Check my math answers, please?<span>1. Lines PL, AE, and RT are all parallel to each other. What is the length of segment LT? http://oi47.tinypic.com/27wr5eu.jpg
a. 14
b. 7
c. 8 <<<<<<my answer
d. 6 2. A phone company worker needs to know the height of a cell tower, so he decides to use a 3 m pole and shadows cast by the sun, as shown in the diagram. Both shadows end at point B. What is the height of the tower? http://oi49.tinypic.com/2d1qouv.jpg
a. 30 m <<<<<<my answer
b. 36 m
c. 45 m
d. 50 m 3. What is the length of segment AD? http://oi45.tinypic.com/sqs2g0.jpg
a. 3
b. 12
c. 15 <<<<<< my answer
d. 20
4.A pair of corresponding sides of two similar pentagons have lengths of 12 cm and 28 cm. What is the ratio of the areas of the two pentagons? http://oi46.tinypic.com/2l9jvbn.jpg
Option A: 12/28 <<<<<my answer
Option B: 27/343
Option C: 28/12
Option D: 9/49
5. If a dilation transforms pre-image AEB to create image ADC, which is the proper term for point A? http://oi45.tinypic.com/2n6u1s8.jpg
a. contraction point
b. center of dilation
c. scale factor <<<<<my answer
d. pre-image point
6. A pre-image segment with endpoints (2, -1) and (4, 2) is dilated to the image segment with endpoints (4, -2) and (8, 4). What is the scale factor for the dilation? http://oi45.tinypic.com/6q9x5j.jpg
a. 2
b. 4<<<<my answer
c. 6
d. 8
7. The volumes of two similar solids are 20 cm^3 and 540 cm^3. Which is the ratio of the corresponding sides of the larger figure to the smaller figure?
a. 27
b. 9
c. 6
d. 3 8. On the coordinate plane, the origin is the center of a contraction with a scale factor of p. Which shows the coordinates of the image points for pre-image points (x, y)? a. (p + x, p + y)
b. (x - p, y - p)
c. (px, py)
d. (p - x, p - y) <<<<<my answer 9. Two right triangles are similar. Which of the following must the similar triangles have?
a. every pair of sides congruent
b. congruent corresponding angles and proportional side lengths <<<<<my answer
c. at least one pair of congruent sides
d. an obtuse angle
10. The vertices of a pre-image are located at points (-3, 3), (0, 0), and (-2, -1). If the image triangle has vertices with coordinates (9, 9), (0, 0), and (-6, -3), what type of dilation is it?
a. expansion
b. contraction
c. reflection <<<<<my answer
d. rotation 11. The diagram shows a 76 m building with a flagpole outside. The shadows of the building and the flagpole end at point C. What is the height of the flagpole? http://oi50.tinypic.com/35lsyl2.jpg
5.68 m
12 m
14.25 m <<<<<<my answer
518 m 12. The side lengths of two different cubes are 36 cm and 45 cm. What is the ratio of the volume of the smaller to the volume of the larger (in simplest form)? Note: These cubes are not drawn to scale. http://oi46.tinypic.com/359yaom.jpg
Option A: 4/5 <<<<my answer
Option B: 12/15
Option C: 16/25
Option D: 64/125
13. Which of the following can be used to prove that the two triangles are similar?http://oi50.tinypic.com/2prbthz.jpg SAA Similarity Theorem
Given the function f(x) = x + 3 for x ≤ -1 and 2x - c for x > -1, for the function to be continuous, the right hand limit of the function must be equal to its left hand limit.
For the left hand limit;
The function at the left hand occurs at x<-1
f-(x) = x+3
f-(-1) = -1+3
f-(-1) = 2
For the right hand limit, the function occurs at x>-1
f+(x) = 2x-c
f+(-1) = 2(-1)-c
f+(-1) = -2-c
For the function f(x) to be continuous on the entire real line at x = -1, then
f-(-1) = f+(-1)
On equating both sides:
2 = -2-c
Add 2 to both sides
2+2 = -2-c+2
4 =-c
Multiply both sides by minus.
-(-c) = -4
c = -4
Hence the value of c so that f(x) is continuous on the entire real line is -4
