is the square root of 3 rational?

Answer:

The required equation is: [tex]y = -\frac{8}{5}x+\frac{127}{25}[/tex]

Step-by-step explanation:

The slope-intercept form of a line is given by:

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

For writing equation of a line, slope and a point is needed from which the line passes.

In order to find the slope of line perpendicular to PQ, we have to find slope of PQ first.

Slope is denoted by m and given by the formula

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

Given points are:

P(-1, -4) and Q (7, 1)

Putting the values

[tex]m = \frac{1-(-4)}{7-(-1)}\\m = \frac{1+4}{7+1} = \frac{5}{8}[/tex]

The product of slope of two pependicular lines is -1

Let m1 be the slope of line perpendicular to PQ

[tex]m.m_1 = -1\\\frac{5}{8}.m_1 = -1\\m_1 = \frac{8}{5} * -1\\m_1 = -\frac{8}{5}[/tex]

Now for the point, we have to find the point that divides PQ in ratio 3:2

The formula is:

[tex](x,y) = (\frac{nx_1+mx_2}{m+n} , \frac{ny_1+my_2}{m+n})\\[/tex]

Here

m = 3

n= 2

Putting the values

[tex](x,y) = (\frac{(2)(-1)+(3)(7)}{3+2} , \frac{(2)(-4)+(3)(1)}{3+2})\\= (\frac{-2+21}{5} , \frac{-8+3}{5})\\=(\frac{19}{5} , \frac{-5}{5})\\=(\frac{19}{5} , -1)[/tex]

So we have to write equation of a line with slope -8/5 and passing through point (19/5, -1)

Putting the values in slope-intercept form

[tex]y = -\frac{8}{5}x +b[/tex]

Putting the point in the equation

[tex]-1 = -\frac{8}{5} (\frac{19}{5}) + b\\-1 = -\frac{152}{25} + b\\b = -1+\frac{152}{25}\\b = \frac{-25+152}{25}\\b = \frac{127}{25}[/tex]

Putting the value of b

[tex]y = -\frac{8}{5}x+\frac{127}{25}[/tex]

Hence,

The required equation is: [tex]y = -\frac{8}{5}x+\frac{127}{25}[/tex]

Answer:

Sum

Step-by-step explanation:

Answer:

Sum

Step-by-step explanation:

Sum reason it is

Answer:

its 66.96

Step-by-step explanation:

to find the area we do the length x height of the shape

Answer: 57.97 cm squared

Step-by-step explanation:

Step-by-step explanation:

[tex]2,4,5[/tex]

Answer:

domain: -3 < x <2

range: -2 < x < 4

Step-by-step explanation:

domain is the total x values and range is the total y values

Answer: 5.39 hours

Step-by-step explanation:

For Jill:

Number of hours used = 8.4 hours

Number of bushels of apples picked = 40

Number of bushels of apples picked per hour will be: = 40/8.4 = 4.7619

For Maria:

Number of hours used = 15 hours

Number of bushels of apples picked = 40

Number of bushels of apples picked per hour will be: = 40/15 = 2.6667

We then add the number of bushels of apples picked per hour for both of them together. This will be:

= 4.7619 + 2.6667

= 7.4286

If they worked together, the hours they'll take to pick 40 bushel of apples will be:

= 40/7.4286

= 5.39 hours

Answer: 4 P

Step-by-step explanation: hope this helps!

The solution of the given expression 3p+2p-p will be 4P.

The mathematical expression is the combination of numerical variables and operations denoted by addition, subtraction, multiplication, and division signs.

Mathematical symbols can be used to represent numbers (constants), variables, operations, functions, brackets, punctuation, and grouping. They can also be used to denote the logical syntax's operation order and other properties.

Given expression is 3p+2p-p. The expression will be simplified as:-

E = 3p+2p-p

Add the values 3p and 2p first.

E = 5p - p

Subtract p form 5p.

E = 4p

Therefore, the solution of the given expression 3p+2p-p will be 4P.

