Answer:
It is B.
Step-by-step explanation:
Edge2021
[tex]w -z =\sqrt{2}(cos(\frac{3\pi}{4} )+i~sin(\frac{3\pi}{4} ))[/tex]
What is complex number?"The number of the form a + ib where a, b are real numbers and [tex]i=\sqrt{-1}[/tex] "
What is polar form of complex number?"The polar form of complex number z = x + iy is [tex]z=r~(cos\theta+i~sin\theta)[/tex] where [tex]r=\sqrt{x^{2} +y^{2} }[/tex] and [tex]\theta=tan^{-1}(\frac{y}{x} )[/tex]"
For given question,
We have been given two complex numbers in polar form.
[tex]w=\sqrt{2}(cos(\frac{\pi}{4} )+i~sin(\frac{\pi}{4} ))[/tex] and [tex]z=2(cos(\frac{\pi}{2} )+i~sin(\frac{\pi}{2} ))[/tex]
We simplify above complex numbers.
[tex]w=\sqrt{2}(cos(\frac{\pi}{4} )+i~sin(\frac{\pi}{4} )) \\\\w=\sqrt{2}(\frac{1}{\sqrt{2} } +i~ \frac{1}{\sqrt{2} } ) \\\\w=1+i[/tex]
And the second complex number is,
[tex]z=2(cos(\frac{\pi}{2} )+i~sin(\frac{\pi}{2} ))\\\\z=2(0+i~1)\\\\z=0+2i[/tex]
Now if we find the value of w - z
⇒ w - z = (1 + i) - (0 + 2i)
⇒ w - z = 1 - i
Now we find the polar form of complex number.
[tex]r=\sqrt{1^{2} +(-1)^{2} } \\\\r=\sqrt{2}[/tex]
And the value of [tex]\theta[/tex] would be,
[tex]\theta=tan^{-1}(\frac{-1}{1} )\\\\\theta=tan^{-1}(-1)\\\\\theta=\frac{3\pi}{4}[/tex]
So, w - z in the polar form would be [tex]1+i=\sqrt{2}(cos(\frac{3\pi}{4} )+i~sin(\frac{3\pi}{4} ))[/tex]
Therefore, [tex]w -z =\sqrt{2}(cos(\frac{3\pi}{4} )+i~sin(\frac{3\pi}{4} ))[/tex]
Learn more about the complex numbers here:
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Carlo drives into the city for work. His
average drive time is 48 minutes but
can vary by 15 minutes depending on
the traffic conditions on his way. Which
equation can he use to determine the
shortest and longest average drive
times?
Answer:
The most likely time 48 mins but there is differently some traffic if it normal takes 48 mins it would be 40.5 mins with no traffic.
Step-by-step explanation:
what is the x intercept of the line represented by the equation below 3x+6y=30
Answer:
(10,0)
Step-by-step explanation:
3x+6y=30
3x+6(0)=30
3x=30
x=10
Answer:
hmmm? well I guess I can solve for x in relation to y and vice versa
but to actually solve for x and y you will need another equation of x and y
3x=30+6y
x=10+2y=2y+10
-6y=30-3x
-2y=10-x
2y=-10+x=x-10
y=(1/2)x-5
well, y=(1/2)x-5 is a line with slope 1/2 and y-intercept (0,b) of
Consider the conditional statement: "If the store has the Playstation 5 in stock, then I will buy one." What is the conclusion of the statement?
Erica went bowling with her friends. She paid $3 to rent shoes and then $5 for each game of bowling. If she
spent a total of $23, then how many games did Erica bowl?
Answer:
4 games
Step-by-step explanation:
23 - 3 = 20
20 / 5 = 4
last one i think if not i will post the last one this is confusing
Answer: 23
Step-by-step explanation: Because you do 34-11
Answer:
45 units
Step-by-step explanation:
Expression: |-34 + 11|Simplify: 34 + 1134 + 11 = 45 unitsI hope this helps!
The school doubledutch team needs to raise at least $850 to buy new practice equipment. The team received a donation of $125, and also earns $4 per ticket sold. What is the least number of
tickets that need to be sold for the team to have enough money for the new practice equipment?
181 tickets
Answer:
$850 equipment
$125 from donation
they need $725
Step-by-step explanation:
if they earn $4 per ticket,
725÷4= 181.25
thus they need to sell atleast 182 tickets to have enough money
Answer:
850$ from equipment
and 150$ from it
If (x – 5) is a factor of f(x), which of the following must be true?
A: A root of f(x) is x=-5
B: A root of f(x) is x=5
C: Both x=-5 and x=5 are roots of f(x)
D: Neither x=-5 nor x=5 are a root of f(x)
Answer:
i believe it is B
Step-by-step explanation:
x-5=0
+5 +5
x=5
Katrina wants to build a fence around her Square Garden the garden has an area of 121 square feet How much Fencing will Katrina Need?
