11. A box of apples has a mass of 17.5 kg.)
A box of pears has a mass of 15.5 kg.
a) Write an algebraic expression for the
total mass of a boxes of apples and
p boxes of pears.
b) Use your expression to determine the
total mass of a shipment of 32 boxes of
apples and 41 boxes of pears.

a) 17.5a + 15.5p = t

b) Total mass of the shipment is 1195.5kg

Step-by-step explanation:

Mass of 1 box of apple= 17.5kg

Mass of 1 box of pears = 15.5kg

a) expression for getting total mass:

Let the no. of boxes of apple be 'a'

Let the no. of boxes of pears be 'p'

Let the total mass be 't'

17.5a + 15.5p = t

b) a = 32

p = 41

17.5a + 15.5p = t

17.5(32) + 15.5(41)  = t

560 + 635.5 =t

1195.5 = t

Total mass of the shipment is 1195.5kg

hello from mrbilldoesmath!

answer:

x - 3

discussion:

x^2 - 9 = (x-3) (x+3)   so

(x^2-9)/ (x + 3) = x-3

you,

mrb

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