semester 2 - algebraic reasoning

The slope-intercept form of a linear equation is y = mx + b, where x and y are coordinates of an ordered pair, m is the slope of the line, and b is where the line crosses the y-axis.Which is an equivalent equation solved for the slope, m?

m = V-b/x

Which equation is represented by Ms. Wilson's model? n2 + 3n + 40 = (n - 8)(n - 5) n2 + 13n + 40 = (n + 8)(n + 5)n2 + 40n + 13 = (n + 8)(n + 5)n2 + 40n + 3 = (n - 8)(n - 5)

n2 + 13n + 40 = (n + 8)(n + 5)

The circumference of a circle can be found using the formula C = 2πr.Which is an equivalent equation solved for r?

r = C/2π

The formula for the circumference of a circle is C = 2πr, where r is the radius and C is the circumference. The equation solved for r is r =c/π2 .Find the radius of a circle that has a circumference of 16.

r=8

A linear function and its inverse are given.y=4x-3 and y=1/4xWhich tables could be used to verify that the functions are inverses of each other? Select two options.

x -23y -5 and x -5y -23

Consider the function.f(x)= 2 1/2-3 1/3x What is the x-intercept of f-1(x)?

(2 1/2, 0)

Which expression is equivalent to n2 + 26n + 88 for all values of n?(n + 8)(n + 11)(n + 4)(n + 22)(n + 4)(n + 24)(n + 8)(n + 18)

(n + 4)(n + 22)

What is the factored form of the polynomial? x2 + 9x +20(x − 4)(x − 5)(x − 2)(x − 10)(x + 4)(x + 5)(x + 2)(x + 10)

(x + 4)(x + 5)

What is the factored form of the polynomial? x2 − 12x + 27?(x + 4)(x + 3)(x − 4)(x + 3)(x + 9)(x + 3)(x − 9)(x − 3)

(x − 9)(x − 3)

The binomial (y − 2) is a factor of y2 − 10y + 16. What is the other factor?(y − 5)(y + 5)(y − 8)(y + 8)

(y − 8)

Consider the function.f(x)=(3/4)x+12 What is the y-intercept of f-1(x)?

-16

What is the difference of the polynomials? (-2x3y2 + 4x2y3 - 3xy4) - (6x4y - 5x2y3 - y5)

-6x4y - 2x3y2 + 9x2y3 - 3xy4 + y5

The volume, V, of a rectangular prism is determined using the formula , where l is the length, w is the width, and h is the height of the prism. Carltren solves for w and writes the equivalent equation w = V/lh.Using this formula, what is the width of a rectangular prism that has a volume of 138.24 cubic inches, a height of 9.6 inches, and a length of 3.2 inches?

4.5 inches

Which expression represents the total perimeter of her sandwich, and if x = 1.2, what is the approximate length of the crust?

8x2 + 34; 45.52 centimeters

What is the additive inverse of the polynomial -9xy2 + 6x2y - 5x3?

9xy2 - 6x2y + 5x3

The temperature measured in Kelvin (K) is the temperature measured in Celsius (C) increased by 273.15. This can be modeled by the equation K = C + 273.15.When solved for C, the equation is

C = K - 273.15

Quadratic function f(x)=x^2

Domain all real numbers, range is y greater than or equal to zero

Exponential function

Domain all reals, range y greater than 0

Variable Matrix

Matrices that contain variables in their sets and equations

Equal Matrices

Matrices that have the same dimensions and are equal to each other.

Constant Matrix

Matrix that remains the same. Neither the dimensions nor the numbers change.

Consider this function.f(x) = |x - 4| + 6 If the domain is restricted to the portion of the graph with a positive slope, how are the domain and range of the function and its inverse related?

Since the range of the original function is limited to y 6, the domain of the inverse function is x ≥ 6.

What is the domain of a function?

The complete set of possible values of the independent variable. The set of all possible x-values which will make the function "work", and will output real y values

Consider the function and its inverse.f(x)=x^2 +4 and f^-1(x)=-√x-4 When comparing the functions using the equations, which conclusion can be made?

The domain of f(x) is restricted to x ≤ 0, and the domain of f-1(x) is restricted to x ≥ 4.

What is the range of a function?

The range of a function is the complete set of all possible resulting values of the dependent variable (y, usually), after we have substituted the domain.The range is the resulting y-values we get after substituting all the possible x-values.

Consider the tables that represent ordered pairs corresponding to a function and its inverse.When comparing the functions using the values in the table, which conclusion can be made?

The range of f(x) includes values such that y ≥ 1, so the domain of f-1(x) includes values such that x ≥ 1.

Coefficient Matrix

The variables in a set of matrices.

Zero Matrix

When all factors to a matrix or matrix equation are equal to zero.

The sum of two polynomials is 8d5 - 3c3d2 + 5c2d3 - 4cd4 + 9. If one addend is 2d5 - c3d2 + 8cd4 + 1, what is the other addend?

X 6d5 - 2c3d2 - 3c2d3 - 4cd4 + 8

What is the sum of the polynomials?(7x3 - 4x2) + (2x3 - 4x2)

X 9x3