Answer:
The modulus of the complex number 6-2i is:
[tex]|z|\:=2\sqrt{10}[/tex]
Step-by-step explanation:
Given the number
[tex]6-2i[/tex]
We know that
[tex]z = x + iy[/tex]
where x and y are real and [tex]\sqrt{-1}=i[/tex]
The modulus or absolute value of z is:
[tex]|z|\:=\sqrt{x^2+y^2}[/tex]
Therefore, the modulus of [tex]6-2i[/tex] will be:
[tex]z=6-2i[/tex]
[tex]z=6+(-2)i[/tex]
[tex]|z|\:=\sqrt{x^2+y^2}[/tex]
[tex]|z|\:=\sqrt{6^2+\left(-2\right)^2}[/tex]
[tex]=\sqrt{6^2+2^2}[/tex]
[tex]=\sqrt{36+4}[/tex]
[tex]=\sqrt{40}[/tex]
[tex]=\sqrt{2^2}\sqrt{2\cdot \:5}[/tex]
[tex]=2\sqrt{2\cdot \:5}[/tex]
[tex]=2\sqrt{10}[/tex]
Therefore, the modulus of the complex number 6-2i is:
[tex]|z|\:=2\sqrt{10}[/tex]
1) In a survey, Eric, the team manager, asked all 120 soccer players in the league which drink they preferred during
and after the game.
Drink During Game After Game
Sports Beverage 70
10
Juice
10
80
Water
40
30
Directions: For each statement below, tell if it accurately represents the information from the survey AND
explain how you made each decision. (SHOW YOUR THINKING)
a. During the game, players prefer juice to water by a ratio of 4 to 1.
b. 25% of the players prefer water after the game.
c. More than half of the players prefer a sports drink during the game.
What is 3/4 divided 5/16 in its simplest form?
Step-by-step explanation:
3/4÷5/16
3/4×16/5
=12/5(2 2/5)
(3/4) divided by (5/16) in its simplest form is 12/5.
To divide two fractions, you can multiply the first fraction by the reciprocal of the second fraction. The reciprocal of a fraction is obtained by flipping the numerator and the denominator. So, to divide (3/4) by (5/16), you can multiply (3/4) by the reciprocal of (5/16):
(3/4) ÷ (5/16) = (3/4) * (16/5)
Now, multiply the numerators and denominators:
Numerator: 3 * 16 = 48
Denominator: 4 * 5 = 20
3/4) ÷ (5/16) = 48/20
To simplify this fraction, find the greatest common divisor (GCD) of the numerator and the denominator, and then divide both by the GCD:
GCD of 48 and 20 is 4.
(48/4) ÷ (20/4) = 12/5.
To know more about simplest form:
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Mrs. Fekin bought herself a new water jug. The jug of water holds 64 ounces. If she drinks 4 ounces per hour, after how many hours will the jug have 32 ounces in it?
Answer:
(64-32)/4=8
Step-by-step explanation:
Your answer is 8. Simple Math
brainliest answer to whoever verifies this correctly!!
Answer:
that looks right
Step-by-step explanation:
During one week, a truck driver spent 51 hours driving 3,468 miles. Which rate best represents the relationship between the miles and the hours?
Answer:
68
Step-by-step explanation:
jsjsjwjwjwjwjqjqjjqkqkakajajajajajjajaj
Answer:
csgrerhhhrsdShuavkilrqadccddvny
Step-by-step explanation:
Amie works 6 hours each Saturday and 4 hours each Monday. She also makes $20 a week as a dog walker. She makes a total of $130 each week. If h represents Amie’s hourly rate, which equation can be used to find Amie’s hourly rate?
6 h + 20 = 130
(6 + 4) h = 130
(6 + 4) h + 20 = 130
4 h + 20 = 130
Answer:
C
Step-by-step explanation:
Answer:
(6 + 4) h + 20 = 130
Step-by-step explanation:
i got it right on my test hope this helps! <3
If your breakfast costs $12 and you are
charged 9% sales tax, what is the total
cost of your meal?
