Is 8/9 + 1/10 = 39/90 reasonable or unreasonable

 Hello there!

We have the equation 8/9 + 1/10 = 39/90 and we want to know if this is "reasonable"

Now let's compute the sum:

8/9 + 1/10 here both fractions have different denominators, then we need to find a common denominator, let's try 90.

8/9 = 8/9*(10/10) = 80/90

1/10 = 1/10(9/9) = 9/90

you can do these changes because multiplying by 10/10 or 9/9 is the same as multiplying by 1, then our sum is:

8/9 + 1/10 = 80/90 + 9/90 = 89/90

Then the initial equality is unreasonable, because of 89/90 ≠ 39/90

the length of o'p' is .

step-by-step explanation:

it is given that the quadrilateral m'n'o'p' is the image of quadrilateral mnop after dilation.

the center of dilation is origin and the scale factor is 1.5.

in dilation the image and preimge are similar figures. it means the sides of image and preimage are proportional.

the scale factor is defined as

the scale factor is 1.5.

multiply both sides by op.

note: if the value of op is given, then multiply the value of op with 1.5 to get the length of side o'p'.

therefore length of o'p' is .

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