Given: ABCD is a kite. Put a checkmark in every box that must be
true. Has two pairs of parallel sides
Has exactly one pair of parallel sides
All four sides are congruent
Has exactly one pair of congruent sides
Both pairs of opposite sides are congruent
Two pairs of consecutive sides
(but not all four sides) are congruent
There are right angles at all four vertices
The diagonals are perpendicular
The diagonals are congruent
The diagonals bisect each other
Ty
4
-6S
I
Use calculations and words to show
this quadrilateral meets the
definition of a kite.

1)  The correct options are;

2) Yes, the quadrilateral meets the condition for the definition of a kite

Step-by-step explanation:

1) A kite has two pairs of adjacent equal sides, therefore a kite consists of two isosceles triangles adjacent to each other sharing the same base

Which shows that the diagonals which consists of the base of the two isosceles triangles and the bisector of the angles on the opposite sides of the common base of the isosceles triangles are perpendicular to each other

Therefore, the correct options are;

2) The coordinates of the given quadrilateral are;

D = (-3, 4), A = (3, 6), B = (5, 0), C = (-2, -4)

Therefore, the length of DA = √((-3 - 3)² + (4 - 6)²) = 2·√10

the length of AB = √((5 - 3)² + (0 - 6)²) = 2·√10

The length of DC = √((-3 - (-2))² + (4 - (-4))²) = √(65)

The length of CB = √((-2 - 5)² + (-4 - 0)²) = √(65)

Therefore, the figure has two pairs of congruent consecutive sides but not all four sides

The slope of the bisector CA = (6 -(-4))/(3 - (-2)) = 2

The slope of the bisector DB = (0 - 4)/(5 - (-3)) = -0.5 = -1/2

Therefore, the diagonals are perpendicular which shows that the quadrilateral meets the condition for the definition of a kite.

answer

106 emergencies

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)

=====================================

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

=====================================

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).