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Questions and Answers
What is the value of g(12) for the function g defined by g(x) = 3(x + 8)?
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?
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?
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)?
Which expression is equivalent to (x + 7)(x² - 3x + 2)?
What does the equation C = 7/5 p indicate about the cost of pears?
What does the equation C = 7/5 p indicate about the cost of pears?
Which of the following is the graph of a function where Y = f(x)?
Which of the following is the graph of a function where Y = f(x)?
Which expression is equivalent to 3x² + 6x - 24?
Which expression is equivalent to 3x² + 6x - 24?
What equation gives the expected number of bacteria after x days for an initial population of 500? The population doubles every 4 hours.
What equation gives the expected number of bacteria after x days for an initial population of 500? The population doubles every 4 hours.
Which value of x satisfies the equation x² + 5x - 9 = 5?
Which value of x satisfies the equation x² + 5x - 9 = 5?
Which equation could define f(x) for the graph of y = f(x)?
Which equation could define f(x) for the graph of y = f(x)?
How would you best describe the range of y = -2x⁴ + 7?
How would you best describe the range of y = -2x⁴ + 7?
If cos A = 5/8 in right triangle ABC, what is the value of cos B?
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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