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This article is about the math term. For other uses, see Slope (disambiguation).

For the grade (incline or gradient or pitch or slope) of any physical feature, see Grade (slope).

Slope: {\displaystyle m=\left({\frac {\Delta y}{\Delta x}}\right)=\tan(\theta )}{\displaystyle m=\left({\frac {\Delta y}{\Delta x}}\right)=\tan(\theta )}

In mathematics, the slope or gradient of a line is a number that describes both the direction and the steepness of the line.[1] Slope is often denoted by the letter m; there is no clear answer to the question why the letter m is used for slope, but its earliest use in English appears in O'Brien (1844)[2] who wrote the equation of a straight line as "y = mx + b" and it can also be found in Todhunter (1888)[3] who wrote it as "y = mx + c".[4]

Slope is calculated by finding the ratio of the "vertical change" to the "horizontal change" between (any) two distinct points on a line. Sometimes the ratio is expressed as a quotient ("rise over run"), giving the same number for every two distinct points on the same line. A line that is decreasing has a negative "rise". The line may be practical - as set by a road surveyor, or in a diagram that models a road or a roof either as a description or as a plan.

The steepness, incline, or grade of a line is measured by the absolute value of the slope. A slope with a greater absolute value indicates a steeper line. The direction of a line is either increasing, decreasing, horizontal or vertical.

A line is increasing if it goes up from left to right. The slope is positive, i.e. {\displaystyle m>0}m>0.

A line is decreasing if it goes down from left to right. The slope is negative, i.e. {\displaystyle m<0}m<0.

If a line is horizontal the slope is zero. This is a constant function.

If a line is vertical the slope is undefined (see below).

The rise of a road between two points is the difference between the altitude of the road at those two points, say y1 and y2, or in other words, the rise is (y2 − y1) = Δy. For relatively short distances, where the earth's curvature may be neglected, the run is the difference in distance from a fixed point measured along a level, horizontal line, or in other words, the run is (x2 − x1) = Δx. Here the slope of the road between the two points is simply described as the ratio of the altitude change to the horizontal distance between any two points on the line.

In mathematical language, the slope m of the line is

{\displaystyle m={\frac {y_{2}-y_{1}}{x_{2}-x_{1}}}.}m=\frac{y_2-y_1}{x_2-x_1}.

The concept of slope applies directly to grades or gradients in geography and civil engineering. Through trigonometry, the slope m of a line is related to its angle of incline θ by the tangent function

{\displaystyle m=\tan(\theta )}m = \tan (\theta)

Thus, a 45° rising line has a slope of +1 and a 45° falling line has a slope of −1.

Answer:

45h that the answer I think

Answer:

C and h are both variables so the answer is ∞.

Answer:19x^2-68x

Step-by-step explanation:

first, add the 2x on the side of the large rectangle to the 2x on the pool side to find the length. then find the area of the entire image (4x•8x-10=32x^2-40x) now find the area of the pool (2x•6x-14=12x^2-28x) and add it to the area of the hot tub (x•x=x^2) (13x^2-28x) finally subtract that from the area of the entire image (32x^2-40x=19x^2-68x)!

Answer:

2 + n + 6 = 8 + n

Step-by-step explanation:

that should be the answer

Answer:

1 1/3?

Step-by-step explanation:

Answer:

The numbers would be 80 and 8

Step-by-step explanation:

Hope this helps

Answer:

We have, x - y = 72

    and, x = 10y

so, 10y - y = 72

         y = 8

so, x= 80

Step-by-step explanation:

Answer:

yes

Step-by-step explanation:

Answer:

sure

Step-by-step explanation:

Answer:

512 ways

Step-by-step explanation:

Given

Selection

Faculty Member = 1

Male Student = 1

Female Student = 1

Parent = 1

School Board Member = 1

Select from:

Faculty Member = 2

Male Student = 4

Female Student = 4

Parent = 4

School Board Member = 4

Required

Determine how many ways they can be selected

There are 2 faculty members of which 1 will be selected from.

Any of these two members may be selected.

So, Selection = 2

There are 4 male students of which 1 will be selected from.

Any of these four students may be selected.

So, Selection = 4

There are 4 female students of which 1 will be selected from.

Any of these four students may be selected.

So, Selection = 4

There are 4 parents of which 1 will be selected from.

Any of these four parents may be selected.

So, Selection = 4

There are 4 school board members of which 1 will be selected from.

Any of these four members may be selected.

