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1. Name the quadrant, if any, in which each point is located. (a) (-3, 6) (b) (7, -5) Solution:(a) (-3, 6) --------- II Quadrant.(b) (7, -5) --------- IV Quadrant.
2. Complete the table for the given equation & graph the equation;x + 2y = 5
Solution:
x + 2y = 5 Put the value of x = 0 in the equation x + 2y = 50 + 2y = 5 2y = 5 2y/2 = 5/2y = 5/2 (0, 5/2)Put the value of y = 0,x + 2 × 0 = 5 x = 5 (5, 0)Put the value of x = 2,2 + 2y = 5 2 – 2 + 2y = 5 - 2 2y = 32y/2 = 3/2y = 3/2 (2, 3/2)Put the value of y = 2,x + 2 × 2 = 5 x + 4 = 5x + 4 – 4 = 5 – 4x = 1 (1, 2)
Solution:6x-5y=30 Put the value of x = 0 in the equation 6x - 5y = 30. 6 × 0 - 5y = 30 -5y = 30 -5y/-5 = 30/-5y = -6 (0, -6)Put the value of y = 0,6x - 5 × 0 = 30 6x = 306x/6 = 30/6x = 5(5, 0)Put the value of x = 3,6 × 3 - 5y = 30 18 - 5y = 3018 – 18 – 5y = 30 – 18-5y = 12-5y/-5 = 12/-5y= -12/5(3, -12/5)Put the value of y = -2,6x – 5(-2) = 306x + 10 = 306x + 10 – 10 = 30 – 106x = 206x/6 = 20/6x = 10/3 (10/3, -2)
4. Find the x-and y-intercepts of the following equations.2x + 3y = 12
Solution:2x + 3y = 12Put the value of x = 02 × 0 + 3y = 123y = 123y/3 = 12/3y = 4Therefore, y-intercept = (0, 4)Now, put the value of y = 02x + 3 × 0 = 122x = 122x/2 = 12/2x = 6Therefore, x-intercept = (6, 0)
5. Find the x-and y-intercepts of the following equations. X + y = -2
Solution:x + y = -2
Put the value of x = 00 + y = -2y = -2
Therefore, y-intercept = (0, -2)
Put the value of y = 0x + 0 = -2x = -2
Therefore, x-intercept = (-2, 0)
6. Find the midpoint of each segment with the given endpoints.
(-10, 4) & (7, 1)Solution:
(-10, 4) and (7, 1)
Midpoint = <(x1 + x2)/2, (y1 + y2)/2>Here, x1 = -10, x2 = 7, y1= 4 and y2 = 1= <(-10 + 7)/2, (4 + 1)/2>= (-3/2, 5/2)Answer: (-3/2, 5/2)7. Find the midpoint of each segment with the given endpoints.(3,-6) và (6, 3)Solution:(3,-6) & (6, 3)Midpoint = <(x1 + x2)/2, (y1 + y2)/2>Here, x1 = 3, x2 = 6, y1= -6 và y2 = 3= <(3 + 6)/2, (-6 + 3)/2>= (9/2, -3/2)
Answer: (9/2, -3/2)
8. Decide whether the lines are parallel, perpendicular or neither.x + 4y = 7 and 4x – y = 3
Solution:
x + 4y = 7
4y = -x + 7
y = (-1/4) x + 7
Slope of the equation x + 4y = 7 is -1/4.
Again, 4x – y = 3
y = 4x – 3
Slope of the equation 4x – y = 3 is 4.
Since multiplying both the slope of the equation = -1/4 × 4= -1
Therefore, the given two equations are perpendicular to each other.
Answer: Perpendicular
9. The ship has coordinates (2,3) the equation of the other line is x+y=2 find the shortest distance from the ship khổng lồ the line.
Solution:x + y = 2
x + y – 2 = 0
Distance from (2, 3) to lớn the line x + y – 2 = 0
= (2 + 3 – 2)/√(12 + 12)= 3/√(1 + 1) = 3/√2= (3 × √2)/(√2 × √2)= (3√2)/2 units.Answer: (3√2)/2 units 10. Covert khổng lồ scientific notation 0.000000373Solution:0.000000373= 3.73 × 10-7Answer: 3.73 × 10-711. Covert khổng lồ decimal notation 5.347 x 10-8Solution:5.347 x 10-8= 5.347/100000000= 0.00000005347Answer: 0.0000000534712. Multiply & write the result in scientific notation (3 x 105) (3 x 103)Solution:(3 x 105) (3 x 103)= 9×105 + 3= 3 × 3 × 105 × 103= 9 × 108Answer: 9 × 10813. Simplify: 5 - 2 <8 - (2 x 2 - 4 x 4)>Solution:5 - 2 <8 - (2 x 2 - 4 x 4)>= 5 - 2 <8 - (4 - 16)>= 5 - 2 <8 - (-12)>= 5 - 2 <8 + 12>= 5 - 2 <20>= 5 – 40= -35Answer: -35
14. Fill in the blank:(a) The point with coordinates (0,0) is called ........of a rectangular coordinate system.(b) to lớn find the x-intercept of a line, we let....equal 0 và solve for ......; to find y-intercept, we let ......equal 0 và solve for.......Solution:(a) The point with coordinates (0,0) is called origin of a rectangular coordinate system.(b) lớn find the x-intercept of a line, we let y equal 0 & solve for x ; lớn find y-intercept, we let x equal 0 & solve for y .15. Name the quadrant, if any, in which each point is located. (a) (1, 6)(b) (-4, -2) Solution:(a) (1, 6) --------- I Quadrant.(b) (-4, -2) --------- III Quadrant.
16. A restaurant meal for a group of people cost $85 total. This amount included a 6% tax & an 18% tip, both based on the price of the food. Which equation could be used khổng lồ find f, the cost of the food?
A. 85 = 1.24f B. 85 = 0.24c C. 85 = 1.06f + 0.18 D. 85 = f + 0.24
17. Three friends cốt truyện the cost of a pizza. The base price of the pizza is phường and the extra toppings cost $4.50. If each person’s nội dung was $7.15, which equation could be used to lớn find p, the base price of the pizza?
A. 7.15 = 3p - 4.50
B. 7.15 = 1/3(p + 4.50)
C. 7.15 = 1/3p + 4.50
D. 7.15 = 3(p + 4.50)
Answer: B. 7.15 = 1/3(p + 4.50)
18. A tile setter is joining the angles of two tiles, A and B, to lớn make a 90-degree angle. The degree measure of Angle A can be represented as 3y + 2 and of Angle B as 5y. Which equation represents this situation?
A. 90 = 3y +2 – 5y B. 3y + 2 = 90 + 5y C. 90 = 8y + 2 D. 5y + 2 = 90 + 3y
Answer: C. 90 = 8y + 2
19. One-fourth of the distance between two cities is 100 miles less than two-thirds the distance between the cities. Which equation expresses this situation?
1/4d - 100 = 2/3d ,
1/4d = 2/3d -100,
1/4d = 2/3d +100,
1/4d - 2/3d = 100
Answer: 1/4d = 2/3d -100
20.
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What value of b makes the equation that follows true?
x2 + bx – 35 = (x + 5)(x – 7)
A. -2 B. 12 C. 2 D. -12
Answer: A. -2
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