4. Given the irrational number .14147…. choose an inequality which approximates to the 4th decimal place.
a) .14 < x <.15
b) .141 < x < .142
c) .1413 < x < .1414
d) .1414 < x <.1415
B?
6. Choose an inequality to match this description: The height E of Mount Everest, is greater than the height R of Mount Rainier. Mount Rainier is higher than Mount Fuji, F.
a) E < R < F
b) F < R < E
c) E > R > F
d) Both (b) and (c
D?
If x < 0 and y > 0, then it is always true that _______.
a) xy is a negative number
b) x + y is a negative number
c) xy is a positive number
d) x + y is a positive number
D?
If a < 0 and x < y, then it is always true that ________.
a) multiplying x and y by a reverses the inequality
b) y – x > a
c) y > a
d) Both (a) and (b)
A?
If b > 0 and x > b - y, then it is always true that ________.
a) 0 is not an element of b
b) b > y
c) x + y > 0
d) Both (b) and (c)
B?
Qu.2-D,Qu.3-A,Qu.5-C
Number 6 id D
For question 4, you are given the irrational number .14147... and you need to choose an inequality that approximates to the 4th decimal place. The correct answer is b) .141 < x < .142. This is because .141 is less than .14147, and .142 is greater than .14147. So, the inequality captures the range in which the number .14147... falls, approximating to the 4th decimal place.
For question 6, you are given a description about the heights of Mount Everest, Mount Rainier, and Mount Fuji. The height of Mount Everest, E, is greater than the height of Mount Rainier, R, and Mount Rainier is higher than Mount Fuji, F. The correct answer is d) Both (b) and (c). This is because option b) F < R < E satisfies the ordering described in the question, and option c) E > R > F also satisfies the ordering. So, both options b) and c) are correct.
For the third question, if x < 0 and y > 0, it is always true that d) x + y is a positive number. This is because when you add a negative number (x) to a positive number (y), the sum is always positive.
For the fourth question, if a < 0 and x < y, it is always true that a) multiplying x and y by a reverses the inequality. This is because when you multiply both sides of an inequality by a negative number (a), the inequality sign is reversed.
For the fifth question, if b > 0 and x > b - y, it is always true that b) b > y. This is because if x > b - y, adding y to both sides of the inequality gives x + y > b, which means b is less than the sum of x and y, so b > y. Option c) x + y > 0 is not always true, as it depends on the specific values of x and y. Therefore, the correct answer is b) b > y.