Mathematics, 26.11.2020 22:10 garrettcameron12

1.) We can write a equation of a line when we know only the slope and the of any point of the line. 2.) Given only two points, it is easy to find the equation of the line when you find first the .

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Answer from: toriflaherty

1) coordinates

2) slope

Step-by-step explanation:

The equation of a line is given by the two equations:

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

y-y_1=m(x-x_1) , where x₁ and y₁ is the location of any point on the line, and m is the slope.

→ As such, we know that given the slope and the coordinates of any point on a line, we can write the line's equation.

We can also find the slope of a straight line between two points with the following equation:

$m = \frac{y_2-y_1}{x_2-x_1}$ , where m is the slope, x1 and y1 is the location of the first point, and x2 and y2 is the location of the second point. Remember: rise (y) over run (x).

→ So, given only two points, it is easy to find the equation of the line when you first find the slope.

Answer from: Quest

step-by-step explanation:

in standard form:

a= dictionaries

b= maps

you have to buy 3 dictionaries, so put a 3 next to the a (dictionaries) so that you can multiply them by each other.

a3+b= 60 (the amount of money you have)

we already know the cost of a=15 so replace a with $15

($15 x 3)+b=60

multiply 15 and 3 to get $45 and replace it with $45

45+b=60

and then replace b with 15 to get the total:

45+15=60

that means you have $15 left after buying 3 dictionaries.

15 divided by the cost of a map ($5) equals 3.

so you can buy 3 maps.

sorry if it was confusing!

Answer from: Quest

solution:

the given function is ,

$f(x) = 4 x^3 - 72 x^2 + 320 x,$

= $4x( x^2- 18 x + 80)\\\\ 4 x(x^2-10 x -8 x + 80) \\\\ 4 x[(x-10)(x-8)]$

the three roots of this quadratic function is , 0 ,8 and 10.all the roots are real and rational.

if a quadratic equation is of the form ,

$f(x) = a x^3+ b x^2 + c x+d,$

sum of the roots = a + b +c= 0+8+10=18= $\frac{-b}{a}$

product of roots taken two at a time = a b + b c+ c a = 0+80+0=80 = $\frac{c}{a}$

product of roots = a b c = 0= $\frac{d}{a}$

there are 11 doors in a hall starting from 0 to 11.the entry in the hall is permitted through gate number 0 and exit is allowed through only gate number 8 and 10.so, three roots(0,8,10) of quadratic function $f(x) = 4 x^3 - 72 x^2 + 320 x,$ is given by entry and exit route of this hall.

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