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#SPJ2

Answer:

D

Step-by-step explanation:

Took This Test Too :P

Answer: It’s $4.00

Step-by-step explanation:

Answer:

9mph

Step-by-step explanation

4 1/2 *2 - 9

Answer:

The statement that best describes how to determine if the plane clears the tower is;

Use the Pythagoras Theorem where the distance to the tower is a leg of the right triangle and the distance in the air is the hypotenuse. Find the other leg. Convert to feet to compare to the tower height

Step-by-step explanation:

The given parameters are;

The length the plane will travel before lifting = 1300 yards

The distance further the plane will travel after lifting off the ground = 705 yards

The horizontal distance from the point of lifting off the ground to control tower = 700 yards

The distance of the path of the plane after lifting off the ground, the horizontal distance from the point of lifting off the ground to control tower and the height of the control tower form a right triangle with sides given as follows;

The distance of the path of the plane after lifting off the ground = The hypotenuse side of the triangle

The horizontal distance from the point of lifting off the ground to control tower and the height of the control tower = The two legs of the right triangle

Let h, represent the height of the control tower, let x represent the horizontal distance from the point of lifting off the ground to control tower and let R represent the distance of the path of the plane after lifting off the ground, we have;

h = √(R² - x²)

We have;

R = 705 yards

x = 700 yards

∴ h = √(R² - x²) = h = √(705² - 700²) = 5·√281

The height of the control tower, h = 5·√281 yards

1 yard = 3 feet

∴ 5·√281 yards = 3 × 5·√281 feet ≈ 251.446 feet

Therefore, given that the height of the control tower = 250 feet, the plane at the height of approximately 251.446 feet clears the tower.

The height of the control tower = 250 feet and the plane  the height of approximately 251.446 feet clears the tower.

The statement that best describes how to determine if the plane clears the tower is;

Use the Pythagoras Theorem where the distance to the tower is a leg of the right triangle and the distance in the air is the hypotenuse. Find the other leg. Convert to feet to compare to the tower height

The given parameters are;

The length the plane will travel before lifting = 1300 yards

The distance further the plane will travel after lifting off the ground = 705 yards.

The horizontal distance from the point of lifting off the ground to control tower = 700 yards

The distance of the path of the plane after lifting off the ground, the horizontal distance from the point of lifting off the ground to control tower and the height of the control tower form a right triangle with sides given as follows.

The distance of the path of the plane after lifting off the ground = The hypotenuse side of the triangle.

The horizontal distance from the point of lifting off the ground to control tower and the height of the control tower = The two legs of the right triangle.

Let h, represent the height of the control tower, let x represent the horizontal distance from the point of lifting off the ground to control tower and let R represent the distance of the path of the plane after lifting off the ground, we have;

[tex]h = \sqrt{(R^2 - x^2)}[/tex]

We have given that

R = 705 yards

x = 700 yards

[tex]h = \sqrt{(R^2 - x^2)} \\ h = \sqrt{(705^2 - 700^2)}\\ h= 5\times \sqrt {281}[/tex]

The height of the control tower,[tex]h = 5 \sqrt {281}[/tex] yards.

1 yard = 3 feet

[tex]5\sqrt {281} yards= 3 \times 5\times \sqrt{281} feet \approx 251.446 feet[/tex]

Therefore, given that the height of the control tower = 250 feet, the plane at the height of approximately 251.446 feet clears the tower.

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Answer:

m = undef

General Formulas and Concepts:

Step-by-step explanation:

Step 1: Define

Point (-4, -16)

Point (-4, -5)

Step 2: Find slope m

Answer:

150

Step-by-step explanation:

r150 naka cdi lang HAHAHAHAHAHA

Answer:

Lets say S is speed

S= m/ t

m/t would give us his speed in miles per minute.

