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Given the circle equation \((x-h)^2 + (y-k)^2 = r^2\), identify the center and radius.
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Center is (2,1) and radius is 3.
What is the y-intercept and slope of a line in slope-intercept form?
The y-intercept is -3 and the slope is \( \frac{3}{4} \).
How would you solve for R values in an integer inequality and calculate the sum of the largest and smallest?
Solve the inequality, then identify and sum the relevant integers within the constraints.
What steps would you use to find the area of a 45-degree triangle given base and height?
Use the formula \( \text{Area} = \frac{1}{2} \times \text{base} \times \text{height} \). Calculate consistently with the Pythagorean Theorem if needed.
How do you calculate the roots of \( 3x^2 - 5x + 8 = 36 \) using factoring?
Subtract 36 to get \( 3x^2 - 5x - 28 = 0 \), then factor and find the roots \( x = 4 \) and \( x = -\frac{7}{3} \).
How do you simplify the expression \( y^4^5 \times y^{-8} \)?
By realizing it's \( \frac{1}{y^4} \).
How do you calculate the area of a shaded region using circle and triangle areas?
Subtract the area of the triangle from the circle's area.
What is the slope between points \((1/2, -2/3)\) and \((-2/5, 1/4)\)?
-\(\frac{55}{54}\)
What is the new average with an additional score of 99?
The new average is 87.
Given \( \sin(z) = -\frac{7}{25} \) and \( \tan(z) < 0 \), what quadrant is \( z \) in?
Quadrant 4
Explain the process for calculating cost balances based on apples and bananas.
Use simultaneous equations to find the cost per item.
What is the sum of the solutions for the equation \( x^2 + 4x - 45 = 0 \)?
-4
How do you evaluate the trigonometric identity simplification?
Use appropriate trigonometric identities for simplification.
If \( f(x) = 5x^3 - 2x + 7 \), what is \( f(2) \)?
43
How do you solve \( x + \frac{6}{x} = 5 \) for x?
Find values of x that satisfy the equation, like 2 and 3.
How do you solve the system \( 3x - 4y = 3 \) and \( 2x + 3y = 19 \)?
Solve to find \( x = 5 \) and \( y = 3 \); then substitute to find expressions.
How do you isolate x in the equation \( \frac{3x}{4} + 5 = 11 \)?
Subtract 5 from both sides then multiply by 4 and divide by 3.
What is the perimeter of a square with an area of 36?
24
How do you calculate the average score of five tests: 86, 93, 79, 82, 90?
Add the scores and divide by 5, for a total of 86.
What approach is used for solving a trigonometric expression involving conjugates?
Multiply by a conjugate to simplify the expression to a cosine form.
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