Answer:
Maria's homework time is now 9 hours 12 minutes.
Step-by-step explanation:
Since Maria decides to increase her homework time by 15%.
Then,
15% of 8 hours =
x 8 hours
= 0.15 x 8 hours
= 1.2 hours
(Note that: 1.2 hours = 1 hour 12 minutes)
15% of 8 hours = 1 hour 12 minutes
her new homework time = 8 hours + 1 hour 12 minutes
= 9 hours 12 minutes
Maria's homework time is now 9 hours 12 minutes.
Answer:
x = 4
y = 4
Step-by-step explanation:
the front triangle has two 40° angles (sum of all ∡'s must be 180°)
the unlabeled lower-left angle then is 40°; this angle corresponds to the angle in the other triangle labeled as 10y°
therefore, 10y = 40 so y = 4
Since opposite angles in a parallelogram are congruent then we can write:
40° + 25x° = 100° + 10(4)°
25x° = 140 - 40°
25x = 100°
x = 4
The dimension that would give the maximum area is 20.8569
<h3>How to solve for the maximum area</h3>
Let the shorter side be = x
Perimeter of the semi-circle is πx
Twice the Length of the longer side
![[70-(\pi )x -x]](https://tex.z-dn.net/?f=%5B70-%28%5Cpi%20%29x%20-x%5D)
Length = ![[70-(1+\pi )x]/2](https://tex.z-dn.net/?f=%5B70-%281%2B%5Cpi%20%29x%5D%2F2)
Total area =
area of rectangle + area of the semi-circle.
Total area =
![x[[70-(1+\pi )x]/2] + [(\pi )(x/2)^2]/2](https://tex.z-dn.net/?f=x%5B%5B70-%281%2B%5Cpi%20%29x%5D%2F2%5D%20%2B%20%5B%28%5Cpi%20%29%28x%2F2%29%5E2%5D%2F2)
When we square it we would have
![70x +[(\pi /4)-(1+\pi)]x^2](https://tex.z-dn.net/?f=70x%20%2B%5B%28%5Cpi%20%2F4%29-%281%2B%5Cpi%29%5Dx%5E2)
This gives
![70x - [3.3562]x^2](https://tex.z-dn.net/?f=70x%20-%20%5B3.3562%5Dx%5E2)
From here we divide by 2

The maximum side would be at

This gives us 20.8569
Read more on areas and dimensions here:
brainly.com/question/19819849
#SPJ1
The answer is
111/9 miles
or you can say
11 2/9 miles
Answer:
a = (4/3)b
Step-by-step explanation:
The governing equation here has the form y = kx, where k is the constant of proportionality.
Let's rewrite that as a = kb, and then substitute -4 for a and -3 for b:
-4 = k(-3), or k = 4/3
Then a = (4/3)b