Which of the following inequalities is not true? |-9| ≠ |9| -2 ^2 < 3 -7 ≤ -5 |-1| ≥ 0

(a) |-9| ≠ |9| is NOT TRUE.

(b)   is TRUE

(c)  -7 ≤ -5 is TRUE

(d) |-1| ≥ 0 is TRUE.

Step-by-step explanation:

Solving each expression separably:

(a)  |-9| ≠ |9|

By the definition of MODULUS FUNCTION:  IxI = x, if x > 0

                                                                              = (-x) if x <, 0

⇒ I-9I = -(-9)  = 9, and I9I = 9

So, I-9I = I9I . Hence, |-9| ≠ |9| is NOT TRUE.

(b)  

⇒  

and (-8) < 3.

Hence,     is TRUE

(c) -7 ≤ -5

-7 < -5  on the number line of integers.

Hence, -7 ≤ -5 is TRUE

(d) |-1| ≥ 0

I(-1)I  = -(-1)  = 1

and 1 > 0

Hence, |-1| ≥ 0 is TRUE.

step-by-step explanation:

part a. the differences are decreasing, so we know the sequence is not arithmetic. the ratios are constant (=3/4), so we know the sequence is geometric.

part b. from part a, we know the common ratio is 3/4, so each term is 3/4 of the one before. the initial term is the number of gallons at h=1.

g[h] = (3/4)·g[h-1]

g[1] = 384 . . . . initial value required for a recursive definition

part c. the general formula for a geometric sequence is

a[n] = a[1]·r^(n-1)

we have a[1] = 384, r = 3/4, and the term number given by h. the formula that follows is

g[h] = 384·(3/4)^(h-1)

part d. filling in the value and doing the arithmetic, we have

g[12] = 384·(3/4)^11 ≈ 384·0.042235136 ≈ 16.2183 . . gallons

part e. each gallon is 4 quarts, so

16.2183 gal × 4 qt/gal = 64.8732 qt

25/6

step-by-step explanation:

you multiply 4 by the denominator (4*6=24) and add it to the numerator which makes it 25/6.