Answer:
D
Step-by-step explanation:
We want to simplify the expression:
[tex]\displaystyle \frac{6i}{9+2i}[/tex]
To do so, we can remove the imaginary unit in the denominator by multiply it by the conjugate.
The conjugate of a + bi is a - bi.
Hence, we will multiply the fraction by 9 - 2i:
[tex]\displaystyle =\frac{6i}{9+2i}\left(\frac{9-2i}{9-2i}\right)[/tex]
Multiply:
[tex]\displaystyle = \frac{6i(9-2i)}{(9+2i)(9-2i)}[/tex]
Difference of two squares:
[tex]\displaystyle = \frac{6i(9-2i)}{(9)^2 -(2i)^2}[/tex]
Simplify:
[tex]\displaystyle = \frac{54i-12i^2}{(81)-(4i^2)} = \frac{54i-(-12)}{81-(-4)} = \frac{12+54i}{85}[/tex]
Hence, our answer is D.
ayudenme con esto por favor
Answer:
the answer is on the computer
Step-by-step explanation:
please I can't understand this question ⁉️
please help
Answer:
gauth math
got it perfect answer
Karima earns $400 per week plus a holiday bonus of $250. Write an expression to represent the total amount she earns after working w weeks. Then, find the amount she earns after she works 4, 12, and 36 weeks.
Expression:
Earnings at 4 weeks:
Earnings at 12 weeks:
Earnings at 36 weeks:
Answer:
Step-by-step explanation:
Earnings per week = $ 400
Earning for 'w' week = 400*w + holiday bonus
= 400w + 250
Earnings at 4 weeks = 400*4 + 250
= 1600 + 250
= $ 1850
Earnings at 12 weeks = 400*12 + 250
= 4800 + 250
= $ 5050
Earnings at 36 weeks = 400*36 + 250
= 14400 + 250
= $ 14650
2f - 3(4f - 5g) + 5g + 7fg
Help pls how to solve it?
Step-by-step explanation:
2f - 3(4f - 5g) + 5g +7fg
multiply the 3 in
2f - 12f - 15g + 5g + 7fg
add or subtract common terms
-10f -10g +7fg will be your final answer
Answer:
Step-by-step explanation:
As the question did not say how to 'solve the question', I would assume it will be to simplify the equation, as there is no way of solving an expression without an answer.
Simplify:
2f - 3(4f-5g) + 5g +7fg
Get rid of the parentheses
2f - 12f - 15g + 5g +7fg
Simplify similar expressions
-10f - 10g + 7fg
Therefore, 2f - 3(4f-5g) + 5g +7fg simplified is equal to -10f - 10g + 7fg.
Someone please help :))
Explain how you can use absolute value to tell whether
the sum of two integers is positive or negative.
Answer:
Let the integers are p and q.
In case both integers are positive or negative, you add the numbers up and apply their sign to the sum.
Examples:
10 + 88 = 98-20 + (-15) = -35In case one of the integers is negative and one positive.
p < 0, q > 0Use absolute value in this case.
Subtract the numbers and apply the sign of the number with the greater absolute value.
Examples:
- 10 + 15 = |15 - 10| = |5| = 5- 15 + 10 = - |15 - 10| = - |5| = -5Step-by-step explanation:
Let the numbers be x and y
If both are of same signs then
|x + y| = x + y
-|x + y| = -(x + y) = -x - y
If one is negative and one is positive
-|x + (-y)| = -|x - y| = -x + y
-|y + (-x)| = -|y - x| = -y + x
60 CHALLENGE The Queen Isabella Memorial Bridge connects South Padre Island, Texas, to
Port Isabel on the mainland. Suppose one crew began building from South Padre Island,
and another crew began building from Port Isabel. The two crews met 6256.5 feet from the
South Padre Island side of the bridge approximately 2.5 years after construction began.
a. Suppose the South Padre Island crew built an average of 208.5 feet per month.
Together the two crews built 12,513 feet of bridge. Determine the average number of
feet built per month by the Port Isabel crew.
307
b. About how many miles of bridge did each crew build?
c. Is this answer reasonable? Explain.
