Enter an equation along with the variable you wish to solve it for and click the Solve button.
- Scientific Notation To Decimal Converter online calculator. Directions To convert 123.456e+5 to a Whole Number and Decimal Number, enter the digits in appropriate boxes.
- May 19, 2020 1.1.1 just came out. Added a smart group option to match contacts that are a company or a person Template preferences now apply to new contacts created by Cardhop's parser Fixed smart group criteria for 'is set' and 'is not set' not working in some cases Fixed an issue where Cardhop could hang at launch in certain situations Various fixes and improvements.
Cardhop 1.2.3 MacOS Full macOS;; KoLomPC; 0 comments; 514 views; Hi everyone and have a nice day as you know we have opened the file sharing server so that you can quickly and without delay download the files, unfortunately for financial reasons we have to close it, if you want to continue to use it for downloading files. Java SE 1.4 Downloads. Go to the Oracle Java Archive page. Thank you for downloading this release of the Java TM Platform, Standard Edition Development Kit (JDK TM).The JDK is a development environment for building applications, applets, and components using the Java programming language.
In this chapter, we will develop certain techniques that help solve problems stated in words. These techniques involve rewriting problems in the form of symbols. For example, the stated problem
'Find a number which, when added to 3, yields 7'
may be written as:
3 + ? = 7, 3 + n = 7, 3 + x = 1
and so on, where the symbols ?, n, and x represent the number we want to find. We call such shorthand versions of stated problems equations, or symbolic sentences. Equations such as x + 3 = 7 are first-degree equations, since the variable has an exponent of 1. The terms to the left of an equals sign make up the left-hand member of the equation; those to the right make up the right-hand member. Thus, in the equation x + 3 = 7, the left-hand member is x + 3 and the right-hand member is 7.
SOLVING EQUATIONS
Equations may be true or false, just as word sentences may be true or false. The equation:
3 + x = 7
will be false if any number except 4 is substituted for the variable. The value of the variable for which the equation is true (4 in this example) is called the solution of the equation. We can determine whether or not a given number is a solution of a given equation by substituting the number in place of the variable and determining the truth or falsity of the result.
Example 1 Determine if the value 3 is a solution of the equation
4x - 2 = 3x + 1
Solution We substitute the value 3 for x in the equation and see if the left-hand member equals the right-hand member. Exhibeo 1 1 4.
4(3) - 2 = 3(3) + 1
12 - 2 = 9 + 1
10 = 10
Ans. 3 is a solution.
The first-degree equations that we consider in this chapter have at most one solution. The solutions to many such equations can be determined by inspection.
Example 2 Find the solution of each equation by inspection.
a. x + 5 = 12
b. 4 · x = -20
b. 4 · x = -20
Solutions a. 7 is the solution since 7 + 5 = 12.
b. -5 is the solution since 4(-5) = -20.
b. -5 is the solution since 4(-5) = -20.
SOLVING EQUATIONS USING ADDITION AND SUBTRACTION PROPERTIES
In Section 3.1 we solved some simple first-degree equations by inspection. However, the solutions of most equations are not immediately evident by inspection. Hence, we need some mathematical 'tools' for solving equations.
EQUIVALENT EQUATIONS
Equivalent equations are equations that have identical solutions. Thus,
3x + 3 = x + 13, 3x = x + 10, 2x = 10, and x = 5
are equivalent equations, because 5 is the only solution of each of them. Notice in the equation 3x + 3 = x + 13, the solution 5 is not evident by inspection but in the equation x = 5, the solution 5 is evident by inspection. In solving any equation, we transform a given equation whose solution may not be obvious to an equivalent equation whose solution is easily noted.
The following property, sometimes called the addition-subtraction property, is one way that we can generate equivalent equations.
If the same quantity is added to or subtracted from both membersof an equation, the resulting equation is equivalent to the originalequation.
In symbols,
a - b, a + c = b + c, and a - c = b - c
are equivalent equations.
Example 1 Write an equation equivalent to
x + 3 = 7
by subtracting 3 from each member.
Solution Subtracting 3 from each member yields
x + 3 - 3 = 7 - 3
or
x = 4
Notice that x + 3 = 7 and x = 4 are equivalent equations since the solution is the same for both, namely 4. The next example shows how we can generate equivalent equations by first simplifying one or both members of an equation.
Example 2 Write an equation equivalent to
4x- 2-3x = 4 + 6
by combining like terms and then by adding 2 to each member.
Combining like terms yields
x - 2 = 10
Adding 2 to each member yields
x-2+2 =10+2
x = 12
To solve an equation, we use the addition-subtraction property to transform a given equation to an equivalent equation of the form x = a, from which we can find the solution by inspection.
Example 3 Solve 2x + 1 = x - 2.
We want to obtain an equivalent equation in which all terms containing x are in one member and all terms not containing x are in the other. If we first add -1 to (or subtract 1 from) each member, we get
2x + 1- 1 = x - 2- 1
2x = x - 3
If we now add -x to (or subtract x from) each member, we get
2x-x = x - 3 - x
1 2 4 Sequence
x = -3
![Cardhop Cardhop](https://insmac.org/uploads/posts/2017-10/1508480855_cardhop_01.jpeg)
where the solution -3 is obvious.
The solution of the original equation is the number -3; however, the answer is often displayed in the form of the equation x = -3.
Since each equation obtained in the process is equivalent to the original equation, -3 is also a solution of 2x + 1 = x - 2. In the above example, we can check the solution by substituting - 3 for x in the original equation
2(-3) + 1 = (-3) - 2
-5 = -5
The symmetric property of equality is also helpful in the solution of equations. This property states
If a = b then b = a
This enables us to interchange the members of an equation whenever we please without having to be concerned with any changes of sign. Thus,
If 4 = x + 2 then x + 2 = 4
If x + 3 = 2x - 5 then 2x - 5 = x + 3
If d = rt then rt = d
There may be several different ways to apply the addition property above. Sometimes one method is better than another, and in some cases, the symmetric property of equality is also helpful.
Example 4 Solve 2x = 3x - 9. (1)
Solution If we first add -3x to each member, we get
2x - 3x = 3x - 9 - 3x
-x = -9
where the variable has a negative coefficient. Although we can see by inspection that the solution is 9, because -(9) = -9, we can avoid the negative coefficient by adding -2x and +9 to each member of Equation (1). In this case, we get
2x-2x + 9 = 3x- 9-2x+ 9
9 = x
from which the solution 9 is obvious. If we wish, we can write the last equation as x = 9 by the symmetric property of equality.
SOLVING EQUATIONS USING THE DIVISION PROPERTY
Consider the equation
3x = 12
The solution to this equation is 4. Also, note that if we divide each member of the equation by 3, we obtain the equations
whose solution is also 4. In general, we have the following property, which is sometimes called the division property.
If both members of an equation are divided by the same (nonzero)quantity, the resulting equation is equivalent to the original equation.
In symbols,
are equivalent equations.
Example 1 Write an equation equivalent to
-4x = 12
by dividing each member by -4.
Solution Dividing both members by -4 yields
In solving equations, we use the above property to produce equivalent equations in which the variable has a coefficient of 1.
Example 2 Solve 3y + 2y = 20.
We first combine like terms to get
5y = 20
Then, dividing each member by 5, we obtain
In the next example, we use the addition-subtraction property and the division property to solve an equation.
![Cardhop Cardhop](https://i2.wp.com/handcraftedbyjoy.com/wp-content/uploads/2019/08/Encouragement-Card-Hop.jpg?fit=4000%2C4000&ssl=1)
Example 3 Solve 4x + 7 = x - 2.
Solution First, we add -x and -7 to each member to get
4x + 7 - x - 7 = x - 2 - x - 1
Next, combining like terms yields
3x = -9
Last, we divide each member by 3 to obtain
SOLVING EQUATIONS USING THE MULTIPLICATION PROPERTY
Consider the equation
The solution to this equation is 12. Also, note that if we multiply each member of the equation by 4, we obtain the equations
whose solution is also 12. In general, we have the following property, which is sometimes called the multiplication property.
If both members of an equation are multiplied by the same nonzero quantity, the resulting equation Is equivalent to the original equation.
In symbols,
a = b and a·c = b·c (c ≠ 0)
are equivalent equations.
Example 1 Write an equivalent equation to
by multiplying each member by 6.
Solution Multiplying each member by 6 yields
In solving equations, we use the above property to produce equivalent equations that are free of fractions.
Example 2 Solve
Solution First, multiply each member by 5 to get
Now, divide each member by 3,
Example 3 Solve .
Solution First, simplify above the fraction bar to get
Next, multiply each member by 3 to obtain
Last, dividing each member by 5 yields
FURTHER SOLUTIONS OF EQUATIONS
Cardhop 1 2 4 Player Games
Now we know all the techniques needed to solve most first-degree equations. There is no specific order in which the properties should be applied. Any one or more of the following steps listed on page 102 may be appropriate.
Steps to solve first-degree equations:
- Combine like terms in each member of an equation.
- Using the addition or subtraction property, write the equation with all terms containing the unknown in one member and all terms not containing the unknown in the other.
- Combine like terms in each member.
- Use the multiplication property to remove fractions.
- Use the division property to obtain a coefficient of 1 for the variable.
Example 1 Solve 5x - 7 = 2x - 4x + 14.
Solution First, we combine like terms, 2x - 4x, to yield
5x - 7 = -2x + 14
Next, we add +2x and +7 to each member and combine like terms to get
5x - 7 + 2x + 7 = -2x + 14 + 2x + 1
7x = 21
Finally, we divide each member by 7 to obtain
In the next example, we simplify above the fraction bar before applying the properties that we have been studying.
Example 2 Solve
Solution First, we combine like terms, 4x - 2x, to get
Then we add -3 to each member and simplify
Next, we multiply each member by 3 to obtain
Finally, we divide each member by 2 to get
SOLVING FORMULAS
Equations that involve variables for the measures of two or more physical quantities are called formulas. We can solve for any one of the variables in a formula if the values of the other variables are known. We substitute the known values in the formula and solve for the unknown variable by the methods we used in the preceding sections.
Example 1 In the formula d = rt, find t if d = 24 and r = 3.
Solution We can solve for t by substituting 24 for d and 3 for r. That is,
d = rt
(24) = (3)t
8 = t
It is often necessary to solve formulas or equations in which there is more than one variable for one of the variables in terms of the others. We use the same methods demonstrated in the preceding sections.
Example 2 In the formula d = rt, solve for t in terms of r and d.
Solution We may solve for t in terms of r and d by dividing both members by r to yield
from which, by the symmetric law,
In the above example, we solved for t by applying the division property to generate an equivalent equation. Sometimes, it is necessary to apply more than one such property.
Example 3 In the equation ax + b = c, solve for x in terms of a, b and c.
Solution We can solve for x by first adding -b to each member to get
then dividing each member by a, we have
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Cardhop 1.3.5 September 8, 2020
- Improved handling of duplicate information being entered into the parser
- Fixed an issue where text entered into the parser would appear offset in some situations
- Fixed an issue where the print preview wouldn't appear in some situations
- Various fixes and improvements
Cardhop 1.3.4 May 18, 2020
- Added option to filter by job title in smart groups
- Emailing a contact will include the name of the contact in the new message window
- Improved calculation of age for Chinese lunar birthdays
- Fixed an issue where contact details wouldn't appear correctly when in full screen
- Fixed an issue where All Contacts wouldn't appear for some Exchange accounts
- Various fixes and improvements
Cardhop 1.3.3 December 10, 2019
- Cardhop will ask you to reauthorize your G Suite account if Google Admin API access has been disabled by your organization
- Added Copy Picture option when clicking on a contact's photo
- Improved editing alternate birthday fields
- Fixed a potential crash when printing envelopes
- Various fixes and improvements
Cardhop 1.3.2 August 14, 2019
- File size of exported vCards with images are now smaller
- Fixed some potential crashes
- Various fixes and improvements
Cardhop 1.3.1 July 11, 2019
- Added paper orientation options when printing envelopes and lists
- Added GitHub to list of social networks
- Fixed a crash when looking up contacts on Gravatar
- Various fixes and improvements
Cardhop 1.3 June 18, 2019
- Preference to show nicknames in contact lists
- Support for sending messages to groups with the parser (e.g. message /friends Hey guys)
- New templates when adding new smart groups to make it easier to quickly add new smart groups
- Various fixes and improvements
Cardhop 1.2.5 May 21, 2019
- Fixed an issue connecting to some Exchange 2013 directories
- Hid company checkbox on Exchange because Exchange doesn't support company-only contacts
- Various fixes and improvements
Cardhop 1.2.4 May 10, 2019
- Fixed a potential crash with some Chinese names
- Various fixes and improvements
Cardhop 1.2.3 May 1, 2019
- Ages are now shown next to birthdays in the list
- Can now drag contacts from directories to accounts or groups to make a copy of the directory contact
- Pasting emails containing mailto: links will automatically remove the mailto: prefix
- Various fixes and improvements
Cardhop 1.2.2 April 11, 2019
- WhatsApp action now opens the WhatsApp app if it is installed
- Better sorting of options in Add Field menu
- Better handling of sorting contacts with accents and non-Latin characters
- Various fixes and improvements
Cardhop 1.2.1 March 30, 2019
- Fixed an issue with Exchange and Office 365 directory contacts not showing phone numbers or emails
- G Suite directory contacts will now show additional information and photos
- Improved matching of contacts with accents when searching
- Fixed a crash on macOS 10.11 and 10.12
Cardhop 1.2 March 27, 2019
- Directories: Add Google, Exchange, and Office 365 directories to look up users on Google Contacts, G Suite, and Exchange Global Address List
- Favorites! Mark commonly used contacts as favorites. Favorites sync between all devices, including with Cardhop for iOS
- Added Copy Contact URL option to copy a URL which will show a contact in Cardhop from another app
- Fixed a potential crash when using smart groups on macOS Mojave
- Improved matching of contacts that have an email address but no first or last name
- Various fixes and improvements
Cardhop 1.1.6 October 25, 2018
- Fixed a potential crash when using smart groups on macOS Mojave
- Improved matching of contacts that have an email address but no first or last name
- Various fixes and improvements
Cardhop 1.1.5 September 25, 2018
- Support for Dark Mode on macOS Mojave
- Improved handling of names entered as Last, First (such as Smith, Alice)
- Various fixes and improvements
Cardhop 1.1.4 August 7, 2018
- Fixed a crash on macOS El Capitan
- Various fixes and improvements
Cardhop 1.1.3 August 3, 2018
- Added Instagram as a social profile type
- Added an option to skip already used labels when printing a sheet of labels
- Pressing return when a contact is selected will now begin editing the contact
- Dragging and dropping a contact into another app will now drop the contact name and a link to the contact
- Selecting a contact picture from a file will now show options to crop the picture
- Fixed an issue when using Skype to call phone numbers without a country code
- Various fixes and improvements
Cardhop 1.1.2 May 8, 2018
- Fixed an issue where adding contacts didn't work for some people
- Fixed an issue where creating a contact with emoji didn't work
- Fixed some DYMO labels printing with the wrong orientation
- Various fixes and improvements
Cardhop 1.1.1 May 5, 2018
- Added a smart group option to match contacts that are a company or a person
- Template preferences now apply to new contacts created by Cardhop's parser
- Fixed smart group criteria for 'is set' and 'is not set' not working in some cases
- Fixed an issue where Cardhop could hang at launch in certain situations
- Various fixes and improvements
Cardhop 1.1 May 2, 2018
- Full support for French, German, Italian, Spanish, English, and Japanese (including parsing and address/phone formats)
- Smart groups: Create dynamic smart groups that automatically update based on specific search criteria
- Template preferences to customize fields and labels for new contacts
- Printing support: Print customized envelopes, labels, and lists of contacts
- Quick Action for printing: Type “print” or use a Quick Action button to quickly print a contact or group
- “Add Notes with Timestamp” option to quickly insert the current date and time into the notes of a contact
- Typing into a related name field now suggests other names in your contacts
- Various fixes and improvements
Cardhop 1.0.7 February 27, 2018
- Various fixes and improvements
Cardhop 1.0.6 January 23, 2018
- Improved parsing of phone numbers with extensions
- Fixed a crash when opening preferences on macOS El Capitan
- Various fixes and improvements
Cardhop 1.0.5 December 19, 2017
- Added option to set the default country calling code for phone numbers
- Improved parsing of email signatures that include images
- Fixed an issue where birthdays wouldn't appear at the end of the year
- Various fixes and improvements
Cardhop 1.0.4 December 12, 2017
- Fixed a crash when encountering some types of contact data
Cardhop 1.0.3 December 10, 2017
- Fixed an issue where the default account setting wasn't saved
- Fixed some contact parsing issues
- Fixed an issue where the end of very long notes could get hidden
- Fixed an issue where deleted info from a contact could return if changes were detected in Contacts
- Improved compatibility with Skype 8 when dialing phone numbers
- Various fixes and improvements
Cardhop 1.0.2 November 8, 2017
- Improved editing of linked contacts that are on multiple accounts
- Added AppleScript support for sending text to Cardhop
- Added Skype for Business action
- Fixed first and last name order when viewing Chinese, Japanese, and Korean contacts
- Various fixes and improvements
Cardhop 1.0.1 October 21, 2017
- Skype action now allows calling phone numbers through Skype
- Increased maximum allowed width of groups sidebar
- Fixed some crashes when encountering invalid contact data
- Fixed a crash when using Share My Card
- Various fixes and improvements
Cardhop 1.0 October 18, 2017
- Initial release