17. a triangle has two sides that measure 9 feet and 15 feet. which could be a possible value for the third…

17. a triangle has two sides that measure 9 feet and 15 feet. which could be a possible value for the third side of the triangle? (9.3) a. 12 b. 25 c. 6 d. -6 in exercises 18 - 20, solve the inequality. (9.6,9.7,9.8) 18. - 4 - y > 17 a. y > 21 b. y > - 21 c. y < - 21 d. y > - 2d 19. 6g < - 45 a. g < 7.5 b. g > 7.5 c. g < - 7.5 d. g > - 7.5 20. 3(e - 4) > 4e - 15 a. e > 3 b. e < - 3 c. e < 3 d. e > - 3 21. which set of numbers could be the side lengths of an acute triangle? a. 1,4,5 b. 4,4,5 c. 3,4,5 d. 2,4,5 22. classify the triangle with side lengths 3, 5, and 7. a. acute b. right c. obtuse d. isosceles 23. a ladder placed 12.5 feet from a building touches the building exactly 30 feet from the ground. what is the length of the ladder? (9.4) a. 32.5 feet b. 35 feet c. 17.5 feet d. 9.219 feet in exercises 24 and 25, use the box - and - whisker plot, showing the ages of media specialists in the spring city schools. (9.9) 24. what is the median? a. 19 b. 22 c. 34 d. 36 25. which number is the interquartile range? (9.4) a. 3 b. 12 c. 20 d. 14

17. a triangle has two sides that measure 9 feet and 15 feet. which could be a possible value for the third side of the triangle? (9.3) a. 12 b. 25 c. 6 d. -6 in exercises 18 - 20, solve the inequality. (9.6,9.7,9.8) 18. - 4 - y > 17 a. y > 21 b. y > - 21 c. y < - 21 d. y > - 2d 19. 6g < - 45 a. g < 7.5 b. g > 7.5 c. g < - 7.5 d. g > - 7.5 20. 3(e - 4) > 4e - 15 a. e > 3 b. e < - 3 c. e < 3 d. e > - 3 21. which set of numbers could be the side lengths of an acute triangle? a. 1,4,5 b. 4,4,5 c. 3,4,5 d. 2,4,5 22. classify the triangle with side lengths 3, 5, and 7. a. acute b. right c. obtuse d. isosceles 23. a ladder placed 12.5 feet from a building touches the building exactly 30 feet from the ground. what is the length of the ladder? (9.4) a. 32.5 feet b. 35 feet c. 17.5 feet d. 9.219 feet in exercises 24 and 25, use the box - and - whisker plot, showing the ages of media specialists in the spring city schools. (9.9) 24. what is the median? a. 19 b. 22 c. 34 d. 36 25. which number is the interquartile range? (9.4) a. 3 b. 12 c. 20 d. 14

Answer

Explanation:

Step1: Recall triangle - side length rule

The length of the third side (x) of a triangle with side lengths (a) and (b) must satisfy (|a - b|\lt x\lt a + b). Given (a = 9) and (b = 15), then (|9 - 15|=6) and (9 + 15 = 24), so (6\lt x\lt24). Option A (12) is in this range.

Step2: Solve (-4 - y>17)

Add 4 to both sides: (-y>17 + 4), so (-y>21). Multiply both sides by - 1 and reverse the inequality sign: (y<-21). The answer is C.

Step3: Solve (6g<-45)

Divide both sides by 6: (g<-\frac{45}{6}=-7.5). The answer is C.

Step4: Solve (3(e - 4)>4e-15)

Expand the left - hand side: (3e-12>4e - 15). Subtract (3e) from both sides: (-12>e - 15). Add 15 to both sides: (3>e) or (e < 3). The answer is C.

Step5: Recall acute - triangle condition

For a triangle with side lengths (a), (b), and (c) ((c) is the longest side), the triangle is acute if (a^{2}+b^{2}>c^{2}). For option B with (a = 4), (b = 4), (c = 5), (4^{2}+4^{2}=16 + 16=32) and (5^{2}=25), (32>25).

Step6: Classify the triangle

For side lengths (a = 3), (b = 5), (c = 7) (where (c) is the longest side), (a^{2}+b^{2}=3^{2}+5^{2}=9 + 25 = 34) and (c^{2}=49). Since (a^{2}+b^{2}<c^{2}), the triangle is obtuse. The answer is C.

Step7: Use the Pythagorean theorem

Let the distance from the building be (a = 12.5) and the height on the building be (b = 30). By the Pythagorean theorem (c=\sqrt{a^{2}+b^{2}}=\sqrt{12.5^{2}+30^{2}}=\sqrt{156.25 + 900}=\sqrt{1056.25}=32.5). The answer is A.

Step8: Find the median of box - and - whisker plot

The median of a box - and - whisker plot is the value at the vertical line inside the box. Here, the median is 34. The answer is C.

Step9: Calculate the inter - quartile range

The inter - quartile range (IQR) is the difference between the third quartile ((Q_{3})) and the first quartile ((Q_{1})). (Q_{1}=22) and (Q_{3}=36), so (IQR=36 - 22 = 14). The answer is D.

Answer:

  1. A. 12
  2. C. (y < - 21)
  3. C. (g < - 7.5)
  4. C. (e < 3)
  5. B. 4, 4, 5
  6. C. obtuse
  7. A. 32.5 feet
  8. C. 34
  9. D. 14