A. 13 Feet
B. 26 Feet
C. 39 Feet
D. 44 Feet
Answer:
D. 44 because its the primemiter
50,000x2.109.........
Answer:
105450
Step-by-step explanation:
easy
Answer:
50,000x2.109
Step-by-step explanation:
Abigail drew a scale drawing of the oldest house in her town. The actual house is 64 feet long. Abigail's scale drawing is 8 inches long. What scale did Abigail use to draw the house? 8 inches equal 1 foot 8 inches equal 18 foot 1 inch equals 18 foot 1 inch equals 8 feet
Answer:
1 inch equals 8 feet
Step-by-step explanation:
Given that;
Abigail drew a scale drawing of the oldest house in her town.
The actual length of the house = 64 feet long
Abigail scale drawing = 8 inches long
The scale he used in drawing the house is determined by choosing a perfect scale:
i.e
If 8 inches is used to draw an actual length of a house which is 64 feet long,
Then 1 inch should be able to draw (64 feet * 1 inch)/ 8 inches
So, 1 inch should be able to draw 8 feet long
The scale used to draw the given house is required.
The scale used to draw the diagram is 1 inch equals 8 feet.
Scale diagramsActual length of the house = 64 feet
Scale drawing length = 8 inches
So,
[tex]64\ \text{feet}=8\ \text{inches}[/tex]
Now, the inches to feet is required.
So, we divide both sides with 8.
[tex]\dfrac{64}{8}\ \text{feet}=\dfrac{8}{8}\ \text{inches}\\\Rightarrow 8\ \text{feet}=1\ \text{inch}[/tex]
So, 1 inch in the diagram is 8 feet of actual length.
Learn more about scale diagrams:
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What is the perimeter of the parallelogram?
29 cm
80 cm
58 cm
32 cm 2
Step-by-step explanation:
2 sides of the parallelogram are 13cm and the other 2 sides are 16cm
Perimeter of the parallelogram
= 2 * 13cm + 2 * 16cm
= 26cm + 32cm
= 58cm.
Answer:
58 [tex]cm^{2}[/tex]
Step-by-step explanation:
Ava says that 100
12 is equivalent to 2 (52 – 6). Is this true or false?
O True
False
Answer:
False
Step-by-step explanation:
Assuming that the first equation is 10x - 12, you need to solve both equations in order to see if the equations are equivalent from each other.
[tex]10x-12[/tex]
[tex]10x-12=2(5x-6)[/tex]
[tex]=2(5x-6)[/tex]
Then...
[tex]2\times(52-6)[/tex]
Use Order of Operations...
[tex]52-6=46[/tex]
[tex]2\times46=92[/tex]
[tex]2(5x-6)<96[/tex]
Therefore "false" or the second option is your answer.
Hope this helps.
The ratio of 8 less than a number to 28 more than that number is 2 to 5. What is the number?
a. 32
b. 30
c. 28
d. 15
Answer:
let the number be x
then
(x-8): (x+28) = 2:5
on solving
5x-40= 2x+56
3x = 96
x = 32
Step-by-step explanation:
The graph shows the amount of money paid when purchasing bags of peanuts at the zoo:
I REALLY NEED HELP!!!
A graph is shown. The x-axis is labeled from 0 to 9. The y-axis is labeled from 0 to 13. Four points are shown on the graph on ordered pairs 0, 0 and 1, 4 and 2, 8 and 3, 12. These points are joined by a line. The label on the x-axis is Bags of peanuts. The title on the y-axis is Total cost in dollars.
What does the point (0, 0) on the graph represent? (4 points)
a
The cost of one bag of peanuts
b
The cost of zero bags of peanuts
c
The cost of two bags of peanuts
d
The cost of three bags of peanuts
Answer:
B, the cost of 0 bags
Step-by-step explanation:
Answer:
b) The cost of zero bags of peanuts
Explanation:
Because it is at (0,0), that means it's at $0 and 0 bags of peanuts based on the labels for the x and y axis.
A zoo has the ratio to zebras (1 giraffe for every 4 zebras) What percent of this grouping of animals are giraffes? What percent of this grouping are zebras?
Answer:
20% of the animals are giraffes
80% of the animals are zebras
=====================================
Explanation:
Let's say there are 5 animals. This would mean there's 1 giraffe and 4 zebras, since we have four zebras per giraffe.
The percentage of giraffes is 1/5 = 0.20 = 20%
and the percentage of zebras is 4/5 = 0.80 = 80%
The requried percentage of giraffes is 20% and the percentage of Zebras is 80%.
What is the Ratio?The ratio can be defined as the proportion of the fraction of one quantity towards others. e.g.- water in milk.
What are percentages?the percentage is the ratio of the composition of matter to the overall composition of matter multiplied by 100.
