All categories

3 years ago

Write an equation in standard form for a line that goes through the points(5,1) and (7,-3).

Mathematics

1 answer:

PolarNik [594]3 years ago

7 0

Answer:

Equation of line =

y = -2x + 11

Step-by-step explanation:

Using the formula for equation of a line with two points

(y_2 - y_1) / (x_2 - x_1) = (y - y_1) / (x - x_1)

Using the points we are provided with

( 5,1)(7,-3)

x_1 = 5

y_1 = 1

x_2 = 7

y_2 = -3

Inserting those values

( -3 - 1) / (7 - 5) = (y - 1) / (x - 5)

-4/2 = (y - 1) / (x - 5)

Cross multiply

-4(x - 5) = 2 ( y - 1)

Open the brackets

-4x + 20 = 2y - 2

-4x +20 +2 = 2y

-4x + 22 = 2y

Divide through by 2 to get the value of y following the rules

y = mx + C

-4x + 22 = 2y

-4x + 22 / 2 = 2y/2

-4x + 22 / 2 = y

We can still separate

-4x / 2 + 22/ 2 = y

-2x + 11 = y

y = -2x + 11

You might be interested in

Three consecutive integers can be represented by n, n + 1, and n + 2. if the seum of three consecutive integers is 57, what are

Helen [10]

Sum means add
sum of the 3 is
n+n+1+n+2

it add to 57
n+n+1+n+2=57
3n+3=57
minus 3 both sides
3n=54
divide both sides by 3
n=15
n+1=16
n+2=17

the integers are 15,16, and 17

8 0

3 years ago

Weekly demand for milk at a small grocery store is normally distributed with a mean of 251 gallons per week and standard deviati

slavikrds [6]

Solution

Given

mean = 251

standard deviation = 33

(a)

$\begin{gathered} P(Z$

Hence, X = 300

7 0

2 years ago

Read 2 more answers

An Open rectangular tank of length 18 cm and breadth 16 cm contains water to a depth of 13 cm. The water is poured into a cylind

san4es73 [151]

Answer:

Step-by-step explanation

Volume of tank = l* b*h

= 18*16*13

=3744 cubic cm

Volume of cylinder = volume of tank

πr²h = 3744

3.14* (17/2)² * h = 3744

h= 3744 *2 *2/*17*17*3.14

h=16.5 cm

4 0

3 years ago

A rectangular box which is open at the top can be made from an12-by-18-inch piece of metal by cutting a square from each corner

algol [13]

Answer:

h=2.35in, l=13.3in and w=7.3in

Step-by-step explanation:

In order to solve this problem, we must start by drawing a diagram that will represent the prolem. (Look at attached picture)

From the diagram we can see that the length ad the width of the box are found by using the following expressions:

L=18-2x

W= 12-2x

H=x

next, we can make use of the volume formula of a rectangular prism, which is the following:

V=WLH

so we can substitute the expressions we got before on the formula:

V=x(12-2x)(18-2x)

and for ease of calculation, we can multiply the terms, so we get:

$V=x(216-24x-36x+4x^{2})$

$V=x(4x^{2}-60x+216)$

$V=4x^{3}-60x^{2}+216x$

So now we can find the derivative of the volume:

$V'=12x^{2}-120x+216$

and set it equal to zero, so we get:

$12x^{2}-120x+216=0$

and now we can solve. We can start by factoring the left side of the equation, so we get:

$12(x^{2}-10x+18)=0$

which yields:

x^{2}-10x+18=0

This one can only be solved by using the quadratic formula:

$x=\frac{-b\pm \sqrt{-b^{2}-4ac}}{2a}$

so we substitute the corresponding values:

$x=\frac{-(-10)\pm \sqrt{-(-10)^{2}-4(1)(18)}}{2(1)}$

which yields:

x=7.65in or x=2.35in

we keep the 2.35in only, because the 7.65in returns an impossible box, since that would make the width a negative width.

So the 2.35in height would give us the greatest box. Now we can use it to find the height, the width and the length of the box.

Height=x=2.35

W=12-2x=12-2*2.35=7.3in

L=18-2x=18-2(2.35)=13.3in

5 0

3 years ago

Which sampling would be appropriate to survey 120,000 people?

kipiarov [429]

Answer: Id say b

Step-by-step explanation: a would be too high and a bit too detailed. Whereas c and d will be inaccurate.

8 0

3 years ago