Expand and simplify 6(2x - 3) – 2(2x + 1)

The point that represents the quotient [tex]\frac{3 - i}{i}[/tex] is (C)

The quotient is given as:

[tex]Quotient = \frac{3 - i}{i}[/tex]

Rationalize the expression

[tex]Quotient = \frac{3 - i}{i} \times \frac ii[/tex]

Expand the above expression

[tex]Quotient = \frac{3i - i^2}{i^2}[/tex]

Evaluate all exponents

[tex]Quotient = \frac{3i - (-1)}{-1}[/tex]

Remove bracket

[tex]Quotient = \frac{3i +1}{-1}[/tex]

Rewrite the above expression as follows:

[tex]Quotient = -3i -1[/tex]

Further, rewrite as:

[tex]Quotient = -1-3i[/tex]

In the above expression, the real part is -1, and the imaginary part is -3.

This point is represented by point C, because:

[tex]C = (-1,-3)[/tex]

Hence, the point that represents the quotient [tex]\frac{3 - i}{i}[/tex] is (C)

Read more about complex numbers at:

https://brainly.com/question/2218826

Answer:

Triangle 6: 74

Triangle 7: 29

Triangle 8: 61

Triangle 9: 33

Step-by-step explanation:

Every triangle has a total degree angle of 180 degrees. Add the two sides that  are known and subtract the sum from 180 degrees to find out the last angle.

Answer:

There isn't a picture

Step-by-step explanation:

Answer:

8 meters

Step-by-step explanation:

This is a question that deals with Proportion

Height of flagpole/Shadow of flagpole = Height of Luke/Shadow of Luke

Length of the shadow of Luke = x

= 12/24 = 4/x

We cross Multiply

12 × x = 24 × 4

x = 24 × 4/12

x = 8 meters

Hence, the length of the shadow of Luke = 8 meters

Answer:

So, m∠6 = 180° - x°.

Step-by-step explanation:

The answer is 180 degrees

Answer:

[tex] \frac{28}{45} [/tex]

Step-by-step explanation:

Please see the attached picture for the full solution.

Answer:

Step-by-step explanation:

1. Make a proportion.

Set the numbers equal to each other.

I chose the numbers 9, 12, 15, and of course x.

Make the fractions in a way that the x is in the numerator if you want to make your life easier.

15/9 = x/12

2. Simplify

Cross multiply the numbers.

This will give you the equation of

9*x and 15*12

3. Make an equation

Simplify the numbers by mulitplying them

9x = 180

4. Divide both sides by 9

9x = 180

/9      /9

Hope this helped,

Kavitha Banarjee

Answer:

-3/2

Step-by-step explanation:

The slope is found by

m = ( y2-y1)/(x2-x1)

Using the points (-4,11) and ( 0,5)

m = ( 11-5)/( -4-0)

  = 6/-4

  = -3/2

Answer:The slope of the line would be 1/3 because if you put those two coordinates in the table then you can see the the difference between 5 and 1 is 4 and the difference between 9 and 21 is 12 then do 4 divided by 12 and you get 1/3 for your slope.

Step-by-step explanation:  I know math just trust me i am a sraight A student.

9514 1404 393

Answer:

  false

Step-by-step explanation:

You can check to see if the sum of squares of the smaller two numbers is equal to the square of the larger.

  8² +15² vs 17.5²

  64 +225 vs 306.25

At this point, you need go no further. The sum of two integers will not have a fractional part, so cannot be equal to 306.25.

  289 vs 306.25 . . . . the long side is too long for a right triangle.

__

If you were familiar with some of the Pythagorean triples, you would know that the closest triple is {8, 15, 17}, so (8, 15, 17.5) does not represent a right triangle.

A few common Pythagorean triples are ...

