Quick Math Answers for Algebra

Introduction to quick math answers for algebra:

Algebra is the branch of mathematics concerning the study of the rules of operations and relations, and the constructions and concepts arising from them, including terms, polynomials, equations and algebraic structures. The part of algebra called elementary algebra is often part of the curriculum in secondary education and introduces the concept of variables representing numbers. (Source: From Wikipedia). In this article, we are going to see some of the math algebra problems quick help.

Quick Math Algebra Problems:

Example problem 1:

Simplify the expression: 14b + 6 - 21a + 15b + 13 + 15a

Solution:

14b + 6 - 21a + 15b + 13 + 15a

Combine the like terms in the given expression

-21a + 15a + 14b + 15b + 6 + 13

Add the like terms in the expression

(-21 + 15)a + (14 + 15)b + (6 + 13)

-6a + 29b + 19

So, the answer is -6a + 29b + 19.

Example problem 2:

Solve for the value of c: 9c - 2 = 79

Solution:

9c - 2 = 79

Add 2 on both sides of the equation

9c - 2 + 2 = 79 + 2

9c = 81

Divide by 9 on both sides of the equation

`(9c) / 9 = 81 / 9`

c = 9

So, c = 9 is the solution of the given equation.

Few more Math Algebra Problems Quickly:

Example problem 3:

Find the x and y intercept of the equation: 12x + 6y = 48.

Solution:

12x + 6y = 48

To find the x intercept value, plug y = 0 in the given equation

12x + 6(0) = 48

12x = 48

x = 4

So, the x intercept is (4, 0).

To find the y intercept value, plug x = 0 in the given equation

12(0) + 6y = 48

6y = 48

y = 8

So, the y intercept is (0, 8).

Example problem 4:

Solve the inequality: 20y - 43 < 17

Solution:

20y – 43 < 17

Add 43 on both side of the inequality

20y- 43 + 43 < 17 + 43

20y < 60

Divide by 20 on both sides of the equation

`(20y) / 20 < 60 / 20`

y < 3

So, the solution is (-infinity, 3).

Practice Math Algebra Problems Free Help Quickly:

1)      Simplify the expression: -15x + 16y + 13x - 12y. (Answer: -2x + 4y)

2)      Solve for the variable z:  10z + 34 = 24 + 8z (Answer: z = -5).

3)      Solve for the variable x:  13x - 68 = 10 (Answer: x = 6).

Sum of Two Irrational Numbers

Introduction to sum of two irrational numbers:

Let us study about sum of two irrational numbers. Irrational numbers are defined as the numbers which cannot be written in the form of simple ratios of two integers.
The irrational numbers are commonly said to have infinite values. These irrational numbers can get added with each other by approximating or rounding those infinite values to some nearest values.
Some examples for sum of two irrational numbers are discussed below.

Two Irrational Numbers:

Two irrational numbers – example 1:

Add the following two irrational numbers 3.4256… and 2.3227…


Solution:

The two given irrational numbers are 3.4256… and 2.3227…
To add the two given irrational numbers follow the steps below given steps:
3.426 + 2.323 (by rounding the values with three decimal points)
Therefore the added value of the two given irrational number is found to be as ‘5.749’


Two irrational numbers – example 2:

Add the following two irrational numbers 0.436… and 12.987…


Solution:

The two given irrational numbers are 0.436… and 12.987…
To add the two given irrational numbers follow the steps below given steps:
0.44 + 12.99 (by rounding the values with two decimal points)
Therefore the added value of the two given irrational number is found to be as ’13.43’
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Two irrational numbers – example 3:

Add the following two irrational numbers `sqrt(3) and sqrt(12)`


Solution:

The two given irrational numbers are `sqrt(3) and sqrt(12)`
To add the two given irrational numbers follow the steps below given steps:
`sqrt(3) + sqrt(12) `
`sqrt(15)` = 3.872983…
3.873 (round the values with three decimal points)
Therefore the added value of the two given irrational number is found to be as ‘3.873’


Two irrational numbers – example 4:

Add the following two irrational numbers 6.2328… and `sqrt(8)`


Solution:

The two given irrational numbers are 6.2328… and `sqrt(8)`
To add the two given irrational numbers follow the steps below given steps:
6.2328… + `sqrt(8)`
6.2328… + 2.8284…
6.233 + 2.828 (by rounding the values with three decimal points)
Therefore the added value of the two given irrational number is found to be as ‘9.061’
Two irrational numbers – exercises:

Add the following two irrational numbers `sqrt(2) and sqrt(6).` (Answer: 3.863)
Add the following two irrational numbers 0.2028… and 9.45454... (Answer: 9.658)

Second Grade Math

Introduction to second grade math:

In the second grade math the students learn about the counting and number patterns, comparing and ordering, place values, estimation and rounding, names of numbers, logical reasoning, addition one digit and two digit, subtraction one digit and two digit, addition three digits, subtraction three digits, probability and statistics, multiplication and division, and mixed operations.

Second Grade Math Counting and Place Values

Second grade math to study counting and number patterns:

Example problems:

What is the missing number in the given sequence?

10, 20, 30, ____, 50, 60.

Answer: The missing number in this sequence is 40.

Explanation:

Note that the numbers, each number 10 more than the previous number.

Problem 2:

What is the missing numbers in the following sequence?

510, 511, 512, _____, 514, 515, 516, _____, 518, 519.

Answer:

The missing numbers in the following sequence is 513 and 517.

Explanation:

513 is comes between the numbers 512 and 514.

517 is comes between the numbers 516 and 518.

Second grade math to study place values:

In this the students can place the values in the form of ones, tens, and hundreds.

Example problems:

Example 1:

How many hundreds, tens, and ones present in the value 234?

Answer: There are 2 hundreds, 30 tens, and 4 ones present in the above value.

Example 2:

Write the value in the given term.

3 thousands + 6 hundreds + 5 tens + 0 ones = _______.

The correct answer is: 3,650.

Second Grade Math Geometry and Addition

Second grade math to study geometry:

Example 1:

Identify the following figure.

a)      Rectangle

b)      Square

c)       Circle

d)      Triangle

Answer: option b.

Addition:

Example for one digit addition:

5 + 6 = 11.

8 +9 = 17.

9 +5 = 14.

Example for two digit addition:

Example 1:

Add the given two digit number 35 and 23.

35

23

______

58

______

Example 2:

Add the given two digit number 67 and 42

67

42

_____

109

_____

Example for 3 digit addition:

Example 1:

Add the given three digit number 237, 429, and 320.

Write the numbers in vertical form.

237

429

320

______

986

______

Add the following three digit numbers 345 and 123

345

123

______

468

______

Connected Math Variables and Patterns

Introduction about connected math variables and patterns:

Variables are one of the branches in algebra. In math, variables are very necessary concept. It does not change the meaning of expressions. We are mostly use variables to stand for the algebra expression like a,b,c and d. In math, generally variables can be defined using alphabets. Patterns are generally the collection of numbers which are listed in an order under a certain conditions. There are three different types of general patterns like Arithmetic Pattern, Geometric Pattern and Alphabetic Pattern. Here we are going to study about connected math variable and patterns.

Examples of Connected Math Variables:

Example 1:

(6m^2+9) + (-5m^2+7).

Solution:

Step 1: Here we are going to add the two terms

Step 2:  Its also like a normal addition.

Step 3: It can be written as 6m^2-5m^2+9+7.

Step 4: Now we can easily add the terms.

Step 5: Therefore, the answer is m^2+16.

Example 2:

Add (8n3+12) +( -15n3-6)

Solution:

Step 1: Here we are going to add the two binomials.

Step 2:  Its also like a mathematical addition.

Step 3: It can be written as 8n^3-15n^3+12-6.

Step 4: Now we can easily add the terms.

Step 5: Therefore, the answer is 7n^3+6.

These are the examples of connected math variables. Having problem with trig identities solver keep reading my upcoming posts, i will try to help you.

Examples of Patterns:

Example 1:

Compute the missing terms from the pattern given below.

