
total marbles = 18 marbles
9 is 50% of 18