Mathematics Program

Introduction to solve algebra homework answers:

Algebra is one of the main branches of mathematics that deals with calculating unknown variables from the help of known values. Homework problem with answers helps us to understand the concept of algebra. It is the study of rules of operation and relations, algebraic expressions, conditions and polynomials. An algebraic expression represents a scale where all the arithmetic operations are carried out on both the sides of the scale. Algebra homework problem contains problems with complex numbers, matrices, vector etc. The solved homework problems with answers are given below.

solve algebra homework answers : Examples


The following are the solved example problems for algebra homework.

Ex 1:

Solve the algebraic expression

6(c -3) + 5d - 2(c -d -2) + 1

Sol:

Given algebraic expression is

6(c -3) + 5d - 2(c -d -2) + 1

Multiplying the integer with above terms

= 6c - 12 + 5d -2c + 2d + 4 + 1

Grouping the above terms

= 6c + 7d – 7

Ex 2:

Solve the algebraic equation.

x 2 - 3x = 0

Sol:

Given equation is
x 2 - 3x = 0

Take X factor as common
x (x - 3) = 0

So the product x (x - 3) to be equal to zero, then we get

x = 0 or x - 3 = 0

Solve the above simple equations to obtain the solutions.
x = 0
or
x = 3

X= 0 or 3 is the solution.

Ex 3:

Solve the algebraic expression

4(a -1) + 2b - 5(a -b -4) + 5

Sol:

Given algebraic expression is

4(a -1) + 2b - 5(a -b -4) + 5

Multiplying the integer terms

= 4a - 4 + 2b -5a + 5b + 20 + 5

Grouping the above terms

= -a + 7b + 21

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Solve algebra homework answers : Practice problems


Find h (4) and g(4) and h(4) / g(4) and the functions g and h is given as

h (x) = 3x - 8 and g (x) = x 2 - 12

Solution:

Calculate h(4)

h(4) = 3(4) - 8 = 4

Calculate g (4)

g (4) = 4 2 - 12
= 16 -12 = 4

h (4) / g (4) =4/4 =1

Solve the algebraic expression

4(c -1) + 2d - 5(c -d -4) + 5

Solution:

Given algebraic expression is

4(c -1) + 2d - 5(c -d -4) + 5

Multiplying the integer terms

= 4c - 4 + 2d -5c + 5d + 20 + 5

Grouping the above terms

= -c + 7d + 21

Solve the equation     5(-2x - 2) - (-2x - 4) = -4(4x + 4) + 15

Sol:

Given the equation

5(-2x - 2) - (-2x - 4) = -4(4x + 4) + 15

Multiplying the integer with above terms.
-10x - 10 + 2x + 4 = -16x - 16 +15

Grouping the above terms.

-8x - 6 = -16x - 1

Add -8x - 6 to both sides, the above equation becomes

-8x = 7

X= -7/8

The practice problems are given below for homework.

1) Solve the algebraic equation     6(-8y - 3) - (-5y - 5) = -8(2y + 4) + 9

Answer: y = 8/27

2) Solve the algebraic equation.   x 2 - 10x = 0

Answer:   x= 0 or 10

Perfect Squares

Introduction:

Square of number is multiply the same number twice.A × A =A2, here square of  A  is written as A2 Here A is called the base and 2 is called the index or the power.Now observe the following examples:

0^2 = 0 ×0 = 0

1^2 = 1 × 1 = 1

2^2 = 2 ×2 = 4

These examples are square the same number.The square of 0,1,2,3,4 are 0,1,4,9,16 respectively. These square numbers are known as perfect squares. I like to share this Transformations Geometry with you all through my article.


Explain perfect square with examples:


Examples:

1). Is 625 a perfect square?

Yes, because 625 can be expressed as the product of two same numbers as 25 × 25.

2). Is 10 a perfect square?

No, 10 is not a perfect square since 10 cannot be written as the product of two same numbers.

3). Is 144 a perfect square?

Yes, because 144 can be expressed as the product of two same numbers as 12 × 12.

4). Is 70 a perfect square?

No, 70 is not a perfect square since 70 cannot be written as the product of two same numbers. Understanding Graphing Calculators is always challenging for me but thanks to all math help websites to help me out.


Perfect square Examples:


(1). Find the Perfect square of 20

Solution:

20 ^2 = 20 * 20

= 400

(2). Find the Perfect square of 111

Solution:

111 2 = 111 * 111

= 12321

(3). Find the Perfect square of 13

Solution:

13^ 2 = 13 * 13

= 169

(4). Find the Perfect square of 81

Solution:

81^ 2 = 81*81

= 6561

(5). Find the Perfect square of 100

Solution:

100 ^2 = 100 * 100

= 10000

Perfect square Exercises:

(1). Find the Perfect square of 32

(2). Find the Perfect square of 15

(3). Find the Perfect square of 09

(4). Find the Perfect square of 723

(5). Find the Perfect square of 40

Answers:

(1). 1024

(2). 225

(3). 81

(4). 522729

(5). 1600

Perfect Number Examples

Definition:

A perfect number is the positive integer in that is the sum of its proper positive divisors, that is, the sum of the positive divisors excluding the number itself. Equivalently of a perfect number is that a number is half the sum of all of its positive divisors (including itself), or σ(n) = 2n.


