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.
If an plane can fly around the earth at the equator without stopping. It would have traveled about 24,900 miles. Find the radius of the earth.
Step-by-step explanation:
This equation gives circumference (24900 miles). Knowing this the formula to start off finding radius is
[tex]c=2\pi r[/tex]
we know c(circumference) and we know pi(3.1415926535...)
so move the numbers to isolate r(radius) to look something like this
[tex]\frac{c}{2\pi } =r[/tex]
input the known values then solve.
[tex]\frac{24900}{2\pi } =r[/tex]
[tex]\frac{12450}{\pi } =r[/tex]
[tex]3962.95808... =r[/tex]
(round this to whatever value you are looking for)
Hope This Helps :)
You have a bag with 6 green marbles, 15 blue marbles, 8 red marbles, 1 yellow
marble. What is the probability of pulling out a blue marble?
Answer:
1 / 2
Step-by-step explanation:
Total # of marbles in the bag = 30
Total # of blue marbles in the bag = 15
Probability of pulling a blue marble = # of blue / total # of marbles
Probability = 15 / 30
Simplify = 1 / 2
Isabella is ordering pizza for a family dinner. If 2 pizzas will feed 4 people, how many pizzas does she need to order for 12 people?
Answer:
She needs to order 6 pizzas.
Step-by-step explanation:
(My bad I thought it was one pizza that fed 4 people not two)
Answer:
6 pizzas
Step-by-step explanation:
2pizza=4 people
12/4=3
3*2=6
Find the slope of the line that passes through (6,1) and (9,8)
Answer:
2 1/3
Step-by-step explanation:
8-1=7
9-6=3
7/3= 2 1/3
plz help soon asap............................................
Answer:
0
Step-by-step explanation:
y=mx+b
m=0
Jan and two of her friends raised money by having a bake sale. They split the proceeds. If each person received $32.19, how much money did the girls earn in total at their bake sale? Write an equation and solve it to find the answer.
Answer: 1. Equation =3x = M , where x = money each received and M= total money received.
2.total money from bake sale=$96.57
Step-by-step explanation:
STEP 1
Let the total money receive from proceeds be = M
and let the amount of money each receive after the split = x
Since Jan and her two friends raised the money together, the total proceeds will be calculated using the equation
x+x+x= M
3 x = M ---- Equation
STEP 2--- Solving
if 3 x= M
and x =mount of money each receive after the split=$32.19
Therefore total money from bake sale, M = 3x = 3 x 32.19 = $96.57
Answer:
The last one
Step-by-step explanation:
$96.57
Find the volume for 2 different spheres by randomly choosing different radii.
Using the same radii values, find the volume of 2 cylinders where the height of the cylinder is the same as the diameter of the sphere.
Answer:
The volume of a sphere of radius r is:
S = (4/3)*pi*r^3
The volume of a cylinder of radius r and height h is:
C = pi*r^2*h
For this problem the height of the cylinders will be equal to the diameter of the spheres, which is equal to two times the radius.
First, let's use the radius: r = 2.
The volume of the sphere will be:
S = (4/3)*3.14*(2)^3 = 33.49
The volume of the cylinder, where h = 2*2 = 4, is:
C = 3.14*(2^2)*4 = 50.24
Now, let's choose the radius r = 3.
The volume of the sphere will be:
S = (4/3)*3.14*3^3 = 113.04
The volume of a cylinder with this radius and h = 3*2 = 6, is:
C = 3.14*(3^2)*6 = 169.56
The circumference of a circular lawn is 110 feet. If you double the radius, what will the new circumference be?
Answer:
220
Step-by-step explanation:
The new circumference of the circle will be 220 feet if the circumference of a circular lawn is 110 feet.
What is a circle?It is described as a set of points, where each point is at the same distance from a fixed point (called the center of a circle)
We have:
The circumference of a circular lawn is 110 feet.
2πr = 110
r = 55/π
Double the radius:
R = 2r= 110/π
New circumference = 2πR = 2π(110/π) = 220 feet
Thus, the new circumference of the circle will be 220 feet if the circumference of a circular lawn is 110 feet.