Answer:
find 9% of 12
12 times 9 divided by 100
108/100
$1.08
12+1.08
Your mean costs $13.08
-Have a nice meal!
Anna wants to bake 2 1/2 dozen cookies for a party. However, the recipe she has only makes a dozen cookies. If the original recipe calls for 1 1/4 cups of sugar, how many cups of sugar does she need to make the cookies for her party? Express your answer as a mixed number.
Given :
Sugar required for 2 1/2 = 5/2 dozen of cookies is 1 1/4 = 5/4 cups.
To Find :
How many cups of sugar does she need to make the cookies for her party.
Solution :
Let, cups of sugar required to make cookies for her party is x.
So,
[tex]x = \dfrac{\dfrac{5}{4}}{\dfrac{5}{2}}\\\\\\x = \dfrac{1}{2}[/tex]
Therefore, 1/2 cup of cookies is required to make 1 dozen cookies.
Hence, this is the required solution.
Answer: 25/8
Step-by-step explanation:
We would first turn 2 1/2 and 1 1/4 into an improper fraction.
That leaves us with 5/2 and 5/4.
Then, because she needs to make 5/2 dozen cookies and needs 5/4 cups of sugar for every batch, we would multiply 5/2 and 5/4 together.
Therefore x, or the amount of sugar she needs, is 25/8
I will give brainliest to person who answers correctly!
(5*10)-3 with the power of 2 equals what?
Answer:
41 is the answer .......
Heeeeellllllllllllpppppppppp
HELP WILL GIVE BRAINLIEST AND 30 POINTS!!
Students went on a field trip. The destination was 7 miles away. In the first hour, the students walked three tenths of the distance. How far did they walk in the first hour?
ANSWER IS 2.1 miles PLEASE SHOW ALL WORK
Simplify the expression:
X^2 (2x + 3)
Answer:
2x^3+3x^2Step-by-step explanation:
x^2(2x+3)=(x^2)(2x+3)=(x^2)(2x)+(x^2)(3)=2x^3+3x^2Answer:
2x³ + 3x²Step-by-step explanation:
COULD SOMEONE HELP ME ITS URGENT!!!!
Omar flies his plane out of a local airport. The airport is at an altitude of 1100 feet above sea level. He flies his plane to an altitude of 2500 feet above sea level. Which number represents sea level?
A piece of glass with an initial temp of 99 degrees Celsius is cooled at a rate of 3.5 degrees Celsius per minute. Concurrently, a piece of copper with an initial temp of 0 degrees Celsius is heated at 2.5 degrees Celsius per minute. Which of the following systems of equations can be used to solve for the temp, T, in degrees Celsius, and the time, m, in minutes, when the glass and copper reach the same temp?
Answer:
T= 99 - 3.5m
T= 2.5m
Step-by-step explanation:
Using the segment addition postulate, which is true?
Answer:
BC + CD = BD
Step-by-step explanation:
that is the right answer
Answer:
D or BC+CD+BD
Step-by-step explanation:
Leila and Jo are two of the partners in a business. Leila makes $3 in profits for every $4 that Jo makes. If Jo makes $60 profit on the first item they sell, how much profit does Leila make? pls help U_O
Answer:
54
Step-by-step explanation:
hi
If the domain is {0, 2,-6}, what is the range of y = -2x + 3?