Even perfect numbers

In order for 2p − 1 to be prime, it is necessary that p itself is prime. Prime numbers of the form 2p − 1 are known as Mersenne primes, after the seventeenth-century monk Marin Mersenne, who studied number theory and perfect numbers. However, not all numbers of the form 2p − 1 with p a prime are prime

In the first four perfect numbers are generated by the formula 2p−1(2p − 1), with p a prime number:

for p = 2: 21(22 − 1) = 6

for p = 3: 22(23 − 1) = 28

for p = 5: 24(25 − 1) = 496

for p = 7: 26(27 − 1) = 8128.

Noticing that 2p − 1 is a prime number in each instance, Euclid proved that the formula 2p−1(2p − 1) gives an even perfect number In order for 2p − 1 to be prime, it is necessary that p itself is prime. Prime numbers of the form 2p − 1 are known as Mersenne primes. I have recently faced lot of problem while learning Definition of Rational Numbers, But thank to online resources of math which helped me to learn myself easily on net.


Odd perfect numbers

It is unknown whether there are any odd perfect numbers. Various of results have been obtained, but none of that has helped to locate one or otherwise resolve the question of their existence. Carl Pomerance has been presented by a heuristic argument in which suggests that no odd perfect numbers exist.[4] Also, it can been conjectured of that there are no odd Ore's harmonic numbers, except for 1. If true in this would to imply that there are no odd perfect numbers.

Mathematics in Daily Life

Introduction to Everyday Mathematics answers:-

Our life is intertwined with mathematics.

We use mathematics in our daily life.

We use mathematics  to measure the distance, the weights, to find volume, to know the time,  to measure temperature, to dilute liquids, to  make a concentrate of a solution etc. Understanding radian and degree measure is always challenging for me but thanks to all math help websites to help me out.


Use of mathematic in every day with answers

As soon as we get up in the morning, we look at the clock to know the time.

We measure the coffee and  count the slices of bread for the family.

When we go to the market to buy vegetables, we calculate the prices of the purchase.

As we walk home after purchase, we make a note of the day's temperature.

Cooking needs time management, weight management and volume management and temperature adjustment.

We need to pay for the ironed dress to wear for the office, pay for petrol for the motorbike  etc.

The office work also involves mathematical calculations, charts and graphs. Having problem with Radian Measure keep reading my upcoming posts, i will try to help you.


Use of mathematics outside home with answers


When we go shopping, we have to pay the bill, which is a  mathematical calculation.

Discount offered at the shops and taxes also involves calculations.

Buying and selling of various commodities involves profit or loss.

When you share your  food with friends, it involves fractions.

We convert money to bigger or smaller units.

We also convert measurements to higher or lower units in our daily life.


Mathematic in managing outside activities with answers


When we  build a house , we use the calculation called "Time and  Work".   This system is also used for many

other activities like mowing a garden, plucking tea leaf, harvesting a crop etc

We use the form "Time and distance" when we travel.

We use  the form 'Time and speed"  when we go up and down the stream and river.

We also use 'Time and speed" in sports activities, especially races.


Perimeter, area and volume in daily life with answers


If we want to fence our garden, we use the perimete formula of various shapes.

If we want to  have a lawn in our garden, we calculate the area of the lawn.

If we want to store our harvested grains, we use the volume formula.

If we want to pack the grains in sacks, we use the break-up of the volume to smaller volumes.

Thus we note that  purchases, sales, profits , losses, tax, discounts, time, weights, volumes, area, perimeter

work, speed etc are  used daily in our life .

Probability with Replacement

Introduction to Probability with replacement :

To calculate the probability of ball which is strained from a population by using explanation of probability and the calculations can be established by using the relative frequency definitions of probability. In a examination can have n equally likely conclusion, and that a 'success' can take place in s ways (from the n).

Then the probability of a 'success' = s / n


Probability with replacement Problem 1


A pitcher contains 7 orange and 4 green balls. Find the matching probabilities if the balls are replaced after every draw.

(a) Mutually orange

(b) a orange and a green

(c) both the identical color.

Solution:-

a.) Since the balls are restored after each draw,

P(s)is 7 in both cases since we replace it with in each case.