Here,
A zoo has the ratio to zebras (1 giraffe for every 4 zebras)
The total proportion of the zebras and giraffes = 5,
Percentage of giraffe = 1 / 5 × 100% = 20%
Percentage of zebras = 4 / 5 × 100% = 80%
Thus, the requried percentage of giraffes is 20% and the percentage of Zebras is 80%.
Learn more about percentages here:
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can someone help me with this? (look at the image)
Answer:
H = (-1,3)
G = (-1,-1)
Step-by-step explanation:
8) The midsegment of an equilateral triangle measures 6 yards. What is the perimeter of the equilateral
triangle?
A) 18 yards
B) 36 yards
C) 6 yards
D) 9 yards
A robot has a straight arm 20 inches long that can rotate about the origin of a coordinate system. If the robot’s hand is located at (-20,0) and then rotates through an angle of 45°, what is the new location of the hand with the coordinates approximated to the nearest 0.01 inch?
Answer:
The location of the robots hand after rotating 45° counterclockwise from (-20, 0) in inches is (-14.14, 14.14)
The location of the robots hand after rotating 45° clockwise from (-20, 0)) in inches is (-14.14, -14.14)
Step-by-step explanation:
The initial location of the robots hand = (-20, 0)
The angle through which the robot rotates his hand = 45°
∴ We have the length of the robots hand = 20 inches
We note that (-20, 0) is in the 2nd Quadrant
The location of the robots hand after rotating 45° counterclockwise = 135°
Therefore, the location of the robots hand after the rotation = (20×cos(135°), 20×sin(135°)) = (-10·√2, 10·√2) = (-14.14, 14.14)
The location of the robots hand after rotating 45° clockwise from (-20, 0) = 225°
Therefore, the location of the robots hand after the rotation = (20×cos(225°), 20×sin(225°)) = (-10·√2, -10·√2) = (-14.14, -14.14)
Can someone help with this I’ll mark u as brainlist
Answer:i don’t really k ow but i need points to ask questions
Step-by-step explanation:
A 3-pound bag of almonds costs $16.50, a 5-pound bag of walnuts costs $28.75, and a 4-
pound bag of cashews costs $24.80. Which is the best deal from best to worst deal
Answer:
a 3 pound almonds is the best deal with the 5 pound bag of walnuts being the second and the 4 pounds of cashews is the worst deal
Step-by-step explanation:
the almonds cost 5.50$ a pound the 5 pound bag of walnuts cost 5.75$ dollars a pound and the 4 pound bag of cashews cost 6.20$ a pound
c(x) = -5x^2+x
Find c(4)
Answer:
c(4) = -76
Step-by-step explanation:
c(x) x=4 so plug 4 in for x
-5(4)² + (4)
Do parentheses first so... 4² = 16
-5(16) + 4
-5(16) = -80
-80+4 = -76
c(4) = -76
Which of the following statements can be used to show that today's high temperature, 12°F, is warmer than yesterday's high temperature, which was -15°F?
-15°F = 12°F
-15°F ≥ 12°F
-15°F 72°F
Answer:
-15°F < 12°F
Step-by-step explanation:
Hope it helps you in your learning process.
4.A trapezoid with a perimeter of 30 units is
graphed on a coordinate grid. The trapezoid is
dilated by a scale factor of 0.3 with the origin as the
center of dilation. If (x,y) represents the location of
any point on the original trapezoid, which ordered
pair represents the coordinates of the corresponding
point on the resulting trapezoid?
A. (30x, 30y)
B. (X - 0.3, y +0.3)
C. (0.3x, 0.3y)
D. (x + 0.3, y +0.3)
Answer:
It would be (x0.3,y0.3). C is the answer
Step-by-step explanation:
Because if you actually read it, it already gave you the answer which is the scale factor of 0.3
so that would lead to (x0.3,y0.3)
I will give brainliest! In the figure, the circle has a center O and has a radius of 10. If the length of arc AB is between 5 and 6, what is one possible integer value of x?
Answer:
any integer in between 29,30,31,32,33,34 will work.
What is the slope of the line shown?
The probability of a female student being chosen to be on the football team is
1/28 . If there are 840 female students in a school, how many could be on the football team?
Melanie is making lemonade for a family barbecue. Her recipe which yields 1 pitcher contains 6 cups of water, 2
cups of sugar and 1 cup of lemon juice. If she wants to make 3 pitchers of lemonade, how many cups of sugar
will she need?
I need help with this
Answer:
14
Step-by-step explanation:
add
Section 1
Evelyn reads 25 pages in 30 minutes.
Number of Pages
25
400
Time (in minutes)
30
?
If Evelyn reads 400 pages at this same rate, how many minutes will it take her?
O 90 minutes
O 120 minutes
O 375 minutes
0 480 minutes
Pleaseeeee helpppp !!!!!!!!!! Will mark Brianliest !!!!!!!!!!!!!!
Answer:
Square root of 56 so in simplest radical form 4 root 4
Step-by-step explanation: