1,054,848 c. 1,405,888 d. 1,045,828 5. Evaluate: 12xy, when x = 8 and y = 11. a. 31 b. 228 c. 1056 d. 188 6. Write
There are two types of special right triangles: 45-45-90 and 30-60-90. The legs on a 45-45-90 triangle are 1 and 1 and the hypotenuse is the square root of 2. The legs on a 30-60-90 triangle are 1 and the square root of 3 and the hypotenuse is 2. If you were to take the three trigonometric functions of either 45 degree angle, you would get the (square root of 2)/2 for both cosine (x) and sine (y) and 1 for tangent (y/x). If you were to take the three trigonometric functions of the 30 degree angle, you would get the (square root of 3)/2 for cosine, ½ for sine and the (square root of 3)/3 for tangent.
46. Write the function f(x) = 2(x – 2)2 – 5 in standard form. 47. Find the zeros of the following quadratic functions: a) f(x) = x2 + 10x + 21 b) f(x) = (x – 1)2 + 7 c) f(x) = x2 - 4x + 9 48. A popular mixture of potpourri includes pine needles and lavender.
8 5 7 8 (a) 7 7 8 6 6 11 7 5 5 7 9 9 6 7 6 7 Construct a frequency table from the above data and add a cumulative frequency column. For this data, find: (i) the median; (ii) the lower quartile; (iii) the upper quartile. 2 (b) 1 1 1 2 (c) Construct a boxplot for this data. [Turn over [ X100/201] Page three Marks 3. The diagram below represents a sphere.
A circumscribed circle touches each vertex of the triangle. There are also things called the incenter and the circumcenter. The incenter is the center of the inscribed circle and the circumcenter is the center of a circumscribed circle. The relation between a circle and a triangle is that
The radius of a circle is (7x + 3) cm. Write an expression to represent the area of the circle in simplified form. 23. A rectangle has a length of (x + 2) in. and a width of (2x + 3) in.
Given is the augmented matrix of a system of equations: 1 5 6 2 7 1 3 5 1 5 7 13 Write the new form of the augmented matrix after the following row operations. R1 r1 r3 , R2 r2 7r3 6. Four times the number of white marbles exceeded 9 times the number of red marbles by 10. The ratio of blue marbles to red marbles was 3 to 1. There is a total of 65 marbles of all 3 colors.
M<FJG=90, m<GJH=90, m<HJE= 90, m<EJF=90 -The diagonals bisect the angles. m<EFJ= m<JFG, m<FGJ= m<JGH, m<GHJ= m<GHJ= m<JHE, m<HEJ= m<JEF j j E F H G 1 2 M 3 4 5 6 N 7 8 T Transversal The intersections of lines m,n, and t create eight different angles. Line t is called the transversal. You can think of the eight angles as being split into two different groups of four, one group around line m and the other group around line n. Those angles that “match up”---see the like- colored numbers--- are corresponding angles. The corresponding angles in this figure are the angles pairs <1 and <5, <2 and <6, <3 and <7, <4 and <8 1 2 M 3
8. A Graph was created using the second table with ‘X’ values in the y-axis and ‘f’ values in the x-axis. Results Table 1.1: Raw Results Weight (grams) | Trial | Values of f (in Newtons [N]) | Value of X (in centimetres [cm]) | 50 | 123 | 0.5 0.5 0.5 | 11 1 | 100 | 123 | 1 0.8 1 | 2 2.1 2 | 150 | 123 | 1.5 1.45 1.5 | 3 3.1 3.1 | 200 | 123 | 2 2 1.9 | 4 4.1 3.9 | 250 | 123 | 2.4 2.4 2.3 | 54.8 5 | Table 1.2: Averaged Results Weight (in grams) | | Value of X (in centimetres [cm]) | 50 | 0.5 | 1 | 100 | 0.93 | 2.03 | 150 | 1.48 | 3.06 | 200 | 1.96 | 4 | 250 | 2.3 | 4.93 | Distance Stretched (X) in Centimetres (cm) Distance Stretched (X) in Centimetres (cm) Force Applied (f) in Newtons (N) Force Applied (f) in Newtons (N) Analysis of Results The above results
e) Set the left side of the equation equal to the positive square root of the number on the right side and solve for x. f) Set the left side of the equation equal to the negative square root of the number on the right side of the equation and solve for x. A) x² - 2x – 13 = 0 x² - 2x = 13 4x² - 8x = 52 4x² - 8x + 4 = 56 (2x – 2) ± 56 2x – 2 = 56 2x – 2 = 56 2x = 56+2 2x = 56+2 x = 56+2/2 x = 56+2/2 Project 2 C) x² + 12x – 64 = 0 -x² + 12x = 64 4x² + 48x = 256 4x² + 48 + 144 = 400 2x + 12 = ±20 2x +12 = 20 2x + 12 = -20 2x = 8 2x = -32 x = 4 x = -16 The method selected was the method shown in our text. I do not think I will ever have a chance to use this knowledge in a real-world situation. Algebra and Geometry are the hardest subjects for me, and I do not retain the teaching very well, so I am sure I will never use this formula. References Bluman, A.