Ann runs at a pace of 6 miles per hour. How many miles can she run in 30 minutes?

Ann runs at a pace of 6 miles per hour. How many miles can she run in 30 minutes?

Solution:

This is a proportion:

Solve the inequality and express the solution in interval form.

Solution:

For convenience we'll compare an appropriate expression to 0 instead of 1. Then we can find x-values of interest to determine where to shade (i.e. where the inequality is true).

 





















This graph shows our solution another way. Notice that we graph both sides of the inequality. Then we can actually see when the left side is greater...

Find the exact value of the remaining trigonometric functions if cosA= -3/5 and sinA < 0

Find the 11th term of the sequence 1,2,4,8,…

These terms are all powers of 2, so we can write:

Hyperbolic functions: find the inverse of arcsinh(x)

Factor 7x2-16x+4

Volume of similar cylinders

The cylinders shown are similar.

What is the volume of the larger cylinder?

Solution:

Evaluate the functions

Given: f(x) = x³ - 3x and g(x) = x² - 8. What is f(10) - g(10)?


Solution:

Find the inverse of the matrix (if there is one) algebraically.

Find the inverse of the matrix (if there is one) algebraically.  If there isn’t an inverse, say that the matrix is singular

[3 1 2]

[3 2 -1]

[1 1 1]

Two chords intersect with the measures shown in the drawing.

What is the value of x?

Solution:

we know that the product of the lengths of one intersecting chord must be equal to the product of the lengths of the other, so...

For what value of x is if the lines are parallel in this figure?

Solution:

We know that x and 40.03 are supplementary, so x+40.03=180. Therefore x=139.97 degrees

What is the solution set for the given equation? 3|x + 4| = 18

Let's try a different approach this time...

3|x + 4| = 18

has the same solution as

|x + 4| = 6


We look for the number(s) that can add/subtract to obtain 6. We can see that x=2 will work. No other positive number will work, however if we consider negative numbers then -10 seems possible. In fact is does work because |-10+4| = |-6| = 6. So x=-10.

What is the number of turning points in the graph of the function of x defined below?

y = 2x² + 5x - 7

Solution:

The polynomial y has degree n=2 so the maximum number of turns it can have is n-1 = 2-1 = 1. (In fact we know that our polynomial is a quadratic and it opens upwards so this is another way to know it only has one turn).

Find x.

What is the value of x?

Solution:


TV is a diameter, and SU is perpendicular to TV. This means that x=8

The polynomial equation x(x2+4)(x2-x-6)=0 has how many real roots?

Solution:

x2+4 contributes complex zeros. This means that the factors x and x2-x-6 contribute real zeros. Therefore the polynomial has 3 real zeros

What are the coordinates of the vertex of the graph of the function -2(x - 1)2 = y + 5?

so the vertex is (1,5)

If f(x) = 5x2 - 7, what is f(-3)?

Given quadrilateral KLMN, what is the value of x?

Given quadrilateral KLMN, what is the value of x?


Solution:

3x+x+25+80+95=360 (why?)

4x+200=360

4x=160

x=40

if tan(theta) = -3 and cos(theta) < 0, then tan(theta/2) = ?

so

so

 (we take the negative case because cosine is negative for this example)
now

Therefore...


which simplifies to

Evaluate the quotient (5 + i)/(1 + 3i)