2,513
With some give information, we need to solve some algebraic problems that involve a change of units, lets see step by step how we do that:
A) First, we know that:
The bridge was constructed in 2.5 years
Knowing that 1 year = 12 months, we can rewrite:
2.5 years = (2.5)*(12 montsh) = 28 months
The two crews built, together, 12,513 ft of the bridge.
Now, we know that the South Padre Island crew built an average of 208.5 per month.
Then in the 28 months for the whole construction, they built 28 times that amount:
D = (28 months)*(208.5 per month) = 5,838 ft
Then the rest was constructed by the Port Isabel Crew.
They constructed 12,513 ft - 5,838 ft = 6,675ft
So that crew constructed 6,675 ft in 28 months, then the average number of feet built per month (the quotient between the total amount built and the number of months in which that was built) is:
6,675 ft/28 months = 238.39 ft per month.
b)
South Padre Island crew constructed 5,838 ft
Port Isabel Crew constructed 6,675ft
Now we want to transform these to miles.
Remember that;
1 mille = 5280 ft.
Then to transform from ft to miles, we just need to divide our measures by 5280 ft
Then:
South Padre Island crew constructed 5,838 ft = (5,838ft/5280ft) mi = 1.11 mi
Port Isabel Crew constructed 6,675ft = (6,675ft/5280ft) mi = 1.26 mi
c) Is this answer reasonable?
Mathematically, yes, both crews constructed about the same in about the same time, with a small difference that may be related to the sizes of each crew or something like that.
We could conclude that this would not be reasonable if the monthly rates were dramatically different.
If you want to learn more, you can read:
https://brainly.com/question/15051367
Problem 10
(a) A teacher selects a team of three from a group of students. She also
selects a team of two (students can be in more than one team). The
teacher notices that there are twice as many ways of choosing the
team of three as there are the team of two. How many students are
in the group?
(b) For another group of students, there are three times as many teams
of three which can be selected as there are teams of two. How many
teams of three can be selected from this group?
Using the combination formula, it is found that:
a) There are 8 students in the group.b) 165 teams of three can be selected from this group.---------------------------
The order in which the students are chosen is not important, which means that the combination formula is used to solve this question.
Combination formula:
is the number of different combinations of x objects from a set of n elements, given by the following formula.
[tex]C_{n,x} = \frac{n!}{x!(n-x)!}[/tex]
---------------------------
Question a:
3 students from a set of n, thus: [tex]C_{n,3}[/tex]2 students from a set of n, thus: [tex]C_{n,2}[/tex]Twice as many ways to choose the teams of 3 than the teams of 2, thus:
[tex]C_{n,3} = 2C_{n,2}[/tex]
[tex]\frac{n!}{3!(n-3)!} = 2\frac{n!}{2!(n-2)!}[/tex]
We have to solve for n, thus:
[tex]2!n!(n-2)! = 2(3!)(n!)(n-3)![/tex]
[tex](n-2)! = 3!(n-3)![/tex]
From the factorial concept: [tex](n-2)! = (n-2)(n-3)![/tex], thus:
[tex](n-2)! = 3!(n-3)![/tex]
[tex](n-2)(n-3)! = 3!(n-3)![/tex]
[tex]n - 2 = 3![/tex]
[tex]n - 2 = 6[/tex]
[tex]n = 8[/tex]
There are 8 students in the group.
---------------------------
Question b:
First we have to find the total number of students, using the same logic as item a.
[tex]C_{n,3} = 2C_{n,2}[/tex]
[tex]\frac{n!}{3!(n-3)!} = 3\frac{n!}{2!(n-2)!}[/tex]
[tex]2!n!(n-2)! = 3n!3!(n-3)![/tex]
[tex]2(n-2)(n-3)! = 18(n-3)![/tex]
[tex]n - 2 = 9[/tex]
[tex]n = 11[/tex]
---------------------------
The number of teams of three is:
[tex]C_{11,3} = \frac{11!}{3!8!} = 165[/tex]
165 teams of three can be selected from this group.
A similar problem is given at https://brainly.com/question/23302762
Which of the following rules should be used to find the area of a triangle?
Divide area by length.
Divide the sum of the upper and lower sides by 2.
