Maths-
General
Easy
Question
![left parenthesis x minus 3 right parenthesis to the power of 2 end exponent equals 81](data:image/png;base64,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)
What is the sum of the solutions to the given equation?
- 0
- 6
- 9
- 12
The correct answer is: 6
We use the formula
to solve the problem.
Explanations:
Step 1 of 3:
The given equation is— ![open parentheses x minus 3 close parentheses to the power of 2 end exponent equals 81](data:image/png;base64,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)
![rightwards double arrow open parentheses x minus 3 close parentheses to the power of 2 end exponent minus 9 to the power of 2 end exponent equals 0](data:image/png;base64,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)
, using the formula mentioned in the hint section
![rightwards double arrow open parentheses x plus 6 close parentheses open parentheses x minus 12 close parentheses equals 0](data:image/png;base64,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)
Now, to satisfy the above equation, either
or, ![open parentheses x minus 12 close parentheses equals 0](data:image/png;base64,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)
Step 2 of 3:
If
![rightwards double arrow x equals negative 6](data:image/png;base64,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)
And if
![rightwards double arrow x equals 12](data:image/png;base64,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)
Hence, the solutions to the given equation are
and 12.
Step 3 of 3:
Now, sum of the solutions is ![equals negative 6 plus 12 equals 6](data:image/png;base64,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)
Final Answer:
The right option is — 6.
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?
I. The length of ![stack A C with minus on top](data:image/png;base64,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)
II. The measure of ![angle A B C](data:image/png;base64,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)
![](https://mycourses.turito.com/tokenpluginfile.php/c161933dbfaab094c54655ab71e9b8f0/1/question/questiontext/719583/1/1232792/Picture24.png)
Which of the following additional measurements to the triangle provides enough information to determine the length of
?
I. The length of ![stack A C with minus on top](data:image/png;base64,iVBORw0KGgoAAAANSUhEUgAAABcAAAAVCAYAAACt4nWrAAAACXBIWXMAAA7EAAAOxAGVKw4bAAAABGJhU0UAAAAU2v5G4wAAAP5JREFUeNpjYCAM/uPBo2AUDAdQQIQaJSDuAuILQPwNiB8CcTMQC+LTFA7Ev4CYBY+aEiDeAsS2QMwEFZOFOmo+Lk0gWy8B8W4gDsChphyIZ5MTHDOBOBKI44F4ChZ5NSC+S8BXWIEl1KsgIA41BB30EBkfKADkkjPQcIOBc0CsgabuGhCrkGp4PTSSkEErEGch8UER94NUgzWgrkQH9kC8CYnPBsSfSDX8MJ5yGz1JfgFiLmINTgPiCXjklwOxFxJ/LpbgwwokoWmaB4+aZDTL5YH4HRBXIuVEDiD2gVrsAlO4CiqID0gD8S00MVBqWQgNf1DQfQDiNWg+pB0AAJKxN4hLsi9lAAAAh3RFWHRNYXRoTUwAPG1hdGggeG1sbnM9Imh0dHA6Ly93d3cudzMub3JnLzE5OTgvTWF0aC9NYXRoTUwiPjxtb3ZlciBhY2NlbnQ9InRydWUiPjxtcm93PjxtaT5BPC9taT48bWk+QzwvbWk+PC9tcm93Pjxtbz4tPC9tbz48L21vdmVyPjwvbWF0aD4vlbZ6AAAAAElFTkSuQmCC)
II. The measure of ![angle A B C](data:image/png;base64,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)
Maths-General
Maths-
Line
is defined by
. Line
is parallel to line m in the xy - plane and passes through the point (4, - 3). Which equation defines line p ?
Line
is defined by
. Line
is parallel to line m in the xy - plane and passes through the point (4, - 3). Which equation defines line p ?
Maths-General
Maths-
An analyst estimates that the cost of each of the paperback books will increase $0.50 each year after 2016. Which of the following models the cost
, in dollars, of each of the paperback books t years after 2016 ?
![](https://mycourses.turito.com/tokenpluginfile.php/c161933dbfaab094c54655ab71e9b8f0/1/question/questiontext/719594/1/1232790/Picture23.png)
A certain book is available from a publishing company in both hardcover and paperback. The table shows the revenue and cost in 2016 for each of the hardcover and paperback books produced by the company.
An analyst estimates that the cost of each of the paperback books will increase $0.50 each year after 2016. Which of the following models the cost
, in dollars, of each of the paperback books t years after 2016 ?
![](https://mycourses.turito.com/tokenpluginfile.php/c161933dbfaab094c54655ab71e9b8f0/1/question/questiontext/719594/1/1232790/Picture23.png)
A certain book is available from a publishing company in both hardcover and paperback. The table shows the revenue and cost in 2016 for each of the hardcover and paperback books produced by the company.
Maths-General
Maths-
In 2016 the total cost for 200 of the books that were sold was between $2,200 and $2,400. Which of the following could be the number of hardcover books that were sold?
![](https://mycourses.turito.com/tokenpluginfile.php/c161933dbfaab094c54655ab71e9b8f0/1/question/questiontext/719593/1/1232789/Picture22.png)
A certain book is available from a publishing company in both hardcover and paperback. The table shows the revenue and cost in 2016 for each of the hardcover and paperback books produced by the company.
In 2016 the total cost for 200 of the books that were sold was between $2,200 and $2,400. Which of the following could be the number of hardcover books that were sold?
![](https://mycourses.turito.com/tokenpluginfile.php/c161933dbfaab094c54655ab71e9b8f0/1/question/questiontext/719593/1/1232789/Picture22.png)
A certain book is available from a publishing company in both hardcover and paperback. The table shows the revenue and cost in 2016 for each of the hardcover and paperback books produced by the company.
Maths-General
Maths-
![](https://mycourses.turito.com/tokenpluginfile.php/c161933dbfaab094c54655ab71e9b8f0/1/question/questiontext/719592/1/1232788/Picture21.png)
The table gives some values of possible lengths x, in miles, of a monorail system, and their corresponding costs to build f(x), in millions of dollars. Which of the following equations models this relationship?
![](https://mycourses.turito.com/tokenpluginfile.php/c161933dbfaab094c54655ab71e9b8f0/1/question/questiontext/719592/1/1232788/Picture21.png)
The table gives some values of possible lengths x, in miles, of a monorail system, and their corresponding costs to build f(x), in millions of dollars. Which of the following equations models this relationship?
Maths-General
Maths-
![x to the power of 2 end exponent minus 2 x plus c equals 0](data:image/png;base64,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)
In the given equation,
is a constant. If the equation has exactly one solution, what is the value of c ?
![x to the power of 2 end exponent minus 2 x plus c equals 0](data:image/png;base64,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)
In the given equation,
is a constant. If the equation has exactly one solution, what is the value of c ?
Maths-General
Maths-
The 2017 Wyoming state senate had 30 elected members consisting of Democrats and Republicans. Let d represent the number of Democrats who vote yes for a bill, and let r represent the number of Republicans who vote yes for a bill. For a bill to pass, more than half of the 30 senators must vote yes. Which of the following inequalities represents all possible values of d and r for a bill to pass?
The 2017 Wyoming state senate had 30 elected members consisting of Democrats and Republicans. Let d represent the number of Democrats who vote yes for a bill, and let r represent the number of Republicans who vote yes for a bill. For a bill to pass, more than half of the 30 senators must vote yes. Which of the following inequalities represents all possible values of d and r for a bill to pass?
Maths-General
Maths-
For the linear function f, the graph of y = f(x) in the xy -plane passes through the points (0, 2) and (2, 6). Which equation defines f ?
For the linear function f, the graph of y = f(x) in the xy -plane passes through the points (0, 2) and (2, 6). Which equation defines f ?
Maths-General