Mathmatics [Grade 10]

1) Find the value of each variable

T = 11r = 4

T = - 11r = - 4

T = 7r = 12

T = 1r = 5

The given answer states that the values of t and r are 11 and 4 respectively. This is because there is no indication or calculation provided in the question that would change the initial values of t and r. Therefore, the initial values of t = 11 and r = 4 remain unchanged.

Explanation

The given answer states that the values of t and r are 11 and 4 respectively. This is because there is no indication or calculation provided in the question that would change the initial values of t and r. Therefore, the initial values of t = 11 and r = 4 remain unchanged.

2)

Quadrant I.

Quadrant II.

Quadrant III.

Quadrant VI.

The given answer, Quadrant III, is correct because it is the only option that corresponds to the negative x-axis and the negative y-axis. In Quadrant III, the x-coordinates are negative, while the y-coordinates are also negative. This is the only quadrant where both coordinates are negative, making it the correct answer. Quadrant I corresponds to positive x and y coordinates, Quadrant II corresponds to positive x and negative y coordinates, and Quadrant VI corresponds to negative x and positive y coordinates. Therefore, Quadrant III is the only option that fits the given criteria.

Explanation

The given answer, Quadrant III, is correct because it is the only option that corresponds to the negative x-axis and the negative y-axis. In Quadrant III, the x-coordinates are negative, while the y-coordinates are also negative. This is the only quadrant where both coordinates are negative, making it the correct answer. Quadrant I corresponds to positive x and y coordinates, Quadrant II corresponds to positive x and negative y coordinates, and Quadrant VI corresponds to negative x and positive y coordinates. Therefore, Quadrant III is the only option that fits the given criteria.

3)

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Explanation

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4) The radian measure of an angle of 132^o is

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Explanation

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5)

8 /17

8 / 15

8 / 9

15 / 17

The answer 15/17 is obtained by dividing the numerator (15) by the denominator (17). This means that out of a total of 17 equal parts, 15 parts are being considered. Therefore, the fraction 15/17 represents the ratio or proportion of the given quantity.

Explanation

The answer 15/17 is obtained by dividing the numerator (15) by the denominator (17). This means that out of a total of 17 equal parts, 15 parts are being considered. Therefore, the fraction 15/17 represents the ratio or proportion of the given quantity.

6)

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Explanation

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7)

I and II only.

II and III only.

I and III only.

I , II and III.

The given answer states that only options II and III are correct. This means that options I and II are incorrect. The explanation for this answer could be that upon evaluating the options, it is determined that only options II and III fulfill the criteria or conditions given in the question. Options I and II may not meet the requirements or may have incorrect information. However, without the context or details of the question, it is difficult to provide a specific explanation.

Explanation

The given answer states that only options II and III are correct. This means that options I and II are incorrect. The explanation for this answer could be that upon evaluating the options, it is determined that only options II and III fulfill the criteria or conditions given in the question. Options I and II may not meet the requirements or may have incorrect information. However, without the context or details of the question, it is difficult to provide a specific explanation.

8) In what quadrants are tangent values positive?

I and II only.

II and III only.

I and III only.

I and IV only.

Tangent is defined as the ratio of the length of the side opposite the angle to the length of the adjacent side in a right triangle. In quadrant I, both the opposite and adjacent sides are positive, resulting in a positive tangent value. In quadrant III, the opposite side is negative, but the adjacent side is positive, which also leads to a negative tangent value. Therefore, tangent values are positive in quadrants I and III only.

Explanation

Tangent is defined as the ratio of the length of the side opposite the angle to the length of the adjacent side in a right triangle. In quadrant I, both the opposite and adjacent sides are positive, resulting in a positive tangent value. In quadrant III, the opposite side is negative, but the adjacent side is positive, which also leads to a negative tangent value. Therefore, tangent values are positive in quadrants I and III only.

9)

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Explanation

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10) Using calculator , what is tan^-1(0.84) in degrees ?

40o

57.1o

32.85o

98o

The correct answer is 40o because the tangent inverse (tan-1) of 0.84 in degrees is the angle whose tangent is 0.84. Using a calculator, when we find the inverse tangent of 0.84, we get approximately 40 degrees.

Explanation

The correct answer is 40o because the tangent inverse (tan-1) of 0.84 in degrees is the angle whose tangent is 0.84. Using a calculator, when we find the inverse tangent of 0.84, we get approximately 40 degrees.

11) A triangle has sides of 11.2 cm and 9.2 cm. the measure of the angle between them is 73°. What is the area of the triangle?

98.53 cm²

15 cm²

49.3 cm

49.3 cm²

The area of a triangle can be calculated using the formula A = 1/2 * base * height. In this case, the given sides of the triangle are 11.2 cm and 9.2 cm, and the angle between them is 73°. To find the height of the triangle, we can use trigonometry. The height can be calculated as h = sin(73°) * 9.2 cm. Then, we can substitute the values into the formula to find the area: A = 1/2 * 11.2 cm * (sin(73°) * 9.2 cm). Evaluating this expression gives us an area of approximately 49.3 cm².

Explanation

The area of a triangle can be calculated using the formula A = 1/2 * base * height. In this case, the given sides of the triangle are 11.2 cm and 9.2 cm, and the angle between them is 73°. To find the height of the triangle, we can use trigonometry. The height can be calculated as h = sin(73°) * 9.2 cm. Then, we can substitute the values into the formula to find the area: A = 1/2 * 11.2 cm * (sin(73°) * 9.2 cm). Evaluating this expression gives us an area of approximately 49.3 cm².

12)

32.6 mm

19.8 mm

30.76 mm

21.27 mm

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Explanation

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13)

17/15

8/15

15/17

17/8

The answer 8/15 is obtained by dividing 17 by 15.

Explanation

The answer 8/15 is obtained by dividing 17 by 15.

14)

0

All of the above

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Explanation

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15)

11.85 in

140.84 in

280.96 in

23.1 in

The correct answer is 140.84 in. This is the only value in the list that is not a multiple of 11.85 in.

Explanation

The correct answer is 140.84 in. This is the only value in the list that is not a multiple of 11.85 in.

16)

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Explanation

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17)

24/25

24/7

7/25

7/24

The answer 7/25 is obtained by dividing 7 by 25.

Explanation

The answer 7/25 is obtained by dividing 7 by 25.

18)

- 8

8

- 4

4

The given sequence alternates between subtracting 8 and adding 4. Starting from the first number, we subtract 8 to get the second number, then add 4 to get the third number, and so on. Therefore, the next number in the sequence would be 4.

Explanation

The given sequence alternates between subtracting 8 and adding 4. Starting from the first number, we subtract 8 to get the second number, then add 4 to get the third number, and so on. Therefore, the next number in the sequence would be 4.

19)

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Explanation

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20)

23.50

33.70

56.30

290

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Explanation

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Mathmatics [grade 10]