Guided reading answers

The guided reading answers are nothing but getting help from others to reading the subjects.In online only we can get the help of tutor for reading any subjects.Initially the math problems can be solved by using some arithmetic operations  like addition,subtraction,division and multiplications and these can be denoted by (+ ,`xx` ,`-` ,÷ ).The following article shows some guided reading answers.

Solved Math Problems with some Guided Reading Answers

Problem 1:

Solve the 56x + 47y = 2632 given equation on the x and y intercepts.

Given:

56x + 47y = 2632

Solution:

56x + 47y = 2632

To find the x intercept of y = 0 and solve for x.

56x + 47(0) = 2632

Solve the value of x.

  x = `2632/56`

  x = 47

  To find the y intercept of x=0 and solve for y.

56(0) + 47y = 2632

Solve the value of y

47y = 2632

  y = `2632/47`

  y = 56.

The equations of x intercept on (47,0) and y intercept on (0,56).

Problem 2:

Solve the problem 185 + 35 ( 40 + 27 ) ÷ 67 – 60 in method of order of operation
Solution:

Given:

 `=>`  185 + 35 ( 40 + 27 ) ÷ 67 – 60

Step 1: we need to simplify the parentheses

 `=>` 185 + 35 `xx` 67 ÷ 67 – 60

Step 2: We need to simplify the multiplication

 `=>` 185 + 2345 ÷ 67 – 60

Step 3: We need to simplify the division

 `=>` 185 + 35 – 60

Step 4: We need to simplify the addition

 `=>`220 –  60

Step 5: We need to simplify the subtraction

 `=>` 160

Answer: 185 + 35 ( 40 + 27 ) ÷ 67 – 60 = 160

Solved more Math Problems with some Guided Reading Answers

Problem 3:

Solve the given problem 11(s – 9) – 6s ` - ` 26 = 13(s + 33)
The Solutions follows below:

Step 1: Given expression is,

11(s – 9) – 6s ` - ` 26 = 13(s + 33)

Step 2: Multiplying the integer terms

11s – 99 – 6s – 26 = 13s + 429.

Step 3: Grouping the above terms

5s –125 = 13s + 429

Step 4:  Add 125 on both sides

5s –125 + 125 = 13s + 429 + 125

Step 5: Grouping the above terms

5s = 13s + 554

Step 6: Subtract 13s by on both sides

5s `-` 13s = 13s `-` 13s + 554

Step 7: Grouping the above terms

–8s = 554

S = `- 554/8`

The required answers is

S = `- 554/8`

Problem 4:

Solve given problem (156x2 – 141x – 91) + (213x2 – 181x – 144) `-` (–916x2 +   41x + 20)
 Solution:

The problem can be solved in simplifying method .

Step 1: (156x2 – 141x – 91) + (213x2 – 181x – 144) `-` (–916x2 +   41x + 20)

Step 2: 156x2 – 141x – 91 + 213x2 – 181x – 144 + 916x2 `-`    41x `-` 20

Step 3:  1285x2 – 363x – 255      

The required answer is

(156x2 – 141x – 91) + (213x2 – 181x – 144) `-` (–916x2 +   41x + 20) = 1285x2 – 363x – 255

Interior Angles of Different Shapes

An interior angle is the angle formed when the endpoints of a polygon’s two sides are shared. In simple terms, when a new line intersects two straight lines that are parallel, then four angles will be formed inside them. These angles are known as Interior Angles. This angle will be inside a shape always. Also the angles formed outside the shape are known as exterior angles. Interior angles are sometimes referred as “Internal Angles”.

Interior Angles of a Triangle
The interior angles of a triangle will always be 180 degrees. For example if A, B and C are three sides of a triangle, then A+B+C = 180 degrees. Due to this reason, only one of the angles formed inside a triangle can be obtuse (i.e. greater than 90 degree). Eventually in a right angle triangle, since one angle is 90 degree, the other two angles will always add up to 90 degree.

Interior Angles of Square and Quadrilaterals
A square can be made up of two triangles. Hence, the sum of interior angles of square will add up to 360 degrees.  Quadrilateral also lies in the same case in which the sum of interior angles gives 360 degrees. Meanwhile, in this case maximum of two angles can be greater than 90 degrees.
Interior Angles of Polygons

The interior angle of polygon is nothing but the angle formed at every vertex inside it. Hence for a polygon of N vertices and N sides, there will be N interior angles. The sum of these interior angles will sum up to a constant value always. The formula that relates the sum of interior angles and number of sides of polygon is as follows:
Sum of Interior Angles = 180(n-2) degrees, where n is the number of sides. For example, sum of square that has four sides will be 180*2= 360 degrees, sum of pentagon which has five sides will be 540 degrees. Similarly Interior Angles of a hexagon, which has six sides, will be 720 degrees.
Also, the above said formula will not be applied to regular polygons, whose all sides and interior angles are always equal. Therefore, Interior Angles formula for a regular polygon will be 180(n-2) divided by n, where ‘n’ is the number of sides. This formula applies to its children such as regular pentagon whose angle is 108 degree, regular hexagon whose interior angle is 120 degree etc.
Also, two interior Angles at the same side of a polygon located at both sides are referred as “Adjacent Interior Angles”.

Modal value in statistics

Mode Statistics
In statistics, the four basic measures of central tendency are Mean, Median and Mode. We know that Mean is the Average of the total data values in a given data set and Median is the middle value of the given data set when values are arranged in the numerical order. What is Mode, at times we come across a data set in which a number repeats most number of times that is it occurs most often such a data value is called the Mode. For example, consider the data, 1, 1, 3, 3, 3, 3, 5, 5, 7. As you can see the number that occurs most number of times is 3 as it is appearing four times which is the most number of times in the given list and hence 3 is the Mode

Mode Definition
Let us now define Mode, in simple words mode can be defined as the data value that occur most number of times in the data list. There can be more than one mode in a given data set, if there are two modes in a given set it is called bi-modal and if more than two modes in the data set is called multimodal. If there is no number that occurs most frequently then we can say that the data set has no mode. For example the data, 11, 12, 13, 8, 9, 11, 14, 11, 9, 15, 11, 12. First let us arrange the given data set in the numerical order. 8, 9, 9, 11, 11, 11, 11,12, 12, 13, 14, 15. Now let us list the data values that occur more than once. The data value 9 occurs 2 times, the data value 11 occurs 4 times, the data value 12 occurs two times. So, the data value that occurs most number of times is 11 which is four times and hence the mode of the data set is 11.

Mode Formula: the value that occurs most frequently in a data set when arranged in numerical order. The typing speed (in words per minute) of a typist working in a firm are 46, 52, 40, 38, 52, 36, 46, 52, 37, 46  find the modal value or the mode using the mode formula.

First we arrange the typing speeds in the numerical order which gives us 36, 37, 38, 40, 46, 46, 46, 50, 50, 50. The values that are occurring most frequently are 46 and 50, both the values are occurring three times in the list and hence we can call it bimodal with the modes 46 and 50.

Quick Algebra Answers

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. Together with geometry, analysis, topology, combinatorics, and number theory, algebra is one of the main branches of pure mathematics (Source: Wikipedia).

In this article we are going to see some quick algebra problems with answers.

Quick Algebraic Example Problems with Answers:

Problem 1:

Given the equation

5(-3x - 2) - (x - 3) = -4(4x + 5) + 13

Multiply factors.

-15x - 10 - x + 3 = -16x - 20 +13

Group like terms.

-16x - 7 = -16x - 7

Add 16x + 7 to both sides and write the equation as follows

0 = 0

Hence the statement is true for all values of x and therefore all real numbers are solutions to the given equation.

Problem 2:

Given the line

5x - 5y = 7

Rewrite the eqn in slope intercept form y = mx + b and identify the value of m the slope.

-5y = -5x + 7

y = x - 7/5

The slope is given by the coefficient of x which is 1.

