7th grade math equations

7th grade math equations are the basic introduction for students for quadratic equations.

An equation is a mathematical statement, in symbols, that two things are exactly the same (or equivalent). Equations are written with an equal sign, as in the following problem

This algebra tutoring problem explain you more clearly about ,how to form an equation and get the answer for word problems.

Question:-

john traveled 234 miles in 14 days.His trip is for 42 days .Find the number of miles that he can travel in 42 days.


Answer:-

Miles:-  234    x


Days:-   14    42

Unknown quantity is taken as x.

Let's use a technique of cross multiplication from multiplication.com
By cross multiplication,we get

14 x = 234*42

divide by 14 on both sides

we get x=702

So john will travel 702 miles in total 42 days.

Types of angles

Topic:- Angles

In geometry and trigonometry, an angle is the figure formed by two rays sharing a common endpoint, called the vertex of the angle .

There are total 5 types of angles.

1. Acute Angle : an angle that is less than 90°, is called as acute angle.
2. Obtuse Angle:an angle that is greater than 90° but less than 180°
3. Right Angle :an angle that is 90° exactly , is called as right angle.Right angle triangle means an angle of a triangle should be 90°.
4. Straight Angle:an angle that is 180° exactly
5. Reflex Angle : an angle that is greater than 180°

We can recognize the angle in the following picture.
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Multiplication and division of fractions

Multiplication 
In general, when we multiply fractions, we multiply
the two numerators (the top numbers) to make the new
numerator, and multiply the two denominators to make
the new denominator.
For example:

7       4  
---- * -----
5       3


  7 * 4  
= --------
  5 * 3

   28
=  -------
   15


Division


7       4  
---- / -----
5       3

We can change this to multiplication by
simply changing the second fraction like,

7       3  
---- * -----
5       4


  7 * 3  
= --------
  5 * 4

    21
=  -------
    20

a word problem on finding the area

Topic:- Finding Area

Area is a quantity expressing the two-dimensional size of a defined part of a surface, typically a region bounded by a closed curve. The term surface area refers to the total area of the exposed surface of a 3-dimensional solid, such as the sum of the areas of the exposed sides of a rectangle. Area is an important invariant in the differential geometry of surfaces

Question: -

The width of a swimming pool is 10 meters and
length is 30 meters. Then find the area of the
pool.

Solution:-

This geometry help ,will give you the solution of above question.

width of thepool = 10 meters

length of the pool = 30 m

Area of the pool = Area of the rectangle ( as the pool is in the shape of a rectangle) Length

x breadth = 10 x 30

= 300 square meters

So the area of the pool is 300 square meters


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Find the mid point between 2 points

Topic :- Midpoint of 2 points

The midpoint between two points whose coordinates are known will be found. We will also develop a general formula for determining the coordinates of the midpoint and go through an example.
This math help explains ,how to find the midpoint.

Question:

Find the mid-point between

(2,2)and (6,4)

Answer:-

midpoint formula
to points is

  x1+x2          y1+y2
x= -------- , y = -------
    2              2

So ,Let's say.

 ( 2 , 2)   ( 6 , 4 )
   x1  y1     x2  y2


Then the mid point is

       2+6        2+4
   x= ----- , y= ------
        2          2

        8      6
     = ---  , ----
        2       2

     =  4 , 3

So the mid point is (4,3)

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Determine the Attributes of parabola

An Equation of Parabola helps us to find attributes of parabola, after simplification of any given equation we can calculate vertex, focus, directrix etc of the parabola. Here is one such example.

Topic : Parabola

Parabola is a Geometrical figure with standard form x ² = -4ay

Question : Find the vertex, focus, diretrix, and axis of symmetry of the parabola y²+3x-2y-11=0
Solution :

y²+3x-2y-11=0

subtract 3x and add 11 on both the sides

y²+3x-2y-11=0

- 30 + 11 = - 30 + 11
-----------------------------
y²-2y = - 3x + 11

by completing the square method

y²-2y + 1 = - 3x + 11 + 1

(y - 1)² = - 3x + 12

(y - 1)² = - 3(x - 4)

Now x - 4 = 0 so x = 4

and y - 1 = 0 so y = 1

So vertex is (4,1)

Standard form is given by

(y - k)² = 4p(x - h)

so here 4p = -3

p = - 3/4

Focus = (4 + (-3/4), 1) = (4 - 3/4 , 1) = (13/4, 1)

Directix x = 4 - (-3/4)

x = 4 + 3/4

x = 19/4

Axis of symmetry is

x = 4


Solving number of problems like this will help you to solve even difficult problems quickly, for more assistance contact calculus help or geometry help.

A Simple Problem on Finding Integral of a Function

Integral of a Function is very easy to evaluate the value of function. Here is such Integration problem with multi choice answers.

Topic : Integral of a Function

TutorVista helps you to get more multi choice questions and answers and practice the problems.

Problem : The function y(x) satisfying

Choice b is incorrect because of not adding the constant of anti-differentiation to the integral.

Choice c is incorrect because of committing the mistake to write the anti-derivative of 1 / (1 + y²) as cot^-1 y.

Choice d is incorrect because of failing to find the integral correctly.

Hope the Integration of given Function is followed and if you have any more queries write to our calculus help and get your problems rectified.