  {3, 4, 5}, {5, 12, 13}, {7, 24, 25}, {8, 15, 17}, {9, 40, 41}

Answer:

i am so sorry that i dont know

Answer:

it's about 10, but without rounding it's 10.62

Step-by-step explanation:

Step-by-step explanation:

make the coefficients same

then if sign are same subtract the one you wanna cancel it then here it goes

lam gonna start making coefficient of x sam like this:

4.X+7y= -37

1.4X-3y=7

then i will subtract all x or cancel to each other then

4X+28y= -148

-

4X-3y=7

and then -×-=+

add all y

31y=141

y= 4.55 then we take one of the equation then substitute y to 4.55 so i chose first equation

X+7(4.55)=-37

X+31.85=-37

so take 31.85 to the side it will become -31.85

then X=-37-31.85

X=68.85

i hope that it will help you

Note: The must be [tex]0.04v^2[/tex] instead of [tex]0.04v[/tex].

Given:

The stopping distance, d ( in feet) for a van moving at a velocity (speed) v miles per hour is modeled by the equation:

[tex]d=0.04v^2+1.1v[/tex]

To find:

The stopping distance for a velocity of 10 miles per hour.

Solution:

We have,

[tex]d=0.04v^2+1.1v[/tex]

where, d is stopping distance and v is velocity.

Substitute v=10  in the given equation to find the stopping distance for a velocity of 10 miles per hour.

[tex]d=0.04(10)^2+1.1(10)[/tex]

[tex]d=0.04(100)+11[/tex]

[tex]d=4+11[/tex]

[tex]d=15[/tex]

So, the stopping distance for a velocity of 10 miles per hour is 15 ft.

Therefore, the correct option is c.

Answer:

Step-by-step explanation:

Step one:

given data

total number of weeks =52 weeks

study time per week is = 10 hours

total study time for the year = 52*10

=520 hours per year.

Step two:

given that the value of the scholarship for one year is $50,000.

we want to find the amount that an hour of study brings

so we have to divide the total scholarship by the amount of study time

50000/520

=$96.15

your hourly return on your investment in study time is $96.15

Answer:

[tex]P(A\ n\ B) = 0.557[/tex]

Step-by-step explanation:

Given

[tex]P(A) = 0.78[/tex]

[tex]P(B) = 0.65[/tex]

[tex]P(A\ u\ B) = 0.873[/tex]

Required

Determine [tex]P(A\ n\ B)[/tex]

From laws of probability, we have:

[tex]P(A\ n\ B) = P(A) + P(B) - P(A\ u\ B)[/tex]

Substitute in values

[tex]P(A\ n\ B) = 0.78 + 0.65 - 0.873[/tex]

[tex]P(A\ n\ B) = 0.557[/tex]

Hence, [tex]P(A\ n\ B)[/tex] is calculated to be 0.557

Answer:

y=x+4

Step-by-step explanation:

slope intercept form: y=mx+b

m is the slope of the line and b is the y-intercept

slope: 1

y-intercept: 4

hopefully this helps :)

Answer:

y=x+4

Step-by-step explanation:

y=mx+b

m-is the slope and b-is the y-intercept

(x, y) = (0,4)

4=0+b so b =4

substitute in the equation

y=x+4

Answer:

785

Step-by-step explanation:

2500÷10=250

250×3.14=785

Answer:

18

Step-by-step explanation:

Add all the sides. But you are missing two sides. Soo since the top is 4, the bottom is two bc half is two. then the right side is 5 and the left, half is 2 so the other half is 3. 3+2=5! soooo the perimeter is 18.

Answer:

18

Step-by-step explanation:

We add up the side lengths,

[tex]5+4+3+2+2+2= 18[/tex]

by finding missing side lengths with subtraction and logic

and I'm pretty sure this is correct, but I like double-checking things.

This figure is made out of 2 rectangles,

2x5 and 3x2

The perimeter of each is 14 and 10

[tex]14+10-3-3=18[/tex]

the two 3's are the over lapping sides

We also get 18.

Answer:

a) 10 = X + Y

b) X = 1, Y = 9

X = 2, Y = 8

X = 3, Y = 7

X = 4, Y = 6

X = 5, Y = 5

i) The inputted values of X and Y are the solutions of the equation because they sum up to the 10 songs on Nyla's playlist.

