Practice Midterm

9 - Solve the inequality. Write your solution in interval notation. |1-2x|-4<-1

(-1,2)

10(B) - Given the general equation of the circle, do the following. x^2+y^2+4x+2y-20=0. What are the coordinates of the circle's center?

(-2,-1)

19 - Solve the inequality x^2+8x>0 using algebraic methods, not by graphing. Show your work. Write your solution in interval notation.

(-∞,-8)U(0,∞)

1(A) - 4x^2+12x+9

(2x+3)^2

1(B) - 8x^3-27

(2x-3)(4x^2+6x+9)

1(C) - 3x^2+6x-5x-10

(3x-5)(x+2)

10(A) - Given the general equation of the circle, do the following. x^2+y^2+4x+2y-20=0. Use completing the square to put the equation of the circle in standard form.

(x+2)^2+(y+1)^2=25

12 - Find and simplify the difference quotient of the function f(x)=x^2+2x-4. The difference quotient is given by (f(x+h)-f(x))/(h)

2x+h+2

8 - A 20=pound bag of Economy brand cement mix contains 25% cement and 75% sand. How much pure cement must be added to produced a cement mix that is 40% cement? Write your answer in a complete sentence using appropriate units.

5lb of pure cement should be added to the Economy mix.

18(C) - Given the quadratic equation y=2^x-8x+3, do the following. Write the domain and range of the quadratic function in interval notation. All values must be exact.

Domain: (-∞,∞) Range: [-5,∞)

17 - Determine the domain and range of the function h(x)=√x+1. Write your answers in interval notation.

Domain: [-1,∞) Range: [0,∞)

13 - What is the rule used to determine if a graph represents a function?

If a vertical line touches the graph twice while going straight up it does not represent a function.

14 - How can you tell if a graph is odd, even, or neither?

If the graph is symmetrical about the y-axis it is even.

2(B) - A circular swimming pool that is 20 feet in diameter is enclosed by a circular wooden deck that is 3 feet wide. How much fence is required to enclose the deck? Answer in a complete sentence with units.

It will require 26πft of fence to enclose the deck.

3(B) - Given the points (4,-3) and (11,9), do the following. Determine the exact midpoint of the line segment joining the points. Write your answer with integers, fractions, and/or simplified radicals.

M(15/2 , 3)

2(A) - A circular swimming pool that is 20 feet in diameter is enclosed by a circular wooden deck that is 3 feet wide. What is the area of the deck? Answer in a complete sentence with units.

The area of the deck is 69π ft^2.

11 - The maximum safe load for a horizontal rectangular beam varies jointly with the width of the beam and the square of the thickness of the beam and inversely with its length. If an 8-foot beam with support up to 750 pound when the beam is 4 inches wide and 2 inches thick, what is the maximum safe load in a similar beam 10 feet long, 6 inches wide, and 2 inches thick?

The maxim safe load of the 10ft beam is 900lb.

20 - A sign in the shape of a right triangle has one leg that is 3 inches longer than the other leg. The longest side in the triangle is 15 inches. What is the perimeter of the triangle? Write your answer in a complete sentence with appropriate units.

The perimeter is 36 inches.

18(B) - Given the quadratic equation y=2^x-8x+3, do the following. Write the coordinates of the vertex, the y-intercept, and the x-intercept. Label them. All values must be exact.

Vertex: (2,-5) Y-Int: (0,3) X-Int: (2±(√10/2) , 0)

10(C) - Given the general equation of the circle, do the following. x^2+y^2+4x+2y-20=0. What is the radius of the circle?

r=5

15 - Sketch the graph f(x)={x^2+2, x<0 ; {x^2-4, x≥0. Label the x and y- intercepts with their coordinates on the graph. Label one additional ordered pair on each piece of the graph.

this is dumb it wont let me put picture :(

5 - Solve the equation in the complex number system. x^4+3x^2-4=0

x= ±2i ; x=±1

6 - Solve the equation in the real number system. Write exact solutions as integers, fractions, or simplified radicals. √2x+3-√x+1=1

x=3 ; x=-1

7 - Solve the equation (x-1)^2/3=16.

x=65 ; x=-63

4(A) - Given the points (5,9) and (10,29), do the following. Write the point-slope form of the line through the given pair of points. Coefficients and constant terms must be exact.

y-9=4(x-5) or y-29=4(x-10)

16(B) - Given the function f(x)=x^2, do each of the following. Write the equation of the graph if f is shifted left six units.

y= (x+6)^2

16(C) - Given the function f(x)=x^2, do each of the following. Write the equation of the graph if f is reflected across the x-axis and vertically stretched by a factor of 5.

y= -5x^2

18(A) - Given the quadratic equation y=2^x-8x+3, do the following. Write the equation in the form y=a(x+h)^2+k. All coefficients and constant terms must be exact.

y= 2(x-2)^2-5

16(D) - Given the function f(x)=x^2, do each of the following. Write the equation of the graph if f is horizontally stretched by a factor of 2.

y=(x/2)^2

4(B) - Given the points (5,9) and (10,29), do the following. Write the slope intercept form of the line through the given pair of points. Coefficients and constant terms must be exact.

y=4x-11

16(A) - Given the function f(x)=x^2, do each of the following. Write the equation of the graph if f is shifted up three units.

y=x^2+3

3(A) - Given the points (4,-3) and (11,9), do the following. Determine the exact length of the line segment connecting the points. Write your answer with integers, fractions, and/or simplified radicals.

√193