10. On a certain trip, Edgar drive 231 km in exactly tthe same time as Erwin drive 308 km.If erwin's rate exceeded that of Edgar by 13 kph, determine the rate of Erwin. 20 knh 44 knh d 52 knh
Percentage
A percentage is a number indicated as a fraction of 100. It is a dimensionless number often expressed using the symbol %.
Algebraic Expressions
In mathematics, an algebraic expression consists of constant(s), variable(s), and mathematical operators. It is made up of terms.
Numbers
Numbers are some measures used for counting. They can be compared one with another to know its position in the number line and determine which one is greater or lesser than the other.
Subtraction
Before we begin to understand the subtraction of algebraic expressions, we need to list out a few things that form the basis of algebra.
Addition
Before we begin to understand the addition of algebraic expressions, we need to list out a few things that form the basis of algebra.
![10. On a certain trip, Edgar drive 231 km in exactly tthe same time as Erwin drive 308 km.If erwin's rate exceeded that of Edgar
by 13 kph, determine the rate of Erwin.
a. 39 kph
d. 52 kph
b. 44 kph
11. One number is 5 less than the other. If their sum is 135, what are the numbers?
b. 80, 55
c. 48 kph
a. 85, 50
c. 70, 65
d. 75, 60
12. The angle of elevation of the top of the vertical tower from points A and B are 25° and 50°, respectively. The points A and B
are 300 m apart and on the same horizontal plane with the foot of the tower. The horizontal angle subtended by A and B at the
foot of the tower is 90°. Find the height of the tower.
a. 140.54 m
d. 130.27 m
с. 112.55 m
13. The angle of elevation of a pole 10 m horizontally from it is three times the angle of elevation at a point 50 m from it. Find the
b. 128.65 m
angle of elevation 10 m from the pole.
a. 20.71°
с. 62.12°
14. Find each interior angle measure of a quadrilateral if its interior angles are represented by x + 10, 2x+20, 3x-50, and 2x-20.
b. 70°, 140°, 130°, 100° c. 60°, 120°, 100°, 80°
b. 41.14°
d. 58.24°
a. 50°, 100°, 70°, 60°
d. 40°, 80° 40°, 40°
15. Determine the area of the spherical triangle ABC if A = 140°, B = 75°, C = 86° and r= 40 m.
d. 2349 m²
c. 3467 m²
16. Tokyo is located at (139°E, 39°N) while Manila is at (121°E, 14°N). Find the distance between the two cities in nautical miles.
c. 1777
17. Inside square ABCD is a semicircle whose diameter is the side AD of the latter. Line CE is drawn, which is tangent to the
a. 3379 m²
b. 1346 m?
а. 1456
b. 1567
d. 1467
semicircle. Find the length of CE. If the side if the square is 2 cm.
а. 2.25 cm
c. 2.75 cm
18. The radii of two circular pulleys with their centers 10 cm apart are 3 cm and 4 cm, respectively. They are interconnected by a
cross-belt so that they rotate in opposite direction. Find the distance between two points of tangency of the two different circles
b. 2.50 cm
d. 3.00 cm
measured along the belt.
a. 5.14 cm
d. 8.14 cm
c. 7.14 cm
19. A circle of radius 6 cm is inscribed in a square. A smaller circle is drawn tangent to the two sides of the square and the bigger
b. 6.14 cm
circle. What is the radius of the smaller circle?
a. 0.956 cm
b. 1.029 cm
c. 1.125 cm
d. 0.856 cm](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F9dac9831-9bed-4f75-b734-064d3203cdd8%2F5eb8b56f-3acf-41b4-ab79-6ac98632d4bb%2F3iogyz0j_processed.jpeg&w=3840&q=75)
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