Learn more about circle here:
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PLEASE HELP ME OUT WITH THIS ONE.
A) 27 units
B) 34 units
C) 42 units
D) 37 units
Help PLz ignore three i need help on 4
Answer:
Step-by-step explanation:
Remark
The best way to find the slope is to take the two points that are marked.
(5,3) and (0,-1)
Formula
m = (y2 - y1)/(x2 - x1)
Givens
y2 = 3
y1 = -1
x2 = 5
x1 = 0
Solution
m = (3 - -1)/(5 - 0)
m = (3+1) / 5 = 4/5
the line parallel to the line in the graph would be the new with a slope equal to the given line.
The perpendicular to this line would have a slope of
m * m1 = -1
4/5 * m1 = - 1 Multiply by 5
4 * m = -5 Divide by 4
m = -5/4
A line perpendicular to the given line would have a slope of -5/4
What is an equation of the line that passes through the point (-2, 2) and is parallel to the line 2x + y = 1?
An equation of the line that passes through the point (-2, 2) and is parallel to the line 2x+y=1 is y=2x+6.
Given that, the equation of a line is 2x+y=1 and the coordinate point is (-2, 2).
What is an equation of the line?The equation of line is an algebraic form of representing the set of points, which together form a line in a coordinate system. The numerous points which together form a line in the coordinate axis are represented as a set of variables x, y to form an algebraic equation, which is referred to as an equation of a line.
In the equation of a line 2x+y=1, slope is 2.
As we know the slopes of parallel lines are equal, that is m1=m2.
Now, put (-2, 2) and m=2 in y-y1=m(x-x1) and simplify.
That is, y-2=2(x+2)
⇒ y-2=2x+4
⇒ y=2x+4+2
⇒ y=2x+6
Therefore, an equation of the line that passes through the point (-2, 2) and is parallel to the line 2x+y=1 is y=2x+6.
To learn more about an equation of the line visit:
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Review the following information about vectors q and r.
What is the value of a?
q=(-4,1)
31
r = (a, 3)
7(q + r) = (-35, 28)
-5
==========================================
Work Shown:
q = (-4, 1) is one vector
r = (a,3) is another vector
The resultant vector is
q+r = (-4,1)+(a,3)
q+r = (-4+a,1+3)
q+r = (-4+a,4)
Multiply both sides by 7
7(q+r) = 7*(-4+a,4)
7(q+r) = (7*(-4+a),7*4)
7(q+r) = (-28+7a, 28)
---------------
Since 7(q+r) = (-35, 28), we know that,
(-28+7a, 28) = (-35, 28)
which leads to
-28 + 7a = -35
when we equate the x components of each vector. Let's solve for 'a'
-28 + 7a = -35
7a = -35+28
7a = -7
a = -7/7
a = -1
--------------
Check:
q = (-4,1)
r = (a,3) = (-1,3)
q+r = (-4,1)+(-1,3)
q+r = (-4+(-1), 1+3)
q+r = (-5, 4)
7*(q+r) = 7*(-5, 4)
7*(q+r) = (7*(-5), 7*4)
7*(q+r) = (-35, 28)
The answer is confirmed.
Answer:
D. -1
Step-by-step explanation:
edge test
if m*n=-12 and m+n=11 what is m? what is n?
x^2+11x-12=(x+m)(x+n)
Answer:
i think its -10
Step-by-step explanation:
hope im not wrong
Find the slope of a line that passes through the following
ordered pairs. Reduce to lowest terms.
(-8,-5) (-2, -5)
Answer:
I believe the answer is -6,0
What is the solution to the system of equations graphed below? A (2, 4) B (4,2) C (0,6) D (6,0)
Answer: (4,2)
Step-by-step explanation:
The solution would be where the two lines intersect which is the point (4,2)
Answer:
(4,2)
Step-by-step explanation:
(x=4, y=2)
the solution is the point of intersection of the graph
Which inequality is represented by this graph?
Answer:
The answer is D
Step-by-step explanation:
The line is going to the right side so that means that x must be greater than -53 and the dot is filled in so it is also equal to
y=1/3x+2 and on a graph
Using the slope:1/3 and y intercept:2
a research company surveys 8000 people the company expects 6000 to respond favorably if there is a percent error of 2.5% what is the Range of people who will respond Favorably to the survey !!!
please help I'm on a test rn and idk what to do !!