So, Selection = 4

Total number of selection is then calculated as thus:

[tex]Selection = 2 * 4 * 4 * 4 * 4[/tex]

[tex]Selection = 512[/tex]

Hence, there are 512 ways

Answer:

acute angle

Step-by-step explanation:

just took the test

Answer:

x=28

Step-by-step explanation:

Set 2x-4 equal to 60 and solve.

The three angles in the triangle add up to 180. Divide this by 3 and you get 60.

y = 3x + 2 this is the answer if I am right

Answer:

a

Step-by-step explanation:

Step-by-step explanation:

If angles are equal then sides will also be equal.

Cause: Equal angles have equal sides.

You can then prove them by using SAS, SSS ASA, AAS

Answer:

sqrt166, 13, 14

Step-by-step explanation:

Answer:

slope is -2

Step-by-step explanation:

10-8=2

2-3=-1

2/-1

-2

Answer:

2.5

Step-by-step explanation:

:)

Answer:

ummmmmm

Step-by-step explanation:

Answer:

Step-by-step explanation:

(B) 0.752 and 0.232323....

slope is 3

Step-by-step explanation:

y2-y1/x2-x1

so 3-0/-1--2 or 3-0/-1+2

Answer:

B. 15

Step-by-step explanation:

Answer:

The Domain are 3,-5,2,-3

Step-by-step explanation:

hope that helps

Answer:

The domain is (3, -5, 2, -3

Step-by-step explanation:

Plz give brainlyest

Answer:

40 cm ; 30cm ; 20cm

Step-by-step explanation:

Given that:

Sides of a triangle are in the ratio 2:3:4

Let :

length of the sides = 2x, 3x, 4x

longest side = 4x

Mid side = 3x

Shortest side = 2x

Length of longest side is 20 cm longer than shortest side

4x = 2x + 20 - - (1)

4x - 2x = 20

2x = 20

x = 10

Hence,

longest side = 4x = 4*10 = 40 cm

Mid side = 3x = 3 * 10 = 30 cm

Shortest side = 2x = 2 * 10 = 20 cm

Dividing fractions is the same as multiplying the reciprocal.

As an easy way to remember this, you can use the Keep it, Switch it, Flip it method.

Keep: [tex]\frac{4}{9}[/tex]

Switch: the division sign to multiplication.

Flip Flip the numbers of [tex]\frac{2}{1}[/tex], or find it's reciprocal. [tex]\frac{1}{2}[/tex] turns into [tex]\frac{2}{1}[/tex].

Now, your problem looks like this:

[tex]\frac{4}{9}[/tex] * [tex]\frac{2}{1}[/tex] (which should be the answer to your first blank)

Multiply across.

4 x 2 = 8 and 9 x 1 = 9, so: [tex]\frac{8}{9}[/tex] should be the second blank.

Answer:

Step-by-step explanation:

= - 7

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Step-by-step explanation:

Fractions consisting of integers are only undefined if the denominator is zero. All other combinations will give you a rational number.

42 / (-7)

We can multiply both halves of the fraction by -1 to move the negative sign into the numerator:

-42 / 7

Then divide 42 by 7 to get:

-6

Answer:

Step-by-step explanation:

Both the equations that you modelled are correct.

Use the substitution method to solve the system of equations

[tex]R+C = 526\\5R+4C=2327\\[/tex]

Take the first equation

[tex]R+C=526\\C=526-R[/tex]

Now this becomes our third equation and now insert it into our second equation

[tex]5R+4C=2327\\5R+4(526-R)=2327\\5R+2104-4R=2327\\R=2327-2104\\R=223[/tex]

Now insert R = 223 in any equation. Lets insert it into equation number three

[tex]C=526-R\\C=526-223\\C=303[/tex]

So 223 number of roll papers were sold and 303 number of candles were sold.

I have attached the graph below check it out.

Where both the equations of line intersect is our solution thus we can confirm that our answer is correct.

Complete question :

Ella finished a bike race in 37.6 minutes. Miranda finished the race 9 1/10minutes sooner than Ella finished it. How many minutes did it take Miranda to finish the race

Answer:

28.5

Step-by-step explanation:

Time taken by Ella = 37.6 minutes

Time taken by Miranda = 9 1/10 minutes sooner than Ella

Hence,

Miranda's finish time :

37. 6 minutes - 9 1/10 minutes

37.6 - 91/10 minutes

37. 6 minutes - 9.1 minutes

= 28.5 minutes

Answer:

Z = 70

Step-by-step explanation:

14×25 = 5z

350 = 5z

Z = 350/5

Z = 70