Given the ordered pairs A (-6, 4) and B(8, 9). Show all work!
a. Find the equation of the line through AB.
b. Find the equation of the line parallel to line AB and passes through the point (14, -6).
c. Find the equation of the line perpendicular to line AB and passes through the point (-5, -10).

Answer: (-2-2i)(-4+6i) = 20 - 4i

Step-by-step explanation:

We have the expression:

(-2 - 2i)*(-4 + 6i)

the rule we need to know here is that i*i = -1

now, the first step is distribute the parentheses.

(-2 - 2i)*(-4 + 6i) = -2*-4 -2*6i - 2i*-4 - 2i*6i = 8 -12i + 8i -12*(i*i)

= 8 + (8 - 12)i +12 = 20 - 4i

Answer:

Percent increase is 17.6%

We still have to pay 7.50 with the coupon

Step-by-step explanation:

Percent increase = (new- original)/original *100%

                             = (10-8.5)/8.5 * 100%

                             = 1.5/8.5 * 100%

                             = 17.6470588%

Round to the nearest tenth

                                 17.6%

This is an increase since the cost went up.

If we have 25% off, we still have to pay (100%-25%) = 75%

10 *.75 = 7.50

We still have to pay 7.50 with the coupon

Answer:

A) 10^2

Step-by-step explanation:

100 is 10 times 10 or 10 to the second power

100 = 10 * 10 = 10 ^2

Answer:

120° & 240° (given the angles are between 0° and 360°)

Step-by-step explanation:

We want to find [tex]arccos(-\frac{1}{2})[/tex].

This means we want to know the angle(s) for which cosine has a value of [tex]-\frac{1}{2}[/tex].

The basic acute angle that has a cosine of [tex]\frac{1}{2}[/tex]  is 60°. But we want to know NEGATIVE [tex]\frac{1}{2}[/tex]. So in which quadrants is cosine negative? Second and Third

Where α is the basic acute angle (in our case it is 60°)

So 2nd quadrant angle is 180 - 60 = 120°

and 3rd quadrant angle is 180 + 60 = 240°

Answer:

120°

Step-by-step explanation:

arccos means the inverse of cosine.

arccos (-1/2) ⇒ We can rewrite this equation as;

cosФ = 1/2 Find the value of  Ф.

Ф = arccos (-1/2) ⇒ This can be calculated directly from the calculator.

arccos (-1/2) = 120°

or arccos (-1/2) = (180 + 60)

                         = 240°

You can have more than one value of arccos (-1/2) since the cosine is negative in the second and third quadrant.

Answer:

6.6 stone

Step-by-step explanation:

We will use conversions to change kilograms to stones

1 kilogram= 2.2 pounds,

1 stone= 14 pounds

42 kilogram          2.2 lbs           1 stone

---------------       * -------------   * ---------------

                           1 kg                 14 lbs

All the units cancel except stone

(42*2.2)/14  stone

6.6 stone

Answer:

42 kilograms is equal to 6.6 stones.

Step-by-step explanation:

Using the given conversion factors:

1 kilogram = 2.2 pounds

1 stone = 14 pounds

To Find: 42 kilograms into stones  =  ? stones

Solution:

42 kilograms = [tex]42\times 2.2 pounds=92.4 pounds[/tex]

Another conversion factor used:

1 stone = 14 pounds

[tex]1 pound = \frac{1}{14} stones[/tex]

[tex]92.4 pounds=92.4\times \frac{1}{14} stones=6.6 stones[/tex]

So, 42 kilograms is equal to 6.6 stones.

The slope-intercept form:

[tex]y=mx+b[/tex]

m - slope

b - y-intercept

The formula of a slope:

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

We have the y-intercept (0, -3) → b = -3

Chose two points: (6, 1) and (0, -3). Substitute:

[tex]m=\dfrac{-3-1}{0-6}=\dfrac{-4}{-6}=\dfrac{4}{6}=\dfrac{2}{3}[/tex]

Answer: [tex]\boxed{y=\dfrac{2}{3}x-3}[/tex]

X/0.4 = 10x/4

21/9÷31/6 = 21•6/31•9

so solving the equation gives

X=84/465

Answer:

Step-by-step explanation:

19/9÷19/6=2/3

then we have:

x÷0.4=2/3

×0.4.   ×0.4

x=4/15

Boom shaka laka

Answer:

It is given that,

there are 8 balls in the bag numbered 1 to 8

Only one ball color is gray and all others are white

P(X) = probability of getting white ball

P(not X) = Probability of getting gray ball

a)  To find Probabilities P(X) and P(not X)

