# Math SAT Sheet

posted by .

1.) Find the domain and range for:

f(x)= 4x-20/ the square root of 36-x^2

2.) Solve the equation:

log6 (x-11) + log6 (x-6) = 2

3.) Solve the inequality:

x^2 - 2x - 3 is greater than 0

• Math SAT Sheet -

1. remember that the denominator √(36 - x^2) cannot be zero or negative,
so shouldn't -6 < x < +6 ??

2. log6 [(x-11)(x-6)] = 2
(x-11)(x-6) = 6^2
x^2 - 17x + 66 = 36
x^2 - 17x + 30 = 0
(x-15)(x-2) = 0
x = 15 or x = 2

A lot of students would stop here and think they have the right answer, but remember that we can only take logs of positive numbers, so looking at our original we can see clearly that x > 11

so x = 15 is the only answer.

• Math SAT Sheet -

3. x^2 - 2x - 3 > 0
(x-3)(x+1) > 0
"critical" values are x = 3 and x = -1

try a number < -1, say x = -5
statement: (-8)(-4) > 0 ? YES
try a number between -1 and 3, say x = 0
statement: (-3)(1) > 0 False!
try a number > 3, say x = 5
statement: (2)(6)>0 YES

so x < -1 OR x > 3, x any real number.

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The content structure of the provided text is a set of math problems and their solutions, specifically dealing with functions, logarithmic equations, and inequalities.
multiple_questions_with_answers
Given a text passage, determine:
    1. If it contains a mathematical question (including word problems or calculations)
    2. If an answer to that mathematical question is provided in the text

First, describe the content structure you found in 1-2 sentences.

Then provide your analysis in the following format:
TYPE: <one of the following values>
- NO_QUESTION
- SINGLE_QUESTION
- SINGLE_QUESTION_WITH_ANSWER
- MULTIPLE_QUESTIONS
- MULTIPLE_QUESTIONS_WITH_ANSWERS
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# Math SAT Sheet

posted by .

1.) Find the domain and range for:

f(x)= 4x-20/ the square root of 36-x^2

2.) Solve the equation:

log6 (x-11) + log6 (x-6) = 2

3.) Solve the inequality:

x^2 - 2x - 3 is greater than 0

• Math SAT Sheet -

1. remember that the denominator √(36 - x^2) cannot be zero or negative,
so shouldn't -6 < x < +6 ??

2. log6 [(x-11)(x-6)] = 2
(x-11)(x-6) = 6^2
x^2 - 17x + 66 = 36
x^2 - 17x + 30 = 0
(x-15)(x-2) = 0
x = 15 or x = 2

A lot of students would stop here and think they have the right answer, but remember that we can only take logs of positive numbers, so looking at our original we can see clearly that x > 11

so x = 15 is the only answer.

• Math SAT Sheet -

3. x^2 - 2x - 3 > 0
(x-3)(x+1) > 0
"critical" values are x = 3 and x = -1

try a number < -1, say x = -5
statement: (-8)(-4) > 0 ? YES
try a number between -1 and 3, say x = 0
statement: (-3)(1) > 0 False!
try a number > 3, say x = 5
statement: (2)(6)>0 YES

so x < -1 OR x > 3, x any real number.

## Similar Questions

1. ### Pre Algebra

Please help me with some problems. Thank you! Solve the equation by square root property. 3. 2x^2 = 26 I don't understand how to solve this problem. Solve the equation using the quadratic formula. 7. 7x^2=-8x -2 This is what I got …
2. ### Algebra 2

Can someone please explain to me how to solve logarithmic equations?
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1. If square root of 3x-11 +10 = 17, find the value of 10 x . I don't know how to solve with square roots. I subtracted 10 from both sides, so I'm left with square root of 3x-11 = 7...How do I solve for x?
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The problem I have to solve is log with base 2 ^6 multiply by log base 6 ^ 8. I use the change of base formula and got log6/log2 * log8/log6 Which become log6/log2 * log2()^3/ log 6 I'm stuck here thanks.
10. ### Math

Solve: Log5(x-2) + log8(x-4)= log6(x-1)

More Similar Questions

Post a New Question
user
The content structure of the provided text is a set of math problems and their solutions, specifically dealing with functions, logarithmic equations, and inequalities.

TYPE: MULTIPLE_QUESTIONS_WITH_ANSWERS