Question to Find Maximum Distance in the Elliptical Orbit

Topic : Ellipse

Question : Halley's comet has an elliptical orbit with the sun at one focus and a major axis of 1,636,484,848 miles. The closest the comet comes to the sun is 54,004,000miles. What is the maximum distance from the comet to the sun?

Solution :

2a = 1,636,484,848miles
so SC = 54,004,000miles
maximum distance from comet to the sun will be DS.
That is when comet comes at D
there is a maximum distance from sun
So SD = CD - SC ; CD = major axis = 1,636,484,848 miles
= 1,636,484,848 - 54004000
= 1582480848miles
So maximum distance is 1582480848miles.

Word Problem to Find Combinations of Tickets

Topic : Word problem

Question : The owner of a movie theater was counting money from1 days sales. he knew that the total of 150 tickets were sold. adult tickets cost 7.50 annd children tickets coast 4.7.5 each if the total recipt for the day were 891.25 how many of each kind of ticket was sold?

Solution :
Number of adult's ticket sold be 'x'
number of children ticket sold be 'y'

the total tickets are 150
So the first equation becomes x+y = 150 ------ (1)

cost of one adult's ticket be 7.50
cost of a child ticket be 4.75

total amount after selling all the tickets makes another equation
7.50x + 4.75y = 891.25 -------- (2)
________________
(x+y = 150) X 7.50
7.50x + 7.50y = 1125
7.50x + 4.75y = 891.25
- _____ -______-______
2.75y = 233.75
divide by 2.75
y = 233.75/2.75
y = 85
x + y = 150
x = 150 - y = 150 - 85 = 65

Problem to Find Unknown Angle of a Triangle

Topic : Angle of a Triangle

Solved Word Problem on Standard Deviation

Topic : Standard Deviation

Question : The average amount customers at a certain grocery store spend yearly is $636.55. Assume the variable is normally distributed. If the standard deviation is $89.46, find the probability that a randomly selected customer spends between $550.67 and $836.94.

Solution :

A Simple Integration Problem

Topic : Integration

Problem : Integrate x Cos x dx

Solution :

Order of Differential Equation with Example

Topic : Differential Equation
Question : State the Order of Differential Equation with Example.
Solution :
The order of the heighest order derivative occuring in a differential equation is called Order of the Differential Equation.
Example :
1) dy/dx +Cos x = 0
2) d²y/dx² = e^x

Question to Solve for x

Topic : Relation with identities

Question : Solve the expression
(x-1)/(4 + 2x) greater than or equal to (2x-1)/(3 +2)

Solution :
(x-1)/(4 + 2x) greater than or equal to (2x-1)/(3 +2)
(x-1+8x)/4 greater than or equal to (2x-1+6)/3
(9x-1) / 4 greater than or equal to (2x+5)/3
27x-3 greater than or equal to 8x +20
27x-8x greater than or equal to 20+3
19x greater than or equal to 23
x greater than or equal to 23/19

Question on Slope Intercept Form

Topic : Slope Intercept Form

Question : Find the slope of 4x+3y = 6.

Solution :
Slope intercept form of an equation is y = mx +b,
Where ‘m’ is the slope and ‘b’ is the y intercept.
To find the slope of the given equation, it should be in the standard form...
Implies 3y = -4x+6
Dividing by 3 on both sides we get:
3y = -4x + 6
3 3 3
.. y = -4x/3 + 2.
Comparing the above equation with standard form
Slope m = -4/3 and b = 2.

Problem to Solve Simultaneous Equation

Topic : Simultaneous Equation

Question : Solve for x and y,
8x - 3cy = 9c
12x - 7cy = - 39c

Solution :
8x - 3cy = 9c------- (1)
12x - 7cy = - 39c----(2)
Multiply equation (1) by 3 and (2) by 2
24x - 9cy = 27c
24x -14cy = -78c
-------------------
00 + 5cy = +105c (divide both sides by 5c)
So y = 21

Substituting the Value of y in equation (1)
8x - 3c(21) = 9c
8x-63c = 9c (adding +63c on both sides)
8x = 72c
x = 9c

Problem to Find perpendicular line from a point to a line in a coordinate system

Topic : Co ordinate System and a Line Equation

Question : Use co ordinate geometry to show the perpendicular distance between a point (x,y) and a line Ax+By+C= 0, is given by

d = (Ax+By+C) / √(A²+B²)

Solution :

Perpendicular Distance from (0,0) to the line Ax+By+C = 0 is
C
--------------
√(A²+B²)

Effecting the translation (X,Y)=>(X+x,Y+y) the equation of the line changes to :

A(X+x)+B(Y+y)+C=0
AX+BY+(Ax+By+C)=0
Perpendicular distance from the origin is :
(AX+BY+C ) / √(A²+B²) = (Ax+By+C ) / √(A²+B²)

Since the transformation here is an isometry the distance is preserved


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Question on Calculating Payment with Interest

Topic : Interest Applied on Payment.

Question : Noreen bought a house for $2,09,000. She paid 25% down and obtained 7-year mortgage at 7% per annum, amortized over 20 years. Calculate Noreen's monthly mortgage payment.

Answer :
7 year mortgage at 7% annual(assuming compounded annually)
amount = 209,000 * 0.75(since 25% is given as downpayment)= $ 156,750
Total amount with interest = 156750*(1+0.07)^7= 251,706
Monthly Amortized payments over 20 years is 251,706/240 = $1048.77

Hope the Solution is helpful for you.