Chp 4 & 12 Exponents
Use the hint below to solve pg. 675 #11
(a^m)^n = a^(mn)
6(3)= 18
Formula for the area of a trapezoid
A = average of the two base lines * height
A=1/2 (b + b)h
The measure of one complementary angle is 40. What is the other complementary angle's measurement?
50 degrees
what is the formula for slope-intercept form?
y=mx+b
Bonus: Explain what m & b represent.
The slope of a vertical line is always
Undefined
Multiply (x +3) (4x - 5) (write in expanded form)
4x^2 -5x +12x - 15
4x^2 +7x -15
Find the area of a circle with a radius of 5 meters in terms of pi.
A=pir^2=pi5^2=25pi m^2
The measure of one vertical angle is 6x. The other vertical angle is (2x +36). Solve for x and the measure of these vertical angles. (See pg 712 #27 for a drawing)
x =9, 54 degrees 6x = 2x +36
4x = 36, x = 9
This coordinate notation (x,y) -> (x +a, y +b) gives us the image of what kind of transformation?
Translation
What do we add to the x's and the y's to slide the shape into a new position (new image)
The slope of a horizontal line is
always 0. The line goes neither up nor down, neither positive nor negative.
(5^2)^-2
Simplify the expression using positive exponents
(5^2)^-2= 5^[2(-2)] = 5^-4=1/5^4
What is the formula for the area of a circle
A=pir^2
Find the unknown measurement of the trapezoid on page 525 problem 23.
Area = average of both bases * height
1800= 1/2(50 +b)48
1800= (48)(1/2)(50+b) = 24 (50+b) =1200 + 24b
1800-1200 = 24b
600 = 24b, (600/24) = b =25
What is the coordinate notation to reflect a shape or line across the x-axis?
(x, y) --> (x, -y)
The x-coordinate stays the same and the y is the opposite (multiply by a negative one)
What is the formula for finding the slope of a line given two points on the line?
slope = m = rise/run
m=(Delta y)/(Delta x) = (y-y)/(x-x)
Simplify. (from McD chp 12.5)
(n/-7)^2
(n/-7)^2
=(n^2)/(-7)^2
(n^2)/49
Find the volume of a prism with triangular bases with b 4 and height of 3, and height of the prism is 10.
V=Base area * height
V= 1/2 (4*3) * 10
A transversal cuts across two lines. The value of two corresponding angles is 30 degrees and 6x degrees. What must x be in order for the lines to be parallel? See pg. 719 #17
x=5. Parallel lines must have the corresponding angles with the same values so 30=6x. x = 5
If you have a triangle and this is done to it, what type of transformation has happened?
(x,y) --> (3x, 3y)
Dilation. It has been enlarged 3 times. So the scale factor is 3.
Find the x and y-intercepts of this line:
4x + 3y=12
Write the original equation 4x + 3y=12 and then substitute in 0 for y and solve for x and do the same for x.
4x + 3(0)=12
4x =12, x = 3
4(0) + 3y=12, y =4
Simplify (b/c)^3
chp 12.5
(b/c)^3
=b^3/c^3
Formula for volume of a cylinder
V=Base Area * height
V = pir^2h
Find the volume of the cylinder with these dimensions: radius of base is 8, height of cylinder is 2. Leave in terms of Pi.
V = Bh
V=pir^2h = pi8^2(2)=128 pi
Write the point slope formula and explain when we use it.
y - y1 = m(x - x1) Given two points on a line, can write an equation of the line. First calculate slope, then plug in x & y coordinates.
Write the equation of line which is perpendicular to line y = -5x +1 and which passes through the point (0, -9)
Slope of a perpendicular line is the negative reciprocal of the line to which it is perpendicular. (0,-9) means that the y-intercept is -9
y = -5x +1
y = (1/5)x + -9