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raketka [301]
3 years ago
7

If (a+bi)^2=2abi, what must be the relationship between a and b? Show or explain your reasoning.

Mathematics
1 answer:
Klio2033 [76]3 years ago
6 0
(a+bi)^2 =(a+bi)(a+bi)= a^2 +2abi+b^2 i^2 \\  \\ i^2 = -1 \\  \\ (a+bi)^2 = a^2-b^2 +2abi = 2abi \\  \\ a^2 -b^2 = 0 \\  \\ a^2 = b^2 \\  \\ a = b

For the statement to be true, 'a' and 'b' must be equal

*First expand the binomial using FOIL, then set it equal to whats given "2abi".
Then you can find the relationship between a and b.
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Filipo is building a rectangular sandbox . The length of the sandbox is 1 foot longer than twice the width of the sandbox .the p
Alla [95]

Answer:

Part A : D.) 2w + 2(2w+ 1) = 29

Part B : Length of the sandbox is 10 feet.

Step-by-step explanation:

Given,

Perimeter = 29 ft

We need to find the equation for the perimeter and also the length of the sandbox.

Solution,

Let the width of the sandbox be 'w'.

Now as per question said;

The length of the sandbox is 1 foot longer than twice the width of the sandbox.

So we can say that;

Length = 2w+1

Now we know that the perimeter is equal to the sum of twice of length and width.

framing in equation form, we get;

Perimeter = 2(2w+1)+2w

we have given the perimeter, so on substituting the value, we get;

29=2(2w+1)+2w

Hence The equation used to find the width is  29=2(2w+1)+2w.

Now we solve for 'w'.

Applying distributive property, we get;

4w+2+2w=29\\\\6w+2=29

Subtracting both side by '2' we get

6w+2-2=29-2\\\\6w=27

Dividing both side by 6 we get;

\frac{6w}{6}=\frac{27}{6}\\\\w=4.5\ ft

Width of the sandbox = 4.5 ft

Length of the sandbox = 2w+1=2\times4.5 +1 = 9+1=10\ ft

Hence Length of the sandbox is 10 feet.

3 0
3 years ago
Can someone please explain how to figure this out!!
kakasveta [241]
2.9% OF the 500 phones are more than likely defective. In order to figure this out you must do 500*0.029 which would equal 14.5 and rounds off to 15. 15 out of the 500 phones will maybe be defective.
6 0
3 years ago
Up for a Brain Game?
kotegsom [21]

Answer:

-x, x, 4x, 0.2x, (1/4)x

8 0
3 years ago
Read 2 more answers
Median and mean math questions
Harlamova29_29 [7]

Answer: #7 D) neither set. #6. C) the sum of the data values must be 75. #5. The 6th missing temperature must be 80 degrees

Step-by-step explanation: #7. if you eliminate 3 numbers on each side on set A, then the numbers remaining are 2 and 19. In order to find the median add the two numbers, 19+2 which equals 21. Then divide that number by 2 to find your median, or in other words find the average, 21 divided by 2 is 10.5 which is not 12.5, so that set doesn’t work. In set B eliminate 2 numbers on each side. That will leave you with 10 and 9, then again find the average of the numbers. 10+9=19, and 19 divided by 2= 9.5. So therefore neither of the sets have a median of 12.5

#6. If there are five numbers in the data set and you are finding the average to be 15, then the five values must equal 75. In order to find the average of five numbers you must first add all of your values, and then divide by five, for there are five numbers. If you add all of your numbers up it must total 75, because 75 divided by 5= 15 which is the mean. Any other total would not work.

#5. The median of the original set is 72 degrees. In order to find the missing number you need to do some check and guess. Take the original median and add a number relatively close to the other numbers, for example 75, then add the two numbers together, 72+75=147. Then divide that by two, 147 divided by 2= 73.5 which is not the correct median number, its too low, so experiment with higher numbers and repeat the same process until you find a number that, if added to 72, totaled, and then divided by 2 equals 76.

I really hope this helped :)

7 0
3 years ago
What is the slope and the y-intercept of the graph of the linear function shown on the grid ?
VladimirAG [237]

Answer:

Slope: -1/4; Y-Intercept: 1.5

Step-by-step explanation:

Step 1: Find the slope. The best way to do this is to transform the two given points to y=mx+b form. When given two points, the best way to find the slope will be to do y2-y1/x2-x1. In this equation it would be -2-0/2+6, which is -2/8, simplified is -0.25 or -1/4. So we have the slope, which can determine the length of the line.

Step 2: Find the Y-Intercept. Finding the Y-intercept is so much simpler when given a graph, since all you have to do is find where the line goes through the y-axis, which in this case is (0,1.5), meaning that the y-intercept is 1.5 <em>(note: the y-intercept can also be found when x=0, for example (0,9).</em>

Hope this helped, good luck!

5 0
3 years ago
Read 2 more answers
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