Answer:

x = 58

Step-by-step explanation:

Angle Formed by Two Secants = 1/2(difference of Intercepted Arcs)

51 =1/2 (160-x)

Multiply each side by 2

102 = 160-x

Subtract 160 from each side

102-160 = -x

-58 = -x

Multiply by -1

58 =x

Answer:

x = 58

Step-by-step explanation:

[tex]51 \degree = \frac{1}{2} (160 \degree - x \degree) \\ \\ 51 \times 2 \degree = 160 \degree - x \degree \\ \\ 102 \degree = 160 \degree - x \degree \\ \\ x \degree = 160 \degree - 102 \degree \\ \\ x \degree = 58 \degree \\ \\ \huge \red{ \boxed{x = 58}}[/tex]

The parabola can intersect the circle four times as the graph shows below. Each intersection point is a solution in the form (x,y).

Answer:

X=5

Step-by-step explanation:

Answer:

5

Step-by-step explanation:

5x-2=2x+13

-2x     -2x

3x-2=13

    +2   +2

3x=15

divide 15 by 3.

Answer:

0.5 goes on 2 points to the left0, 0.75 goes 3 points to the left of 0, 1.25 goes 1 point to the left from the 1, - 9/4 goes at the very end on the left side, and - 7/4 goes 1 right from the 2.

Step-by-step explanation:

Answer:

The answer is the option C

Step-by-step explanation:

Hope it help

Answer:

c

Step-by-step explanation:

i took the quiz

Answer:

[tex]\frac{4}{5}[/tex]

Step-by-step explanation:

[tex]M=\frac{x2-x1}{y2-y1}[/tex]

[tex]M=\frac{5-1}{-5-(-10)}[/tex]

[tex]M=\frac{4}{5}[/tex]

Answer:

30

Step-by-step explanation:

Its just 14+16 im pretty sure

Answer:

m=-2n/9

Step-by-step explanation:

Answer:

3w-2

Step-by-step explanation:

Given that, after w weeks you sold (3w+8) subscriptions and your friend sold (6w+6) subscriptions.

So, the difference between the number of subscriptions your friend has sold and you have sold after w weeks = (6w+6)-(3w+8)

=6w+6-3w-8

=3w-2

Hence, the required expression is 3w-2.

Answer:

$5,131

Step-by-step explanation:

First, add together the values of the money she lost:

78 + 36

= 114

Then, subtract this from her total amount:

5245 - 114

= 5131

So, in the end, Mrs. Lim had $5,131

Answer:

$5131

Step-by-step explanation:

First, break down the word problem. Mrs. Lim had $5245, spent $78, and gave $36 away to her son. Next, set up an equation.

5246 - 78 - 36 = ?

$5131

Answer:

$720

Step-by-step explanation:

Use the simple interest formula and plug in each variable into the formula

I=PRT

P=$6000

R=3% (0.03)

T=4 years

Answer:

A rational function is any function which can be written as the ratio of two polynomial functions, where the polynomial in the denominator is not equal to zero. The domain of f(x)=P(x)Q(x) f ( x ) = P ( x ) Q ( x ) is the set of all points x for which the denominator Q(x) is not zero.

Hope this helps!!! :D

9514 1404 393

Answer:

  f(x) = (x^2+2)/(x-1)

Step-by-step explanation:

In simplest form, it will be a quadratic divided by (x-1). The quadratic must have no zeros, and a y-intercept of 2.

One such could be ...

  f(x) = (x^2 +2)/(x -1)

__

The numerator polynomial must have no zeros in order to prevent the rational function from having zeros. It must be a function that has a degree an odd number greater than the denominator function. The denominator function can have only one zero, at x=1. The ratio of the functions must have a net odd degree and the overall leading coefficient must be positive in order to make the end behavior match the requirement.

Answer:

11

Step-by-step explanation:

you do 2000 - 350

you would get 1650

and you divide it by 150

it would look like this 1650 ÷ 150 = 11

Answer:

y= 2/5-1

Step-by-step explanation:

You get the 2/5 because you go 2 to the right and go 5 up, the -1 is because the x-int is at -1.