Find the distance between the points (6,3) and (-1,-6).

[tex]\\ \sf\longmapsto (1-6i)+(12+i)[/tex]

[tex]\\ \sf\longmapsto 1-6i+12+i[/tex]

[tex]\\ \sf\longmapsto 1+12-6i+i[/tex]

[tex]\\ \sf\longmapsto 13-5i[/tex]

[tex]\sf{13+(-5i) }[/tex]

Step-by-step explanation:

we have to Simplify the expression(1 – 6i) + (12 + i) to a + bi form

[tex](1 – 6i) + (12 + i)\\\\1-6i+12+i\\\\1+12-6i+i\\\\13-5i\\\\13+(-5i)[/tex]

Answer:

The smaller number is 11.

Step-by-step explanation:

11 + 13 = 24

11 x 13 = 143

Hope this helps!

Answer:

64.2857

Step-by-step explanation:

take the distance traveled divided by the distance which will give you the speed traveling multiplying the distance and the speed will give you the time ot takes

Answer:

7/9

Step-by-step explanation:

Hope this helps you. Have a nice day.

Answer:

j = 1

Step-by-step explanation:

-2.15+1.8+7.45 = 2.1j + 5j

7.1 = 7.1j

7.1/7.1 = j

Answer:

(-5,5)

Step-by-step explanation:

if you replace x and y with the numbers, the answer will be true.

Answer:

7x ³⁹¹

Step-by-step explanation:

1: "x3" was replaced by "x^3".

Answer:

move 7

Step-by-step explanation:

x + 3 y + 7

Answer:

10.17 seconds

Step-by-step explanation:

substitute y=0 into the equation

0=-16x²+153x+98

then use the quadratic formula

a = -16

b= 153

c = 98

Substituting values into the Quadratic equation, you get (Round the values to the nearest hundreth):

x₁= 10.17

x₂= -0.60

We have that, how long it will take for Liu to catch Mariel is mathematically given as

t=3.076s

From the question we are told

Mariel and Liu are running a long-distance race. Mariel runs at a rate of 5.4 m/s, and Liu runs at a rate of 7.6 m/s. If Mariel has a 20 m head start, how long will it take for Liu to catch Mariel?

Generally the equation for the Average speed is  mathematically given as

[tex]v_a=\frac{5.4+7.6}{2}\\\\V_a=6.5m/s[/tex]

Therefore

How long it will take for Liu to catch Mariel is mathematically given as

[tex]t=\frac{20}{6.5}[/tex]

t=3.076s

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Answer:

y =  2x - 1

Step-by-step explanation:

To find out the equation of the line, you will always need the following information in order to determine the linear equation in slope-intercept form, y = mx + b:

1. 2 sets of ordered pairs (x, y)

2. Slope (m)

3. Y-intercept (b)

First, we need to choose 2 points from the graph to solve for the slope:

Let (x1, y1) = (0, -1)

(x2, y2) = (3, 5)

Substitute these values into the following slope formula:

[tex]m = \frac{y2 - y1}{x2 - x1} = \frac{5 - (-1)}{3 - 0} = \frac{5 + 1}{3} = \frac{6}{3} = 2[/tex]

Therefore, the slope (m) = 2.

Next, we need the y-intercept, (b). The y-intercept is the y-coordinate of the point where the graph of the linear equation crosses the y-axis. The y-intercept is also the value of y when x = 0. The y-coordinate of the point (0, -1) is the y-intercept.  Hence, the y-intercept (b) = -1.

Given our slope, m = 2, and the y-intercept (b) = -1, the linear equation is:

y = 2x - 1

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Answer:

You can use 48 and 24

Step-by-step explanation:

You can figure out 48 by simply multiplying 6 times 8. You can figure out the 24 by noticing that 24 is divisible by both 6 and 8. 6 x 4 =24, and 8 x 3=24. I hope this helps!

Answer:

The numbers we could use for the denominators is 48  and 24.

You are correct!

20 Characters

Answer:

y = 1/2x

Step-by-step explanation:

Slope: 1/2

y = 1/2x

Answer:

y = 12/7

Step-by-step explanation:

Slope = (change in Y) / (change in x)

-1/7 = (y - 2) / (3 - 1)

-1/7 = (y - 2)/2

Cross multiply:  -1(2) = 7(y - 2)

                             -2 = 7y -14

                        -2 + 14 = 7y

                                12  = 7y

                               12/7 = y

Let's find y

[tex]\\ \sf\longmapsto m=\dfrac{y_2-y_1}{x_2-x_1}[/tex]

[tex]\\ \sf\longmapsto \dfrac{-1}{7}=\dfrac{y-2}{3-1}[/tex]

[tex]\\ \sf\longmapsto \dfrac{-1}{7}=\dfrac{y-2}{2}[/tex]

[tex]\\ \sf\longmapsto -2=7y-14[/tex]

[tex]\\ \sf\longmapsto 7y=12[/tex]

[tex]\\ \sf\longmapsto y=12/7[/tex]

Answer:

- 1x] = 0

[x] =-15

Answer:

you mean the midpoint: (-1, 23)

9514 1404 393

Answer:

  (a) 3%

  (b) sh 3915

Step-by-step explanation:

a) The extra amount is ...