2, 4, 8, 16, 32, 64, ___, ____

Solution:

Step 1: The first term of the pattern is 2.

Step 2: The second term of the pattern = 2 `xx` 2 = 4.

Step 3: The third term is 4 `xx` 2 = 8.

Step 4: The fourth term is 8 `xx` 2 = 16.

Step 5: Similarly, the missing terms can be determined as follows.

Step 6: The seventh term will be 64 `xx` 2 = 128.

Step 7: The eighth term is 128 `xx` 2 = 256(So, the pattern is we need to multiply 2 with the previous term).

Step 8: Therefore, the pattern is 2, 4, 8, 16, 32, 64, 128 and 256.

Example 2:

Compute the next two terms in the pattern given below.

1, 3, 5, 7, 9, 11, ___, ____

Solution:

Step 1:The first term of the pattern is 1

Step 2:The second term of the pattern = 1 + 2 = 3

Step 3:  The third term is 3 + 2 = 5

Step 4: fourth term is 5 + 2 = 7

Step 5: Similarly, the missing terms can be determined as follows.

Step 6: The seventh term will be 11 + 2 = 13

Step 7: The eighth term is 13 + 2 = 15

Step 8: This is an odd sequence of number.

Step 9: So the exact pattern is 1, 3, 5, 7, 9, 11, 13 and 15.

These are the example problems of connected math variables and patterns.

Negative Whole Numbers

Introduction :
Negative numbers are defined as the numbers that less than zero. It is always an opposite of the positive numbers. A negative whole number means negative numbers which consist of all negative integer numbers. We can add, subtract, multiply and divide by using the negative whole numbers. For example 0, 1, 2, 3… and -1, -2-, 3… etc

Examples of Negative Whole Numbers:

Negative whole numbers example 1:

Simplify (-120) + (-250)

Solution:

Given problem is (-120) + (-250)

We can add the given negative whole numbers by using the following methods:

Positive * negative = negative

In the given problem, first term as -120 and then the second term as + (-250) = -250

Negative + negative = negative

Therefore, -120 + -250= -370

So we get the final result as negative number.

Answer: -370

Negative whole numbers example 2:

Simplify (-200) - (-500)

Solution:

Given problem is (-200) - (-500)

We can subtract the negative whole numbers by using the following methods:

Negative * negative =positive

In the given problem, first term as -200 and then the second term as - (-500) = + 500

But here negative + positive = positive. Because of positive number (500) is larger than negative value (200).

That is, -200 + 500= 300

Here we get the final answer is positive. Understanding Is pi a Rational Number? is always challenging for me but thanks to all math help websites to help me out.

Answer: 300

Negative whole numbers example 3:

Simplify (-400) * (-100)

Solution:

Given problem is (-400) * (-100)

We can multiply the negative whole numbers by using the following methods:

Negative * negative = positive

But here we can just multiply the whole numbers. Then we get

-400 * (-100) = 40000

Answer: 40000

Negative whole numbers example 4:

Simplify (-1200) / (-300)

Solution:

Given problem is (-1200) / (-300)

Here we are dividing the above whole numbers.

Negative / negative = positive

Therefore we get the positive answer.

That is, -1200/-300

Here minus sign are canceled on both numerator and denominator.

Then we get,

1200/300

1200 is 4 times of 300

1200/300= 4

Therefore we get the final answer is 4.

Answer= 4

Practice Problems of Negative Whole Numbers:

Simplify the following problems:

(-100) + ( -50)
(- 120) – ( -60)
( -30) * (-40)
(-400) / (-50)
Answer keys:

-150
-60
1200
8

Trig Word Problems

Introduction to trig word problems:

Greek Mathematician Ptolemy, Father of trigonometry proved the equation sin2A+cos2A=1 using geometry involving a relationship between the chords of a circle. Trigonometry was mainly concerned with establishing the relations between sides and angles of a triangle. The trigonometry consists of angles, quadrants, ratios and Identities, Compound Angles, and trigonometrical Equations. The trigonometry word example problems and practice problems are given below.