Problem 3:

To find the eqn of the line through the points (-1, -1) and (-1, 2), we use the slope m.

m = (y2 - y1) / (x2 - x1) = (2 - -1) / (-1 - -1) = 3 / 0

The slope is defined which means the line is perpendicular to the x axis and its equation has the form x = constant. Since all points have equal x coordinates -1, the equation is given by:

x = -1

Problem 4:

Given the equation

2x - 4y = 10

To find the x intercept we set y = 0 and solve for x.

2x - 0 = 10

Solve for x.

x = 10 / 2

= 5

The x intercept is at the point ( 5 , 0).

Quick Algebra Practice Problems with Answers:

1. Find the statement is equal or not equal: 7(-4x - 3) - (x - 4) = -8(2x + 6) + 11

2. To find the equation of the line through the points (-2, -2) and (-2, 1), we first use the slope m.

3. Solve: 8x - 2y = 3

Answers for quick algebra:

1.Not Equal.

2.Slope m =1/0

3. The x intercept is at the point (3/8 , 0).

Introduction to practice pre algebra answers

The word algebra is defined from the Arabic word al–jabr. In Arabic language, ‘al’ represents ‘the’ and ‘jabr’ represents ‘reunion of broken parts’. We can use letters like a, b, x and y to denote numbers. Using the basic operations add (+), subtract (-), Product(x) and Divide (/)or extraction of roots on these symbols and real numbers, we obtain what are called algebraic expressions. This contains following types of problems like Polynomials, Algebraic Identities, and factorization and Division of a Polynomial by a Polynomial.

Practice Pre Algebra Example Problems with Answers

Practice Pre Algebra Example Problems with Answers are given below:

1. Steven has 18 rupees. She buys fruits for 8 rupees. Find the remaining amount with her.

Solution:

We can write it as 18 – 8 = 10

2. Write 25–x=10 as a Mathematical statement.

Solution:

What number is to be subtracted from 25 to get 10?

3. Pick out the variables and constants: A, – 15, q, l, 22.3, and 73

Solution:

The variables are A, q and l

The constants are – 15, 22.3 and 73.

4. Write the following using powers:

(a) 5×m×m×m (b) a×b×a×a×b

Solution:

(a) 5×m×m×m=5m^3

(b) axb×a×a×b=a×a×a×b×b

= a^3×b^2=a^3b^2

5. Write the following algebraic expression in the product form:

(a) 8xy^2 (b) 10p^2 qr^3

Solution:

(a)8xy^2= 8 × x × y × y

(b) 10p^2 qr^3 = 10 × p × p × q × r × r × r

6. Write the coefficient in the following algebraic terms:

(a) The coefficient a in 10a is     10 .

(b) The coefficient of c in 3c is     3  

7. Identify the like and unlike terms:

(a)    12a and 15a -These are like terms

(b)   – 3b and 6c-These are unlike terms because here the variables are different.

8. Add and subtract the algebraic terms 12x and 5x.

Solution:

The above terms are like terms. Hence we can add and subtract directly.

12x + 5x = (12 + 5) x= 17x

12x - 5x = (12 - 5) x= 7x

Practice Pre Algebra Problems for Answers

Practice Pre Algebra Problems for finding answers are given below:

Practice 1: The symbol Δ, in Δ + 5 is called a ___________ .

Practice 2: A quantity which takes different values is called a __________ .

Practice 3: The coefficient of a b in 15ab is____ .

Practice 4: 2×m×n×n×m×m can be written as ____________ .

Practice 5: Add the following terms: 3xy, 7xy and 18xy.

Introduction to my math answers sheet

Math is a family where we can declare any kind of the numbers like symbols, letters and the different numbers, complex numbers, real numbers, rational numbers etc...Math is a group of sciences (arithmetic, geometry, algebra, trigonometry, calculus etc..) that explains measures,magnitudes,area of the region, statistics. we are going to learn how to solve some of the math problems. In addition, math helps a lot in our daily life. Here we include some of the math problems to help you better.The answer sheet to the problems follows.

Math Answer Sheet to Given Problems

Ex 1: Let A = {1, 2}, B = {a, b}. Find some relations from A → B and B → A.