Answer:
Least Amount Likley: 7800
Favorable:8200
Step-by-step explanation:
Favorable 8000+2.5%
Least 8000-2.5% this is the range
Answer:
Least Amount Likely: 7800
Favorable: 8200
Step-by-step explanation:
Favorable: [tex]8000+2.5[/tex]% [tex]=8,200[/tex]
Least: [tex]8000-2.5%[/tex][tex]%[/tex]% [tex]=7,800[/tex] this is the range
hope this helps:)
URGENT‼️‼️
3. Find the rate of change represented in the
table.
Answer:
14
Step-by-step explanation:
Using any two ordered pairs, say (2, 17) and (4, 45),
Let,
[tex] (2, 17) = (x_1, y_1) [/tex]
[tex] (4, 45) = (x_2, y_2) [/tex]
Rate of change = [tex] \frac{y_2 - y_1}{x_2 - x_1} = \frac{45 - 17}{4 - 2} [/tex]
[tex] = \frac{28}{2} [/tex]
Rate of change = 14
PLEASE HELP FAST AS A MIXED RADICAL READ IT CARFULLY BRAINLIST!
Answer:
[tex]2\sqrt[3]{2}[/tex]
Step-by-step explanation:
This is equal to [tex]\sqrt[3]{8} * \sqrt[3]{2} = 2\sqrt[3]{2}[/tex]
i forget how to do this
Round 3.457 to
the tenths place.
Answer:
3.5
Step-by-step explanation:
If you like to round 3.457 to the nearest tenth, leaving only one number after the decimal point, then you have come to the right post.
Love, gocry
Which value is equivalent to 5 + 4 x 2?
A) 11
B) 13
C) 18
D) 22
PLEASE HELP ME PLEASE!!
Answer:
Is that you in your pfp?
Step-by-step explanation:
Answer:
A then D then C then F thats what I see
Step-by-step explanation:
someone help plz right answer gets brainliest
Answer:
CGIA
Step-by-step explanation:
C is the first line, G is the second, I is the third, and A is the fourth.
I graphed it all. If I helped you, give me brainliest
Kathy is 33 years old. She is 7 years younger than 5 times her daughter's age. The equation,
5x-7= 33, where x equals her daughter's age, can be used to find the age of Kathy's daughter. How
old is Kathy's daughter?
Answer:
Kathy's daughter is 8 years old
Step-by-step explanation:
What we know:
Kathy is 33 years old.
That is 7 years younger than 5 times her daughter's age.
With that, the equation 5x - 7 = 33 can be used to find x.
Step 1:
Move "- 7" to the right side of the equation, and find the opposite of it.
5x = 33 + 7
Step 2:
Add "33" and "+7" to get "40."
5x = 40
Step 3:
Divide both side by "5."
5x/5 = 40/5
x = 8
Thus, Kathy's daughter is 8 years old.
Answer:
8
Step-by-step explanation:
How do you calculate slope in pre algebra
Answer:
Find the slope from a graph
Locate two points on the line whose coordinates are integers.
Starting with the point on the left, sketch a right triangle, going from the first point to the second point.
Count the rise and the run on the legs of the triangle.
Take the ratio of rise over run to find the slope. m = rise / run.
Mrs. Jawahir spends $9.45 on 5 greeting cards. Each card costs the SAME amount. How much did she pay for one greeting card?
Answer:
$1.89 for each Card.
Step-by-step explanation:
The answer is 1.89 because 9.45 divided by 5 is 1,89
i though originally the answer was 1/4x+4 but tgats not it please help
Answer:
what is that
Step-by-step explanation:
me cant see
Answer:
y = 4x
Step-by-step explanation:
You were close, its positive 4 rather than negative 4.
Need Help with this!
Answer: it's about 46.6% for the first card the second card depends on the first card if the first card is even the likelihood of the second being even is 40%, if the first card is odd then the likelihood of the second card being odd too be about 46,6%