18 points
quadrilateral abcd has coordinates a (3, −5), b (5, −2), c (10, −4), d (8, −7). quadrilateral abcd is a rectangle, because opposite sides are congruent and adjacent sides are perpendicular
square, because all four sides are congruent and adjacent sides are perpendicular
parallelogram, because opposite sides are congruent and adjacent sides are not perpendicular
rhombus, because all four sides are congruent and adjacent sides are not perpendicular

The answer is (c) parallelogram, because opposite sides are congruent and adjacent sides are not perpendicular.

Step-by-step explanation: The co-ordinates of the vertices of quadrilateral ABCD are given to be A(3,-5), B(5,-2), C(10,-4) and D(8,-7).

The lengths of the sides are as follows -

Therefore, AB = CD  and  BC = DA.

Also, the slopes of the sides AB(m), BC(n), CD(o) and DA(p) are as follows

For two lines to be perpendicular, the product of their slopes should be -1 and for them to be parallel, their slopes must be equal. So, here no two pair of lines are perpendicular. But, m = o and n = p and so, the opposite sides are parallel.   

Since the opposite sides are congruent and parallel, but not perpendicular, so the quadrilateral ABCD is a parallelogram.

Thus, the correct option is (c).

Parallelogram, because opposite sides are congruent and adjacent sides are not perpendicular

Step-by-step explanation:

I got this right on my Quiz !

why can't you?

step-by-step explanation:

part a

answer: a reasonable domain is where n is a real number. so n can be between 0 and 10. both endpoints are included.

work shown:

n is the number of days after the experiment starts. the smallest n can be is n = 0 which means that 0 days have gone by, and we're at the start. to find out how large n should be, then replace f(n) with 16.13 and solve for n. use logarithms to isolate the exponent.

f(n) = 12*(1.03)^n

16.13 = 12*(1.03)^n

16.13/12 = (1.03)^n

1.34416666666667 = (1.03)^n

(1.03)^n = 1.34416666666667

log[ (1.03)^n ] = log[ 1.34416666666667 ]

n*log[ 1.03 ] = log[ 1.34416666666667 ]

n = log[ 1.34416666666667 ]/log[ 1.03 ]

n = 10.0062999823929

this rounds to n = 10 which is fairly close but not 100% perfect. so this is the largest n can be.

note: if you plug n = 10 into f(n), you'll get roughly 16.127 which rounds to 16.13 (this comes up again in part c)

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part b

answer: the y intercept is 12. it represents the starting height of the plant in cm.

work shown:

plug n = 0 into the f(n) function. simplify

f(n) = 12*(1.03)^n

f(0) = 12*(1.03)^0

f(0) = 12*(1)

f(0) = 12

on day n = 0, aka the starting point, the height f(n) is 12 cm

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part c

answer: the average rate of change is approximately 0.43061036458991 (round however you need to). this represents the average growth rate from day n = 3 to day n = 10. so the plant grew roughly 0.43 cm per day during this timespan, assuming you round to 2 decimal places.

work shown:

compute f(3)

f(n) = 12*(1.03)^n

f(3) = 12*(1.03)^3

f(3) = 13.112724 < we'll use this later

compute f(10)

f(n) = 12*(1.03)^n

f(10) = 12*(1.03)^10

f(10) = 16.1269965521294 < we'll use this later

now use the formula below with a = 3 and b = 10

aroc = average rate of change

aroc = [ f(b) - f(a) ]/[ b - a ]

aroc = [ f(10) - f(3) ]/[ 10 - 3 ]

aroc = (16.1269965521294 - 13.112724)/(10 - 3)

aroc = 3.0142725521294/7

aroc = 0.43061036458991

round this however you need to

note: the plant grew approximately 3.01 cm over 7 days, so roughly 0.43 cm per day is the average growth rate (if you were to round to 2 decimal places).