7<br> +<br> #1. Graph a line to represent the function<br> Y = 4x

Line L passes through the points (0, --3) and (6,9).<br> (a) Find the equation of line L.

valentina_108 [34]

Step-by-step explanation:

Given points are :

$(0,\:-3)=(x_1,\:y_1) \:\&\: (6,\:9)=(x_2 ,\:y_2)$

Equation of line in two point form is given as:

$\frac{y -y_1 }{y_1 -y_2 } = \frac{x -x_1 }{x_1 -x_2 } \\ \\ \therefore \frac{y -( - 3)}{ -3 -9 } = \frac{x -0 }{0 -6 } \\ \\ \therefore \frac{y + 3}{ -12} = \frac{x }{ -6 } \\ \\ \therefore \frac{y + 3}{ 2} = \frac{x }{1} \\ \\ \therefore \: y + 3 = 2x \\ \\ \huge \red{ \boxed{\therefore \: 2x - y - 3 = 0}} \\ is \: the \: required \: equation \: of \: line.$

5 0

3 years ago

As of April 2006, roughly 50 million web domain names were registered (e.g., ). How many domain names consisting of just two let

Furkat [3]

Answer:

a) 676, 1296

b) 17576, 46656

c) 456976, 1679616

Step-by-step explanation:

firstly we know that there are 26 letters in the alphabet.

there are 26 ways of choosing the first character and 26 ways choosing the second character,

Therefore, the possible number of domains with two leeter is;

n = 26²

= 26 × 26

= 676

now when the digits are allowed, there are 26 + 10 = 36 characters to be used in total

therefore the possible number of domains with two characters is;

n = 36²

= 36 × 36

= 1296

b)

there are 26 ways of choosing each character

therefore, the possible number of domains with three letters is

n = 26³

= 26 × 26 × 26

= 17576

when the digits are allowed, there are 26 + 10 = 36 characters to be used in total

therefore , the possible number of domains with three characters is;

n = 36³

= 36 × 36 × 36

= 46656

c)

there are 26 ways of choosing each character, therefore the possible number of domains with four letters is;

n = 26⁴

n = 26 × 26 × 26 × 26

n = 456976

when the digits are allowed, there are 26 + 10 = 36 characters to be used in total

therefore, the possible number of domains with four characters is;

n = 36⁴

n = 36 × 36 × 36 × 36

= 1679616

7 0

3 years ago

Verify that your point from Question 2 is a solution to 2x-y=-12x−y=−1 AND is also a solution to y=5x-5y=5x−5. What does it mean

Vera_Pavlovna [14]

Answer:

(a) Verified

(b) They are simultaneous equations

Step-by-step explanation:

Given

$2x - y = -1$

$y =5x - 5$

Required

Verify that: $(x,y) = (2,5)$ is a solution

We have:

$2x - y = -1$

Substitute: $(x,y) = (2,5)$

$2 * 2 - 5 = -1$

Evaluate all products

$4 - 5 = -1$

Subtract:

$-1 = -1$

<em>Because both sides of the equation are equal, then the point is a solution</em>

Also: $y =5x - 5$

Substitute: $(x,y) = (2,5)$

$5 = 5 * 2 - 5$

Evaluate all products

$5 = 10 - 5$

Subtract:

$5 = 5$

<em>Because both sides of the equation are equal, then the point is a solution</em>

Because the given point is a solution to both equations, then they are simultaneous equation

7 0

3 years ago

A system of equations has no solution. if y = 8x 7 is one of the equations, which could be the other equation? 2y = 16x 14 y = 8

SCORPION-xisa [38]

A system of equations has no solution. if y = 8x+ 7 is one of the equations, The other equation will be y = 8x - 7.

<h3 /><h3>What is the system of two equations?</h3>

A set of two linear equations with two variables is called a system of linear equations. They create a system of linear equations when evaluated collectively.

The first equation is given as:

y = 8x + 7

The equations in the system would have different constant values if the system of equations had no solution.

y=8x+b

Where:

b is a variable that is not equal to 7.

The equation whose standard form is y=ax+b has no solution. Only equation 2 satisfies the generalized form.

Hence.if y = 8x+ 7 is one of the equations, The other equation will be y = 8x - 7.

To learn more about the system of two equations refer to the link;

brainly.com/question/21620502

3 0

2 years ago

An ant looks up to the top of a building at an angle of elevation of 32°. Then, the ant walks an additional 88 feet from the edg

Naddik [55]

Tanα=h/x, tanß=h/(x+88)

solving both for x

x=h/tanα, x=h/tanß-88, since x=x

h/tanα=h/tanß-88

h/tanß-h/tanα=88

(htanα-htanß)/(tanα*tanß)=88

h(tanα-tanß)/(tanα*tanß)=88

h=88(tanα*tanß)/(tanα-tanß)

Since α=32 and ß=22...

h=88(tan32*tan22)/(tan32-tan22)

h≈85.3 feet

8 0

3 years ago

7 + #1. Graph a line to represent the function Y = 4x - 1.