Prove that V is a vector space. V=T(m, n), the set of linear transformations T : R^{m} rightarrow R^{n}, together with the usual addition and scalar multiplication of functions.

Given that 1${\displaystyle {\log }_a\left(3\right)\approx 0.61}$  and l${\displaystyle {\log }_a\left(5\right)\approx 0.9}$ , evaluate each of the following. Hint: use the properties of logarithms to rewrite the given logarithm in terms of the the logarithms of 3 and 5.

$C=\frac{5}{9}(F-32)$

The equation above shows how temperature F, measured in degrees Fahrenheit, relates to a temperature C, measured in degrees Celsius. Based on the equation, which of the following must be true?

1. A temperature increase of 1 degree Fahrenheit is equivalent to a temperature increase of  $\frac{5}{9}$ degree Celsius.

2. A temperature increase of 1 degree Celsius is equivalent to a temperature increase of 1.8 degrees Fahrenheit.

3. A temperature increase of $\frac{5}{9}$ degree Fahrenheit is equivalent to a temperature increase of 1 degree Celsius.

A) I only
B) II only
C) III only
D) I and II only

One of the two tables below shows data that can best be modeled by a linear function, and the other shows data that can best be modeled by a quadratic function. Identify which table shows the linear data and which table shows the quadratic data, and find a formula for each model.

One of the two tables below shows data that can best be modeled by a linear function, and the other shows data that can best be modeled by a quadratic function. Identify which table shows the linear data and which table shows the quadratic data, and find a formula for each model.

if -x^2+y^2=4-4x^2y then find the equations of all tangent lines to the curve when y=-5

Find the formula for an exponential function that passes through (0,6) and (2,750)

Use the given conditions to write an equation for the line in point-slope form and general form.  Passing through (8,-4) and perpendicular to the line whose equation is 

x-6y-5=0

Use the given conditions to write an equation for the line in point-slope form and general form. Passing through (8,-4) and perpendicular to the line whose equation is x-6y-5=0

A polynomial of a degree 5 had rational coefficients and the zeros  $\frac{4}{3},8i$, and $3-5\sqrt{2}$

What are the missing zeros?

Let R be the relation on the set {0, 1, 2, 3} containing the ordered pairs (0, 1),(1, 1),(1, 2),(2, 0),(2, 2),(3, 0). Find reflexive, symmetric and transitive closure of R.

A baseball team plays in a stadium that holds 70,000 spectators. With the ticket price at $11, the average attendance has been 29,000. When the price dropped to $10, the average attendance rose to 35,000. Assuming the demand function, p(x)${\displaystyle p\left(x\right)}$, is linear, find p(x)${\displaystyle p\left(x\right)}$, where x${\displaystyle x}$ is the number of the spectators. Write p(x)${\displaystyle p\left(x\right)}$ in slope-intercept form.

To break even in a manufacturing business, income or revenue R must equal the cost of production the letter C. The cost the letter C to produce X skateboards is the letter C = 108+21X. The skateboards are sold wholesale for $25 each, so revenue the letter R is given by the letter R = 25 X. Find how many skateboards the manufacture needs to produce and sell to break even. (Hint: set the cost expression equal to the revenue expression and solve for X.)