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exis [7]
4 years ago
14

What is the distance between 4-i and -2+3i?

Mathematics
1 answer:
stepan [7]4 years ago
4 0
If you're working with complex numbers, then I'm sure you're comfortable with plotting them on a complex-plane ... real part of the number along the x-axis, and imaginary part of the number along the y-axis.

When you look at it that way, your two points are simply two points on the x-y plane:

           4 - i    ===>  (4, -1)

         -2 + 3i  ===>  (-2, 3) .

The distance between them is

                       D  =  √ (difference in 'x')² + (difference in 'y')²

                           =  √  (6)² + (4)²

                           =  √ (36 + 16)

                           =   √ (52)

                           =      7.211  (rounded)   
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Kyle bought himself a pair of shoes for 89.50 and he bought his nephew a pair for half the price of his shoes. If the sales tax
ycow [4]
Solution-

89.50/2 = 44.75

44.75 is the amount he spent to buy his nephew the pair of shoes.

Now, we are going to add the amount he spent for himself and his nephew together. 

89.50 + 44.75= 134.25

134.25 is the amount he spent in total, now we need to find the final amount with sales tax included.

We can do this by multiplying the total price by .075

134.25 * .075 = 10.07 (I rounded this to the nearest hundredths because we are dealing with money)

Now we need to add the two number together. 

134.25 + 10.07 = 144.32

Answer- 

The total amount Kyle spent is $144.32 


3 0
3 years ago
Robert is a high school basketball player. In a particular game, he made some three point shots and some free throws (worth one
Oksanka [162]

Answer:

let t = number of three-point shots

let f = number of free throw shots

Step-by-step explanation:

t + f = 9      (he made a total of 9 shots altogether)

3t + 1f = 23   (number of shots multiplied by their point value)

substitution method:   t = 9 - f

                                    3(9 - f) + f = 23

                                     27 - 3f + f = 23

                                      -2f = -4

                                         f = 2

find 't':                               t + 2 = 9

                                         t = 7

                                         

8 0
3 years ago
A fair spinner has 12 equal sections: 5 red 4 blue and 3 green. its Spun twice what is the probability of getting the same colou
VLD [36.1K]

Answer:

25/72

Step-by-step explanation:

P( blue) = blue / total = 4/12 = 1/3

P ( blue, blue) = 1/3 * 1/3 = 1/9

P ( red) = red / total = 5/12

P ( red, red) = 5/12 * 5/12 = 25/144

P ( green) = green /total = 3/12 =1/4

P ( green , green) = 1/4 * 1/4 = 1/16

Add these together to get

P( same colour twice) = 1/9+ 25/144 + 1/16

                                      =16/144 + 25/144 + 9/144

                                      =50/144

                                     =25/72

4 0
3 years ago
Solve for x…………………………..
Georgia [21]

Answer:

15x + 15° = 3x + 9° + 78° (exterior angle is equal to the sum of the opposite interior angles)

15x - 3x = 9° + 78° - 15 °

12x = 72°

12x÷12 = 72°÷12

x = 6

6 0
3 years ago
Find the equation of the line that goes through the point ( 6, 5) and has a slope of 1/3
PSYCHO15rus [73]

Answer (<u>assuming it can be slope-intercept form)</u>:

y = \frac{1}{3} x +3

Step-by-step explanation:

Since we already know a point the line intersects and its slope, we can use the point-slope formula y-y_1 = m (x-x_1) to write an equation, then convert it to slope-intercept form.

Substitute values for m, x_1, and y_1. Since m represents the slope, substitute \frac{1}{3} in its place. Since x_1 and y_1 represent the x and y values of one point the line intersects, use the x and y values of (6,5) and substitute them into the equation. Substitute 6 for x_1 and 5 for y_1. Then, isolate y to put it into slope-intercept form and find an answer:

y -5 = \frac{1}{3} (x-6)\\y-5 = \frac{1}{3}x-2\\y = \frac{1}{3} x+3

7 0
3 years ago
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