Answer:
382 cm²
Step-by-step explanation:
The shape can be decomposed into two rectangular prism or cuboids
✔️Dimension of prism 1 (smaller prism):
L = 10 cm
W = 3 cm
H = 7 - 4 = 3 cm
Surface area of prism 1 = 2(LW + LH + WH)
= 2(10*3 + 10*3 + 3*3)
= 2(69)
Surface area of prism 1 = 138 cm²
✔️Dimension of prism 2 (larger prism):
L = 10 cm
W = 8 cm
H = 4 cm
Surface area of prism = 2(LW + LH + WH)
= 2(10*8 + 10*4 + 8*4)
= 2(152)
Surface area of prism 2 = 304 cm²
✅Surface Area of the composite shape = (Surface area of prism 1 + surface area of prism 2) - (2 × area of the base of prism 1)
= (138 + 304) - (2 × L × W)
= 442 - (2 × 10 × 3)
= 442 - 60
= 382 cm²
Both A. and D. are increasing.
Answer:
6d^5 - 3c^3d^2 + 5c^2d^3 + c^3d^4 - 12cd^4 + 8
Step-by-step explanation:
We need to subtract the given polynomial from the sum:-
8d^5 - 3c^3d^2 + 5c^2d^3 - 4cd^4 + 9 - (2d^5 - c^3d^4 + 8cd^4 +1 )
We need to distribute the negative over the parentheses:-
= 8d^5 - 3c^3d^2 + 5c^2d^3 - 4cd^4 + 9 - 2d^5 + c^3d^4 - 8cd^4 -1
Bringing like terms together:
= 8d^5 - 2d^5 - 3c^3d^2 + 5c^2d^3 + c^3d^4 - 4cd^4 - 8cd^4 + 9
- 1
Simplifying like terms
= 6d^5 - 3c^3d^2 + 5c^2d^3 + c^3d^4 - 12cd^4 + 8
Answer:
7.5 hours
Step-by-step explanation:
We can model an equation for this problem.
We can write:
Where
F is the final temperature (15 degrees we need)
m is the rate of temperature change (2 degrees per hour)
and
t is the time, in hours, it will take (we need to find this)
It is given,
F = 15
m = 2
So, t would be:
F = mt
15 = 2t
t = 15/2 = 7.5
So it will take 7.5 hours
We are given equations y =3.5x and y=25x +40.50.
Where x represent time in hours and y represents cost in dollars.
We need to determine that which equation is not the equation of a proportional relationship?
In first equation we have slope 3.5 and y-intercept 0.
In second equation, we have slope 25 and y-intercept 40.50.
<em>In order to have a a proportional relationship, there should be y-intercept =0.</em>
<h3>Therefore, y= 25x + 40.50 is not the equation of a proportional relationship.</h3>