This is simply 7/11 * 7/11 = 49/121

b.) This should be 7/11 * 4/11 = 28/121

c.) As for P(c).

P(c) = (P(two orange and two green)) .,

so

P(two orange or two green) = P(two orange) + P(two green) = P(c)

P(two orange) is given by 49 / 121

P(two green) is given by 16 / 121

now by just plugging in it in the given function we get it as follows

= 49/121 + 16/121 = 65/121.

65 / 121 is the finalised answer. Please express your views of this topic Example of Theoretical Probability by commenting on blog.


Probability with replacement Problem 2


A population of 50 red mice, 200 green mice, selections with replacement:

a) Probability of 3 red mice in 3 selections

b) Probability of selecting, in order, red, red and then Green.

c) If, however, we are not interested in the order (i.e. red, red, green) but just the overall outcome (i.e. 2 red, 1 green), the probability is different:0

Solution:-

a) Probability of 3 red mice in 3 selections = (50/250) * (50/250) * (50/250)

= (1/5) * (1/5) * (1/5) = 0.008

b) Probability of selecting, in order, red, red and then green = (50/250) * (50/250) * (200/250)

= (1/5) * (1/5) * (4/5) = 0.032

c) If, however, we are not interested in the order (i.e. red, red, green) but just the overall outcome (i.e. 2 red, 1 green), the probability is different:0

Possible outcome of 3 selections with replacement

Rounding and Addition

Rounding is one of the major concepts in basic mathematics taught in the middle school but used throughout the growing years. Rounding is a process of changing a number by estimating its nearest value. If a number is followed by a number that is greater or equal to 5, the number can be rounded up and if a number is followed by a number that is less than 5, the number can be rounded down.
• Example 1: If he buys a full collection of Yonex badminton racquets, he will pay just Rs.155 per racquet. If he buys a full collection of Yonex badminton racquets , he will pay just Rs.160 per racquet
• Example 2: The mall has given away about 23% of discount on all fashion wear . The mall has given away about 20% of discount on all kid's fashion wear. Addition at times is done after rounding a number. Below are the steps to add a number after rounding.
• Round the number to its nearest value
• Add the numbers

Examples: 1.
She paid Rs.1190 to the trainer for teaching her tricep dips at home . She also paid Rs.2000 for her gym trainer. How much total she paid including trainer for teaching tricep dips at home and gym trainer. Rs.1190 + Rs.2000 Rs.1200 + Rs.2000 (Rs.1190 is rounded to Rs.1200) Rs. 3200 is the total amount she paid including trainers. 2. Mohan is planning to invest 24% of his salary in Gold. Mohan’s wife on the other hand is planning to invest 65% of her salary in gold. What is the total investment the family makes on gold? 24% + 65% 25 + 65% (24% is rounded to 25%) 90% of their total investment is made on gold. These are the basics about rounded and addition.

calculus derivative problems exam

Introduction for calculus derivative problems exam:

Two mathematicians, Namely Gottfried Leibniz and Isaac Newton, developed calculus. Calculus problems can be dividing into two branches: Differential Calculus problems and Integral Calculus problems. Differential calculus is use to measure the rate of change of a given quantity whereas the integral calculus is use to measure the quantity when the rate of change is known. The output of a function will change when we change the input value of a function. The measure of the change in the function is called as Calculus Derivatives.


Calculus derivative example problems:

The following solving problems are based on the derivatives.

Ex 1:

Determine the derivative dy/dx of the inverse of function f defined by

f(x) = (1/8) x - 2

Sol:

The first is used to find the inverse of f and differentiate it. To find the inverse of f we first write it as an equation

y = (1/8) x - 2

Solve for x.

x = 8y + 16.

Change y to x and x to y.

y = 8x + 16.

The above gives the inverse function of f. Let us find the derivative

dy / dx = 8


Ex 2:

Determine the critical number(s) of the polynomial function f given by

f(x) = x 4 - 108x + 100

Sol:

The domain of f is the set of all real numbers. The first derivative f ' is given by

f '(x) = 4 x^ 3 - 108

f '(x) is defined for all real numbers. Let us now solve f '(x) = 0

4 x^ 3 - 108 = 0

Add 108 on both sides,

4x^ 3– 108 108=108

4x^ 3= 108

x^ 3 = 27

x = 3 or x = -3

Since x = 3 and x = -3 are in the domain of f they are both critical numbers. Is this topic Limits of a Function in Calculus hard for you? Watch out for my coming posts.


Calculus derivative Practice Problems exam:


1) Determine the derivative dy/dx of the inverse of function f defined by

f(x) = x/2+ 3x/2 – 2

Answer:  dy / dx = 2


2) Determine the critical number(s) of the polynomial function f given by

f(x) = x^ 3 - 48x + 10

Answer:  X = 4 or X= -4