For event X, 1,3,4,5,6,7,8 are checked and P(X) = 7/8

for event 'not X' only 2 is checked and P(not X ) = 1/8

b) To find 1 - P(X)

1 - P(X) = 1 - 7/8 = (8 - 7)/8 = 1/8  

c)1 - P(X) is same as P(not X)

Answer: The option B. 1.9 is correct

Explanation:

We are given the below information:

x               Probability P(x)

0                      0.2

1                       0.1

2                      0.4

3                       0.2

4                       0.1

The expected value of x is given below:

[tex]E(x)=\sum x P(x)[/tex]

         [tex]=(0 \times 0.2)+(1 \times 0.1)+(2 \times 0.4)+(3 \times 0.2)+(4 \times 0.1)[/tex]

        [tex]=0+0.1+0.8+0.6+0.4[/tex]

        [tex]=1.9[/tex]

Therefore, the expected value of x is 1.9      

Answer:

1260

Step-by-step explanation:

The least common multiple is the smallest positive number which is a multiple of the two. This means 84, 36, and 15 divide into it evenly. To find the multiple:

84: 2*2*3*7

36: 2*2*3*3

15: 3*5

LCM: 2*2*3*3*5*7= 1260

Answer:

A and B.

Step-by-step explanation:

To get to know the graph with least slope, we have to write all equations in the form y=mx + c.

where m is the slope and c is the the y-intercept.

A. y = x + 6

For this equation m = 1

B. y = -x - 9

For equation B, m = -1

C. y = 2x + 1

In this equation, m = 2

D. y = -7x - 2

In equation D, m = -7

The equation with the highest slope is D while the one with the least slope/steep is A and B.

Answer:

Step-by-step explanation:

-5,5,-5,5,-5,5,-5,5,-5

Answer:

y = 2x^2+12x+3 = 2(x + 3)^2 - 15

Step-by-step explanation:

Discussion Graph

Technically, the vertex form would y = 2(x + 3)^2 - 15. It needs to be more general than equated to zero. I have solved it the way you presented it and graphed it by definition.

Notice they have the same critical point which means they are equivalent

Answer:

You can travel 25 miles

Step-by-step explanation:

19.50-4.00=15.5

15.5-3=12.5

12.5÷0.5=25

Answer:

trapezoid rhombus parallelogram rectangle square

Step-by-step explanation:

It is easier to say that the triangle is the only one that does not apply. It only has 3 sides. The rest all have at least 1 set of parallel lines (trapezoid). The others have 2 sets of parallel lines.

Wrong !

The right response is :

All of the following except a trapezoid

Answer:

x=5

Step-by-step explanation:

In a square, the diagonals are equal.

4x+17 = 12x-23

Subtract 4x from each side.

4x-4x+17 = 12x-4x-23

17 = 8x-23

Add 23 to each side

17+23 = 8x-23+23

40 = 8x

Divide each side by 8

40/8 = 8x/8

5 =x

Answer:

[tex]\frac{21}{25}[/tex]

Step-by-step explanation:

If 84% are fiction, then the fraction of these are simply the percentage over 100:

[tex]\frac{84}{100}[/tex]

Simplified down by dividing by 4:

[tex]\frac{21}{25}[/tex]

Final answer:

To convert 84% to a fraction, divide 84 and 100 by their greatest common divisor, which is 4, resulting in the simplified fraction 21/25 representing the part of Astrid's books that are fiction.

Explanation:

To convert the percentage of Astrid's books that are fiction into a fraction, we simply write the percentage as a ratio out of 100 and then simplify it. Since 84% of her books are fiction, we start with the fraction 84/100. This fraction can be simplified by dividing both the numerator and the denominator by the greatest common divisor, which is 4 in this case.

84 ÷4 = 21
100 ÷ 4 = 25

Therefore, the simplified fraction of Astrid's books that are fiction is 21/25.

Answer:

4 - π

Step-by-step explanation:

(a) Radius of circle

  A = πr²      Substitute value of A

4π = πr²      Divide each side by π

 r² = 4         Take the square root of each side

  r = 2

(b) Area of MON

A = ¼ × area of circle

A = ¼ × 4π

A = π

(c) Area of MONP

 l = r      Substitute the value of r

 l = 2

A = l²      Substitute the value of l

A = 2²

A = 4

(d) Area of MPN

A(MPN) = A(MONP) – A(MON)  

Area(MPN) = 4 - π

Answer:

sqrt(52)

Step-by-step explanation:

Given points P(2,2)  and Q(6,8)

To find distance between points we apply distance formula

[tex]D = \sqrt{(x_2-x_1)^2+(y_2-y_1)^2}[/tex]

(x1,y1) is (2,2)  and (x2,y2) is (6,8)