   10815 -10500 = 315

As a percentage of the marked price, this is ...

  315/10500 × 100% = 3%

__

b) The total paid is the sum of the down payment and the monthly installments:

  10815 = down + 1150×6

  10815 -6900 = down . . . . . . . . . . subtract 1150×6 from both sides

  down = 3915 . . . . . . . . . evaluate

The deposit paid was sh 3915.

Answer:

7/9

Step-by-step explanation:

2+5=7

Denominator stays the same 9

So it's 7/9

Answer:

You sure bout that this is the answer

Step-by-step explanation:

2/9=0.2~ + 5/9=0.5~ =0.777777778 or 7/9

Answer:

-2x - 3

Step-by-step explanation:

1. distribute

( x - 1 ) - (3x + 2)

(x - 1) - 3x - 2

2. Eliminate redundant parentheses

(x - 1) - 3x - 2

x - 1 - 3x - 2

3. Subtract the numbers

x−1 − 3x − 2

x - 3 - 3x

4.

x − 3 − 3x

-2x - 3

Answer:

-5/2

Step-by-step explanation:

5x+2y=6

First, put the equation in slope-intercept form

y = mx+b where m is the slope and b is the y intercept

Subtract 5x from each side

5x-5x+2y=-5x+6

2y = -5x+6

Divide each side by 2

2y/2 = -5/2x +6/2

y = -5/2 x +3

The slope is -5/2x

Lines that are parallel have the same slope

Answer:

5 to the power of 3

Step-by-step explanation:

I took the K12 test :)

The number of friends who received an email on Wednesday can be obtained using the exponential relation between the initial number of mails and the number of days elapsed, which is 125 .

The Number of people who received a mail on Wednesday can be expressed thus :

Therefore, 125 friends received an email on Wednesday.

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Answer:

1.5 or 1 1/2

Step-by-step explanation:

2*9 = 18

4*3 = 12

18/12 = 3/2

1.5 or 1 1/2

9514 1404 393

Answer:

  (b)  -3

Step-by-step explanation:

The "initial value" is the constant in the equation. It is the value that remains when the x-term is removed. It is the result of evaluating the equation when x=0.

  y = -4(0) -3 . . . . substitute x=0

  y = 0 -3

  y = -3 . . . . the "initial value"

Answer:

$13,300

Step-by-step explanation:

$30,400 in to the ratio of 4:5:7

First lets add 4, 5, and 7:

4 + 5 + 7 = 16

Now divide 30,400 by 16 to find 1 share:

30,400/16 = 1900

Since the largest share is 7, we multiply 1900 by 7, since 1900 is equivalent of 1 share

1900 x 7 = 13300

-Chetan K

Answer:

[tex] let \:x \in (A\cap B)'\\\Rightarrow x \notin (A\cap B) \\\Rightarrow x \notin A \:or\: x\notin B\\ \Rightarrow x \in A' \:or \:x \in B'\\\Rightarrow x \in A' \cup B'\\\therefore (A ∩ B)' = A' ∪ B' [/tex]

It is proved that , A Intersection B complement is equal to the union of the complements of the sets A and B i.e., (A ∩ B)' = A' ∪ B'.

What is a set ?

Sets are represented as a collection of well-defined objects or elements.

It is given that A , B , C , X are sets with A , B and C are subsets of X.

Let's assume X be an element of A intersection B complement. or (A ∩ B)'.

i.e.,

X ∈ (A ∩ B)'

Also , we can say that :

X ∉ ( A ∩ B)

This implies :

X ∉ A or X ∉ B

or we can also say that :

X ∈ A' or X ∈ B'

or

X ∈ A' ∪ B'

So , we can conclude that :

(A ∩ B)' = A' ∪ B'

or A Intersection B complement is equal to the union of the complements of the sets A and B.

Therefore , it is proved that , A Intersection B complement is equal to the union of the complements of the sets A and B i.e., (A ∩ B)' = A' ∪ B'.

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Answer:

y = 5/6x - 3

Step-by-step explanation:

y2 - y1 / x2 - x1

-8 - 2 / -6 - 6

-10 / -12

= 5/6

y = 5/6x + b

2 = 5/6(6) + b

2 = 5 + b

-3 = b

Answer:

y = 5/6x - 3

Step-by-step explanation:

Answer:

200 mi

Step-by-step explanation:

8 times 25 mi = 200 mi

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