Step-by-step explanation:

The given parameters are;

The number of songs in the playlist on her phone = 10

The number of authors of the songs on her playlist = 2

The equation that represent the situation is given as follows;

X + Y = 10

Where X represent the number of Beyonce's song on her playlist and Y represent the number of Jennifer Lopez's song on her playlist

b) 5 possible solutions are;

X = 1, Y = 9

X + Y = 1 + 9 = 10

Which gives 1 Beyonce's and 9 Jennifer Lopez's songs

X = 2, Y = 8

X + Y = 2 + 8 = 10

Which gives 2 Beyonce's and 8 Jennifer Lopez's songs

X = 3, Y = 7

X + Y = 3 + 7 = 10

Which gives 3 Beyonce's and 7 Jennifer Lopez's songs

X = 4, Y = 6

X + Y = 4 + 6 = 10

Which gives 4 Beyonce's and 6 Jennifer Lopez's songs

X = 5, Y = 5

X + Y = 5 + 5 = 10

Which gives 5 Beyonce's and 5 Jennifer Lopez's songs

i) The inputted values of X and Y are the solutions of the equation because they sum up to the 10 songs on Nyla's playlist.

Answer:

cos x=√3/2

cos x=60°. (cos60°=√3/2)

{x=60°}

Answer:if the notebooks cost 3.59 and pens cost 1.49, with x representing the notebooks and y representing the number of pens and an amount of $13, the inequality would be written as 3.59x+1.49y13

Step-by-step explanation:

Answer:

$30.41

Step-by-step explanation:

Given that:

Discount off = 15%

Original price = $45

Mark down on item = 25%

Sales tax on final price = 6%

Cost of Jean will be ;

Mark down price :

Original price - (Original price * markdown %)

$45 - ($45 * 0.25) = $33.75

Discounted price :

Markdown price - (markdown price * discount %(

$33.75 - (33.75 * 0.15)

= $28.6875

Final price :

Discounted price + (sales tax * discounted price)

28.6875 + (0.06 * 28.6875)

= $30.40875

= $30.41

Answer:

The magnitude of w is approximately 26.

The angle between w and u is approximately 32.2°.

Step-by-step explanation:

The magnitude of w is approximately 15.1, and the angle between w and u is approximately 62.67 degrees and this can be determined by using the given data.

Given :

a) The magnitude of 'w' is calculated using the below formula:

[tex]w = \sqrt{u^2+v^2+2uvcos\theta }[/tex]

Now, substitute the values of u, v, and [tex]\theta[/tex] in the above formula.

[tex]w = \sqrt{14^2+16^2+2\times14\times16\;cos120 }[/tex]

Simplify the above expression.

[tex]w =15.1[/tex]

b) The angle between w and u is calculated using the below formula:

[tex]tan\beta =\dfrac{vsin120}{u+vcos120}[/tex]

Now, substitute the above values of u and v in the above expression.

[tex]tan\beta =\dfrac{14\times sin120}{14+16\times cos120}[/tex]

Simplify the above expression in order to determine the value of [tex]\beta[/tex].

[tex]\beta = 62.67^\circ[/tex]

The magnitude of w is approximately 15.1, and the angle between w and u is approximately 62.67 degrees.

For more information, refer to the link given below:

https://brainly.com/question/13188123

Answer:

3

Step-by-step explanation:

You would first plug in the points to the slope formula which is as follows:

m = y2 - y1 / x2 - x1

When you plug it in, it should look as follows:

m = 10 - 4 / 7 - 5

You should now add like terms.

m = 6/2

You should now simplify.

m = 3

Answer:

a.It is a good fit because the same number of data points are on each side of the line.

c.The line shows a positive correlation.

e.The rate of change can be represented by the slope of the trend line.

Step-by-step explanation:

Answer: -It is a good fit because the same number of data points are on each side of the line.

- The line shows a positive correlation.

-The rate of change can be represented by the slope of the trend line.

(A, C, E on edg) :)!

To find slope, we must use the slope formula*.

[tex]m = \frac{2 - 0.5}{2 - (-2.5)} = \frac{1.5}{4.5}[/tex]

The slope is 1.5/4.5.