Find the slope of the line through the given points.

(1,2), (-3,2)

Answers

Answer 1

Answer: the slope can be found by using the equation y2-y1 over x2-x1
2-2 over -3-1
= 0 over -4
your slope is 0

Answer 2

Answer: The slope=
$y= (y2-y1)/(x2-x1) (2-2)/(-3-1) (0)/(-4) }$

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What is the factored form of the polynomial? x2 - 15x + 36

Answers

Answer:

$(x-12)(x-3)$

Step-by-step explanation:

We have been given an polynomial $x^2-15x+36$ and we are asked to factor our given polynomial.

We will factor our given polynomial by splitting the middle term in two numbers such that the numbers add up-to -15 and their product will be equal to 36.

We know that -12 and -3 add up-to -15 and their product is 36. So splitting the middle term of our given polynomial we will get,

$x^2-12x-3x+36$

$x(x-12)-3(x-12)$

$(x-12)(x-3)$

Therefore, the factored form of our given polynomial is $(x-12)(x-3)$ .

The factored form of the polynomial $x^2 - 15x + 36$ is $(x - 3)(x - 12)$ .

To find the factored form of the polynomial $x^2 - 15x + 36$ , we can look for two binomials that, when multiplied, give us the original polynomial.

The general form of a quadratic polynomial in factored form is $(x - r_1)(x - r_2).$

where $r_1$ and $r_2$ are the roots of the polynomial.

Now, find two numbers whose product is 36 and whose sum is -15.

The numbers that satisfy these conditions are -3 and -12,

since $(-3) * (-12) = 36$ and

$(-3) + (-12) = -15.$

Therefore, we can factor the polynomial as:

$x^2 - 15x + 36$

$x^2 - 12x-3x+36$

$x(x-12)-3(x-12)$

$= (x - 3)(x - 12)$

So, the factored form of the polynomial $x^2 - 15x + 36$ is $(x - 3)(x - 12)$ .

To learn more on Polynomials click:

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Graph 3x + 2y = 6. Can someone help with this

Answers

Here are two ways to graph it. You can decide which one seems easier to understand or easier to do:

==> Manipulate the equation into the "slope-intercept" form, where 'y' is
all alone on one side and everything else is on the other side:

3x + 2y = 6

Subtract 3x from each side:   2y = -3x + 6

Divide each side by 2 : y = -3/2 x +3

This is the form you want. Just looking at it, it tells you that the slope
of the line on the graph is (-3/2), and it crosses the y-axis at +3 .
That's enough information to draw the line.
===============================================

=> Another way:

Look at the x-axis and the y-axis on the graph paper ... without any graph drawn on it yet. Just look at the 2 axes.

With an 'x'-number and a 'y'-number, you can find any point on it. Right ?

OK. Notice that at every point on the y-axis, x = 0 . And at every point
on the x-axis, y = 0. This can be very very helpful.

Now take your equation: 3x + 2y = 6 .

You know that the graph is going to be a straight line. And it's pretty obvious that if the line isn't horizontal or vertical, then it has to cross both the x-axis and the y-axis somewhere. If you had an easy way to find the two points where it crosses the axes, you could join those 2 points and you'd have your line !

You DO have an easy way to find those points !

If x=0, then the point is on the y-axis. Take your equation, make x=0, and it'll show you where the line crosses the y-axis:

   3(0) + 2y = 6 .

    2y = 6 .

Divide each side by 2 : y = 3 .

There's one point on the line: (0, 3)

Now remember that if y=0 the point is on the x-axis. So take your equation
and make y=0:

      3x + 2(0) = 6

3x = 6

Divide each side by 3 :    x = 2

There's another point on the line, where it crosses the x-axis: (2, 0) .

Shazam ! You have the 2 points where the line crosses the x- and
y- axes. Mark each one with a little dot, put your ruler down along
them, draw a line between them, and extend it as far in each direction
as you want to. That's the graph of your equation.

Plot these coordinates then draw a line through them and that is the line.

(2,0) x intercept
(0,3) y intercept

A soft drink manufacturer produces 3120 cans in an 8 hour day. Cans are packaged 24 to a case. How many cases are produced each week? Each month? (Assume one week is 40 hours and one month is four weeks )

Answers

Week: 3120 x 5 = 15,600 cans ÷ 24 = 650 cases

Month: 650 x 4 = 2,600 cases

Select the postulate that is illustrated for the real numbers.
5•1=5

Answers

Answer:

Multiplication identity

Step-by-step explanation:

We are given that

$5\cdot 1=5$

We have to find which property of real number is used in given expression.

Multiplication identity: It is defined as the number by which multiply any number and get itself.

$a\cdot 1=1\cdot a=a$

Then, 1 is multiplication identity.

$5\cdot 1=5$

When we are multiplying 5 with 1 then we get 5.

Therefore, 1 is multiplication identity.

Hence, multiplication property of real numbers is used in given expression.

Multiplication Identity

A boy leaves on a bicycle trip at the rate of 8 mph. One hour later the father, realizing that his son forgot his camping gear, sets out by car. How fast must the father drive to overtake the boy in 15 minutes?

Answers

Speed of father is 40 mph

Given that;

Speed of boy on bicycle = 8 mph

Total time taken by father = 15 min = 0.25 hour

Find:

Speed of father

Computation:

Distance = Speed × Time

So,

Boy's cover distance = Father's cover distance

[(Speed of boy on bicycle)(Time taken by boy)] = [(Speed of father)(Time taken by father)]

[(8)(1 + 0.25)] = [(Speed of father)(0.25)]

[(8)(1.25)] = [(Speed of father)(0.25)]

Speed of father = 10 / 0.25

Speed of father = 40 mph

Learn more:

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1st equation to find out how far boy will have traveled in 1hr 15 minutes:

8/1=x/1.25 (8 miles over 1 hour = x miles over 1.25 hours)
8(1.25) = 1(x)
10 = x

Now, divide 10 by .25 (15 minutes aka 1/4 hour) to get the speed father will have to drive.

10/.25 = x/1

x = 40 MPH

Plot the following points on the grid and calculate the slope of the line that passes through them (-2, -3) and (4, 5): a) 1 b) 2 c) 3 d) 4"

Find the slope of the line through the given points.(1,2), (-3,2)

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Find the slope of the line through the given points.

(1,2), (-3,2)