Answer:
t = -1, 2
Step-by-step explanation:
Step 1: Define
h(t) = -5t² + 5t + 10
Step 2: Factor
h(t) = -5(t² - t - 2)
h(t) = -5(t - 2)(t + 1)
Step 3: Find roots
0 = -5(t - 2)(t + 1)
0 = (t - 2)(t + 1)
t - 2 = 0
t = 2
t + 1 = 0
t = -1
Use property of proportion:
miles time (hs)
90 2.25
x 1
x = 90 ÷ 2.25
x = 40 miles
Answer:
a) corresponding angles of similar polygons are congruent
b) corresponding sides of similar polygons are proportional
c) a triangle is a polygon
Step-by-step explanation:
By <em>definition</em>, similar polygons have congruent corresponding angles and proportional corresponding sides.
A triangle is a polygon, so two triangles will be similar if they have congruent corresponding angles and proportional corresponding sides.
___
For an n-sided polygon, one only needs to show the conditions are met for n-1 angles and sides. Those will determine the measures of the final angle/side.
Answer:
Side length = 
cm , Height = 
cm , Volume = 
cm³
Step-by-step explanation:
Assume
Side length of base = x
Height of box = y
total material required to construct box = A ( given in question)
So it can be written as
A = x² + 4xy
4xy = A - x²
Volume of box = Area x height
V = x² ₓ y
V = x² ₓ ( 
)
V = 
To find max volume put V' = 0
So taking derivative equation becomes
A = 3 
= 
x = 
put value of x in equation 1
y = 
y = 
y =
So the volume will be
V = × y
Put values of x and y from equation 2 & 3
V = 
V =
Answer:
3.5 km
Step-by-step explanation:
We know that 1000 meters = 1 kilometer
500 meters * 1 kilometer/1000m = 500/1000 kilometer = .5 km
He goes .5 km per day
There are 7 days in 1 week, so multiply by 7
7 * .5 km = 3.5 km