Example Problems for Trig Word Problems:

Trig word problems - Example: 1

The top of a tower was seen from the top and the bottom of a building of height 10 m at angles of elevation 45° and 60°. Determine the height of the tower.

Solution:

 

Let AB be the tower CD be the building of height 10 m.

Let DE be perpendicular to AB from D.

At C, the angle of elevation of A is 60°.

That is ?BCA = 60°

At D, the angle of elevation of A is 45°.

That is ?EDA = 45°

BE = CD = 10 m (since BEDC is a rectangle)

Let AE be x in metres, then AB is = x +10 m

In a right angled triangle ABC

tan60° = AB/BC (or) v3 = (x + 10m)/BC

After solve this, we get

ED = BC = (x + 10m)/v3

In a right angled triangle AED

tan45° = AE/ED   (or)

v3 x = x + 10 m

v3 x – x = 10 m

x( v3 –1) = 10 m

After solving this, we get

= 5 (1.732+1)m = 5 (2.732) m = 13.66 m

Height of the tower AB = x + 10 m = 13.66 m + 10 m = 23.66 m

Trig word problems - Example: 2

Determine the length of the chord of a circle of radius 10 cm subtending at the centre the angle of 144°.

Solution:

Let AB be a chord of a circle with centre 0 of radius 10 cm. Draw OC?AB. Then C is the mid point of AB

?AOB = 144°

?COB = 72°

In right angled triangle OCB

OB/BC = sin 72°

BC = 10 sin 72° cm

= 10 × 0.9511 cm

= 9.511 cm

Length of chord AB = 2 × BC

= 2 × 9.511 cm =  19.022cm . Is this topic Translation Math hard for you? Watch out for my coming posts.

Practice for Trigonometry Word Problems:

1. A flag staff stands on the top of 6 m high tower. From a point on the ground the angle of elevation of given top of the flag staff is 60° and from the same point the angle of elevation of the top of the tower is 45°. Determine the height of the flag staff.

Answer: 4.392

2. A ladder placed that against the wall such that, the ladder are reaches the top of the wall then height 6 m and the ladder is inclined at an angle of 60°. Determine how far the ladder is from the foot of the wall.

Answer: 3.464

Random Prime Number

Introduction :

Prime number is an important topic in mathematics.Prime number is defined as the number which is  divisible by  1 and the number by itself. In this article we shall discuss  random prime number with suitable example problem. In a set of random data we need to identify the prime number.

Random Prime Number Examples:

Prime numbers between 1 and 100:

The following numbers are the least prime numbers

2, 3, 5, 7, 11, 13, 17, 19, 23, 29, 31, 37, 41, 43, 47, 53, 59, 61, 67, 71, 73, 79, 83, 89, 97.

Random prime number example 1:

Solution:

Find is 4 a prime number?

Step 1:

The number of 4 is

Step 2:

Now We should identify 4 is prime number or not.

Step 3:

Factors 4 is  1  2  4

Step 4:

So  4 has three factors. So it is not a prime number.

Random prime number example 2:

Solution:

Find  is 14 a  prime number in the random set of data 1,2.4,7,13,23,14,15

Step  1:

The number of 14 is

Step 2:

Now We should identify 14 is prime number or not.

Step 3:

factors of 14 is  1  2  7  14

Step 4:

So  14 has four factors. So it is not a prime number.


Few more Random Examples:

Random prime number example 3:

Solution:

Find  is 7 a prime number in the random of data 1,2.4,7,13,23,14,15

Step  1:

The number of 7 is

Step 2:

Now We should identify 7 is prime number or not.

Step 3:

Factors of 7 is 1  7

Step 4:

So  7  has  two factors. So it is  a prime number.Having problem with how to add percentages keep reading my upcoming posts, i will try to help you.

Random prime number example 4:

Solution:

Find  is 13 a  prime number in random of data 1,2.4,7,13,23,14,15

Solution:

Step  1:

The number of 13 is

Step 2:

Now We should identify 13 is prime number or not.

Step 3:

Factors of 13 is 1  13

Step 4:

So  13  has  two factors. So it is  a prime number.