Answer:
Step-by-step explanation:
y = f(x) = - 2x + 3
f(0) = 3
f(2) = - 2(2) + 3 = - 1
f(- 6) = - 2(- 6) + 3 = 15
Range is {3, -1, 15}
use the zero-exponent rule to simplify the expression:
-3^0+5^0-2^0-1^0
Answer:
-2
Step-by-step explanation:
PLEASE I BEG YOU JUST EXPLAIN HOW TO GET THE ANSWER ALL YOU HAVE TO DO IS EXPLAIN
Answer:
yo mamma
Step-by-step explanation:
get noob
answer:
4.5 tsp
explanation:
ok so 10 raspberry muffins need 1 1/4 tsp of baking powder so we can represent it like this:
10:1 1/4
then it asks how many tsp of baking powder is needed to make 3 dozens or 36 muffins
the amount of baking powder=x
so,
10:1 1/4=36:x
then you cross multiply,
10x=1 1/4*36
10x=45
x=4.5
Find the Slope of Y=X-2
Answer:
The slope is 1
Step-by-step explanation:
hope this helps
Answer:
Slope= 2.000/2.000= 1.000
Have a beautiful day and stay safe.
I need help ASAP
3k+30=95+k+2k-5
The price of a video game was reduced from $60 to $45. By what percentage was the price of the video game reduced?
A.15%
B.25%
C.75%
D.40%
is it A?
im just not really good at math and I don't have much time left for the test im taking so PLEASE HELP!
Answer:
B. 25%
Step-by-step explanation:
You turn the 25% into a decimal so it would be .25 then you multiply by 60. After that you subtract the answer you have by 60.
[
1
Solve the equation.
y + 3 = y + 9
f
O y= 1
O y = 3
O y = 6
O y = 9
2+2 Add the numbers
Answer:
4
Step-by-step explanation:
2+2=4
Answer:
4 is the answer to 2+2 when we add the numbers
HELPPPPPP PLSSSSSSSSSS ASP HELPPPPPPPPPPPPPPPPPPPPPP
Answer:
if it helps please mark brainliest!
Step-by-step explanation:
essays= x
quizzes=y
2x=60
x=30 1 essay per 30 days
4y=40
y=10 1 quiz every 10 days
120/30=4
120/10= 12
so 4 essays and 12 quizzes in 120 days
if it helps please mark brainliest!
Jim was thinking of a number. Jim doubles it and adds 8.8 to get an answer of 81.7. Form an equation with x from the information.
Answer:
x = 36.45
Step-by-step explanation:
set up equation
2x + 8.8 = 81.7
subtract 8.8 from both sides
2x = 72.9
divide 2 from both sides
x = 36.45
A line has a slope of Negative three-fourths and passes through the point (–5, 4). Which is the equation of the line?
y = negative three-fourths x + one-fourth
y = negative three-fourths x + 4
y = negative three-fourths x minus 2
y = negative three-fourths x minus one-fourth
The answer is A. y=-3/4x+1/4
The required equation of the line is y = (-3/4)x - 2 which passes through the point (–5, 4). The correct answer would be an option (C).
What is the slope of the line?The slope of a line is defined as the gradient of the line. It is denoted by m
Slope m = (y₂ - y₁)/(x₂ -x₁ )
Let the required equation of the line would be as:
y - y₁ = m(x - x₁)
Since the line passes through the point (–5, 4) and slope m = -3/4
So substitute the values in the above equation, and we
y - (-5) = (-3/4)(x - 4)
y + 5 = (-3/4)x - (-3/4)4
y + 5 = (-3/4)x + 3
y = (-3/4)x + 3 - 5
y = (-3/4)x - 2
Thus, the required equation of the line is y = (-3/4)x - 2.
Learn more about the Slope of the Line here:
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Solve a/-6 + 8 = 12. a =
Answer:
a = -24
Step-by-step explanation:
[tex]\frac{a}{-6}+8 = 12 \\\\\frac{a}{-6} = 12 - 8 \\\\\frac{a}{-6}= 4\\\\a = 4*(-6)\\\\a = -24[/tex]
Answer:
-24
Step-by-step explanation:
a/-6 + 8 = 12
a/-6 = 12 - 8
a/-6 = 4
cross multiply,
a = -6 × 4
a = -24
hope you understood
write any algebraic eqaution.
Answer:
(y4x2 + 2xy – y)/(x – 1) = 12
Step-by-step explanation:
Answer:
x3 + 1
Step-by-step explanation: