Questions and Answers
What is the value of g(12) for the function g defined by g(x) = 3(x + 8)?
60
What is an equation of the line that passes through the point (0, 0) and is perpendicular to the line shown?
y = 5/4x
What is the surface area of a right rectangular prism with length 4 cm, width 9 cm, and height 3 cm?
150 cm²
Which expression is equivalent to (x + 7)(x² - 3x + 2)?
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What does the equation C = 7/5 p indicate about the cost of pears?
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Which of the following is the graph of a function where Y = f(x)?
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Which expression is equivalent to 3x² + 6x - 24?
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What equation gives the expected number of bacteria after x days for an initial population of 500? The population doubles every 4 hours.
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Which value of x satisfies the equation x² + 5x - 9 = 5?
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Which equation could define f(x) for the graph of y = f(x)?
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How would you best describe the range of y = -2x⁴ + 7?
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If cos A = 5/8 in right triangle ABC, what is the value of cos B?
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Study Notes
Functions and Equations
- Function ( g ) is defined by ( g(x) = 3(x + 8) ), producing ( g(12) = 60 ).
- Equation of a line through point (0,0) and perpendicular to a given line is ( y = \frac{5}{4}x ).
Geometry and Surface Area
- The surface area of a right rectangular prism (length = 4 cm, width = 9 cm, height = 3 cm) is calculated as ( 2(lw + lh + wh) ), yielding an area of ( 150 , \text{cm}^2 ).
Algebraic Expressions
- The expression ( (x + 7)(x^2 - 3x + 2) ) simplifies to ( x^3 + 4x^2 - 19x + 14 ).
- The expression ( 3x^2 + 6x - 24 ) can be factored as ( 3(x - 2)(x + 4) ).
Cost Comparisons
- For pears with cost ( C = \frac{7}{5}p ), apples cost approximately $0.07 less per pound than pears.
Graphing Functions
- The graph that represents a function ( Y = f(x) ) is labeled as option C.
Exponential Growth
- A population of 500 bacteria doubles every 4 hours, described by the equation ( n = 500(2)^{6x} ) for ( x ) in days.
Solving Equations
- The solution to the equation ( x^2 + 5x - 9 = 5 ) is ( x = -7 ).
Quadratic Functions
- The quadratic function ( f(x) = x^2 - 2x - 8 ) could represent the given graph of ( y = f(x) ).
Trigonometry in Right Triangles
- In triangle ABC with angle C as a right angle, if ( \cos A = \frac{5}{8} ), then ( \cos B = \frac{39}{8} ).
Function Range Analysis
- The range of the function ( y = -2x^4 + 7 ) indicates ( y \leq 7 ), suggesting a maximum point.
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