Plug in the values in the formula

[tex]D = \sqrt{(6-2)^2+(8-2)^2}[/tex]

[tex]D = \sqrt{16+36}[/tex]

[tex]D = \sqrt{52}[/tex]

Answer:

answer is B sqrt65

Step-by-step explanation:

Answer:

27

Step-by-step explanation:

draw 3 groups of 9 somethings or 9 groups of 3 somethings

In the 3x9 array representation there are 3 rows and 9 columns, each initialized with the value 0

Since we know that,

A set of components of the same data type are stored collectively in contiguous memory regions in an array, which is a form of data structure. To organise data sets in a way that is simple to sort and search, computer programmers employ arrays in their programmes. They can make a programme operate more quickly and are more effective at storing data than individual variables.

Sure, here's a simple array that represents a 3x9 grid:

[tex]\left[\begin{array}{ccccccccc}0&0&0&0&0&0&0&0&0\\0&0&0&0&0&0&0&0&0\\0&0&0&0&0&0&0&0&0\end{array}\right][/tex]

In this array, there are 3 rows and 9 columns, each initialized with the value 0.

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Answer:

180

Step-by-step explanation:

60% of 300 tickets equals?

(60/100) * 300 = x

0,6 * 300 = x

180 = x

Answer:

180 tickets

Step-by-step explanation:

We want to find 60 percent of 300

Change 60 percent to a decimal

60% = .6

.6 * 300 = 180

Answer:

1. a= -1

2. k=5

3. x= 10

4. y= -1/5

Step-by-step explanation:

1. 2+1/6a= -4

6= -1/6a

a=6*-1/6

a= -1

2. 7k-3=32

7k=32+3

7k=35

k=5

3. 2x-5=15

2x=20

x=10

4. 3y+2:5= -1:5

-3y=3/5

y= 3/5: -3

y= -1/5

Answer:

A: -1

K: 5

X: 10

Y: -1/5

HOPE THIS HELPS! :)

Answer:

The areas are equal.

Step-by-step explanation:

Let the first rectangle be R and

the second rectangle be R'.

Sine R and R' are identical, their lengths are equal and their breadths are equal.

So, if Inga divided each into equal parts, then each part of both rectangles are equal.

Hence, the colored parts of both rectangles are equal.

Answer:

exact form=-65/4

decimal form=-16.25

Step-by-step explanation: solve for y by simplifying both sides of the equation, then isolating the variable

The solution of expression is,

⇒ y = - 16.25

We have to give that,

An expression to simplify is,

⇒ 26 = - 8/5y

Now, We can simplify the expression as,

⇒ 26 = - 8/5y

Multiply by 5 on both sides,

⇒ 26 × 5 = - 8y

⇒ 130 = - 8y

⇒ - 8y = 130

Divide both sides by - 8,

⇒ y = - 130/8

⇒ y = - 16.25

Hence, the Solution is, y = - 16.25

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Answer:

They're equally as important because they are the same thing, but just meant for finding different sides.

Step-by-step explanation:

Total money Marcus has = $28

Money spent to buy a notebook = $3.75

Money left now = [tex]28-3.75=24.25[/tex]

Money needed to be saved = $11.25

So, the amount of money Marcus can spend = [tex]24.25-11.25=13[/tex]

Cost of a packet of chips = $1.30

The inequality to determine the maximum number of chips he can buy is:

Let the number of chips Marcus can buy = x

As he cannot spend more than $13 to buy chips so equation becomes:

[tex]1.30x\leq 13[/tex]

Solving this we get

[tex]x\leq 10[/tex]

Hence, Marcus can buy a maximum of 10 packs of chips and  save $11.25

Answer:

Coordinate of Q (3,4)

Step-by-step explanation:

Let to points S(-2,-6) and T(5,8)  

Le Q(x,y) be the point in which it divide the ST in the ratio 5:2

If a point (x,y)cut the line in the ratio a : b where the end coordinate are( x1,y1) and (x2,y2)

x = x1 + p/w(x2 - x1) and y = y1 + p/w(y2 - y1)  

where p = a and w = a+b

To find the coordinate of Q

x  = x1 + p/w(x2 - x1 )

x = -2 + 5/7(5 - -2) = -2 + 5=3

y = y1 + p/w(y2 - y1)  

y = -6 + 5/7(8 - -6) = -6 + 10 = 4

Therefore the coordinate of Q is (3,4)

Answer:

J=PM/300

Step-by-step explanation:

300J/P=M

*p              *P

300J=PM

300J/300=PM/300

J=PM/300

Answer:

J=MP/300

Step-by-step explanation:

M=300J/P

now take p to the left hand side of the equation

MP= 300J

MP/300 = J

J= PM/300