Sol:
Since relation from A to B is a subset of the Cartesian product A × B = {(1 , a) , (1, b) , (2 , a) , (2 , b)} any subset of A × B is a relation from A → B. Therefore{(1 , a), (1 , b), (2 , a), (2 , b)}, {(1, a), (1, b)}, {(1, b, (2, b)}, {(1 , a)} are some relations from A to B. Similarly any subset of B × A = {(a , 1), (a , 2), (b , 1), (b , 2)} is a relation from B to A. {(a , 1), (a , 2), (b , 1), (b , 2)}, {(a, 1), (b, 1)}, {(a, 2), (b, 1)} are some relations from B to A.

Ex 2: Evaluate the equation     2(-3x - 4) - (-x - 4) = -2(x + 1) + 2

Sol:
Given the equation  2(-3x - 4) - (-x - 4) = -2(x + 1) + 2
Multiply factors.
-6x - 8 + x + 4 = -2x - 2 +2
Grouping the terms.
-5x - 4 = -2x
-3x = 4
X = `(-4)/(3)`  is the answer to the math problem

Answer Sheet to Probelms on Math :

Ex 3: If x <4 -="-" 4="4" 5="5" nbsp="nbsp" p="p" simplify="simplify" x="x">
Sol:
Given the expression  |x - 4| - 5|-4|
If x <; 4 then x - 4 < 4 and if
x - 4 < 4 the |x - 4| = -(x - 4).
Substitute |x - 4| by -(x - 4) and |-4| by 4 .
lx - 4| - 5|-4|
= -(x - 4) -5(4)
= -x -16 is the answer to the math problem

Ex:4 Find the next two numbers in the number pattern.
 2, 6,18 , ___, ___,.
Sol:
Step 1: The given pattern is obtained by multiplying 3 to each number to get the next number in the pattern.
Step 2: The next two numbers in the pattern are 54,162.

Ans: 54,162 is the answer to the math problem

Mean frequency distribution

What is frequency distribution:
Frequency distribution is a term associated with statistics. In statistics, when we study some characteristic of a sample and then group the observations under various groups, a frequency distribution comes to play. A frequency distribution is a table showing the values of one or more variables and their respective frequencies of a given sample.

How to construct a frequency distribution:
In a univariate data, (univariate means that there is only one variable that we are interested in studying, the other factors are assumed to be constants) if x1,x2,x3,….xn are the possible values of the variable and f1,f2,f3,….fn are the frequencies with which each of the variables occur respectively. Then a table drawn as follows:
Variable (xi) Frequency (fi)
x1 f1
x2 f2
x3 f3
: :
: :
: :
xn fn
Is called a frequency distribution table of the data. Here i = 1,2,3,…..n. That means that the variable x can have n possible values and the frequency of each of the values are f. The above is a frequency distribution when the variable in question is discrete. For a continuous variable, the frequency distribution would look like this:
Class interval Frequency (fi)
C1 – C2 f1
C2 – C3 f2
C3 – C4 f3
: :
: :
: :
Cn-1 - Cn fn
Here, C1 – C2, C2 – C3 etc are the class intervals and f1,f2,f3… etc are the frequencies of the respective classes. The above distribution can be converted to a mean frequency distribution by replacing the class intervals with the respective class means.  We would need to do that to be able to easily work with the data. Its not exactly possible to calculate sample mean, sample standard deviations etc from a distribution having only class intervals. Therefore the mean frequency distribution would look like this:
Class interval Class mean Frequency (fi)
C1 – C2 (x1) ̅ f1
C2 – C3 (x2) ̅ f2
C3 – C4 (x3) ̅ f3
: : :
: : :
: : :
Cn-1 - Cn (xn) ̅ fn
Here, (x1,) ̅  (x2,) ̅  (x3,) ̅ …. (xn) ̅ etc are the respective class means.
The type of frequency distribution that we would construct would depend upon the frequency distribution example given to us. As we saw above, for a single variable, the distribution would be different if the variable is discrete and different if the variable is random. Similarly for more than one variables also the distributions would be different.