Multiply length by width by height.
Multiply base by altitude.
none of these
Answer:
none of these
Step-by-step explanation:
area of the triangle =height ×base and then divide by 2
please help me with this
I will give brainlist
questions number 12 and 13
Answer:
hope this helps you have a great
Chose the correct property
(8•3)4 = 8(3•4)
A) Commutative Property Of Multiplication
B) Associative Property Of Multiplication
C) Neither
Answer:
B) Associative Property of Multiplication
Step-by-step explanation:
The associative property states you can change where the parentheses (grouping terms) are in a multiplication statement, and you'll get the same product.
More generally:
(a * b) * c = a * (b * c)
Answer:
B) Associative Property Of Multiplication
Step-by-step explanation:
The associative property is a math rule that says that the way in which factors are grouped in a multiplication problem does not change the product.
Therefore, changing the grouping of (8x3) or (3x4) does not change the product.
AAAAAAAAAAHHHHHHHHHHHH!!!!!!!!!
Answer:
[tex] \sqrt{12} \times \sqrt{27} \\ = 2 \sqrt{3} \times 3 \sqrt{3} \\ 6 \sqrt{3 } \times \sqrt{3} \\ = 6 \times 3 \\ = 18 \\ thank \: u[/tex]
Answer:
18
Step-by-step explanation:
Simplify the radical by breaking the radicand up into a product of known factors, assuming positive real numbers.
its correct i solved it by paper im lazy typing it here lol, anyways 18 has to be the correct answer.
hope i helped
Calculate the area of each figure.
(PLS HELP )
HELP DUE IN 15 MINS!
Solve for x:
2x - 5 = -x + 19
Answer:
I HOPE IT WILL HELP YOU.
Have a great day ahead.
Find the measure of unknown angle
Answer:
120 + z = 180 (linear pair)
=> z = 180 - 120
=> z = 60
130 + y = 180 (linear pair)
=> y = 180 - 130
=> y = 50
50 + 60 + x = 180 (Angle sum property of a triangle = 180)
=> 110 + x = 180
=> x = 180 - 110
=> x = 70
starting at school, you and your friend ride bikes in different directions- you ride 4 blocks north and your friend rides 3 blocks west. at the end of the adventure, how far apart are you and your friend?
Help please, would be much appreciated
Hey there! I'm happy to help!
We see that all of our y-values go negative and our x-values stay the same. It isn't a rotation because then our x-values will switch, but they haven't switched in our problem, so A and D are incorrect.
Reflecting over the line y=x is just reflecting over a diagonal line, and that will switch the x-value as well.
The correct answer is B. reflect over the x-axis. All of the x-values stay the same here, but the y-values are all on the other side of the x-axis, so they are all negative now, and this matches the change we see with our points.
Have a wonderful day and keep on learning! :D
A wood board 59 inches long is cut into three parts. The first part is twice the
length of the second part. The third part is 5 less than the second part. How long
are the three parts?
Answer:
first part is 32 inches, second part is 16 inches, third part is 11 inches.
Step-by-step explanation:
2x + x + x - 5 = 59
4x + 64
x = 16.
we can then plug 16 in first parts expression, 2x, for 32. second part is just x so 16. 3rd part is 5 less, x-5, so 11.
My backyard is 5.5 metres by 12 metres. (That is a length of 5.5 m and a width of 12 metres). I have poured a concrete slab in the top right corner where I have placed my shed which is 3 metres by 3 metres. I am also going to create a flower bed which will be half a metre from the fence on the left side and top end of the backyard; hugging the fence.
I need to order buffalo grass to cover the rest of the space. How much square metres worth of Buffalo Grass will I need?
How much will it cost me considering that Bunnings sell Buffalo Grass for $14.20 per metre squared?
Step-by-step explanation:
7+7.857836-$(92726940)
Hey guys I need help in these. Thanks in advance^^
1) In which operations does the order of the numbers make a difference to the
final answer? Find out what this rule is called.
2) If evaluating the sum 2+3+4 does it make a difference which two numbers !
add first? Is the same true for the other operations? What's this rule called?
Answer:
Read explanation
Step-by-step explanation:
The two operations that you will get the same answer for no matter what order you do it is addition and multiplication.
Bonus: Technically, if you had something like 1-2-3 you could rewrite it as 1 + (-2) + (-3) and now it won't matter the order and for something like 1/2/3 you could rewrite as 1 * (1/2) * (1/3) and not it wont matter the order too!
This propetie is called the associative property of addition and multiplication.
In the second question since its addition the order you do it in does not matter.
Why: If you think of it logically adding in a diffrent order than the question does not matter since in the end your still adding the same ammount.
Remember: You can only swap the orders if everything is addition or multiplication and remember your order of operations when using this propety in the years to come.
Hoped this helped, Eddie K.W.
Solve the following: -7x + 5 = 8x - 25
Answer:
x=30
Step-by-step explanation:
Subtract 5 from both sides of the equ
Please help quickly!
Answer:
Step-by-step explanation:
Stop doing it
If the surface area of a cylinder is given by SA =
2nr^2+2nrh, calculate the height if the surface area is 30n and the radius is 2.
Answer:
The height is 11/2
Step-by-step explanation:
We know SA = 30n
and r = 2
We are solving for h. So plug in our values
30n = 2n(2)^2 + 2n(2)h
Multiply and square on the right side terms
30n = 8n + 4nh
Divide everything by n
30 = 8 + 4h
Subtract 8 on both sides
22 = 4h
Divide by 4 on both sides
h = 22/4 = 11/2
Check:
30n = 2n(2)^2 + 2n(2)(11/2)
30n = 8n + 22n
30n = 30n
Write the rational numbers whose multiplicative inverse are themselves
Answer:
the rational numbers whose multiplicative inverse are themselves are 1& -1.hope it helps .stay safe healthy and happy.
A bag has 3 red marbles, 2 blue, 4 greens and 1 yellow. What is the probability of pulling a blue, putting it back
in the jar and then pull a green?
Show Your Work
Answer: 2/25
Step-by-step explanation: Since we are replacing the marbles, these two events are independent which means that the outcome of the first does not affect the outcome of the second.
First find the probability of selecting a blue marble.
There are 2 favorable outcomes, the blue marbles,
and 10 possible outcomes, all the marbles in the bag.
So the probability of selecting a blue marble is 2/10 or 1/5.
Always reduce when finding probability
Now we find the probability of selecting a green marble.
There are 4 green marbles and 10 total so the probability of
selecting a green marble is 4/10 or 2/5.
Now we multiply the probabilities.
So we have 1/5 x 2/5 or 2/25.
What is the area of a rectangle with a length of 5 cm and a width of 3 cm
Answer:
15 cm
Step-by-step explanation:
What is the area of a rectangle with a length of 5 cm and a width of 3 cm
Hi there!
»»————- ★ ————-««
I believe your answer is:
15cm²
»»————- ★ ————-««
Here’s why:
⸻⸻⸻⸻
[tex]\boxed{\text{Area of a rectangle is:}}\\\\A = l * w\\----------------\\\rightarrow L = 5; w = 3\\\\\rightarrow A = 5 * 3\\\\\rightarrow A = \boxed{15cm^2}[/tex]
⸻⸻⸻⸻
»»————- ★ ————-««
Hope this helps you. I apologize if it’s incorrect.
It costs $2 per person to ride the Ferris wheel. Write an equation relating the cost, c, to the number of people, n.
Please help.
Answer:
c =2n
Step-by-step explanation:
cost c is given by cost of each person multiplied by number n of people
The factorization of x² + x + xy + y + zx + z is
answer meenu plz
Answer:
[tex]x2+x+xy+y+zx+z \\ =x(x+1+y+y+z)+z \\ =x(x+2y+z+1)+z
[/tex]
Step-by-step explanation:
take like terms together..
x²+x+zx+xy+y+z
x(x+z+y)+y(x+y+z)
(x+y)(x+y+z)
hope it helps
if Mr. Davis ate 20 of the 50 chocolate chip cookies from the bag,what percent of the bag of cookies did he eat?
Answer:
He ate 40% of it
Step-by-step explanation:
20/50 is 2/5, which is basically 4/10 therefore equaling 40%