Answer:
15
Step-by-step explanation:
Thee are 15 triangles in the figure
Answer:
Amount at 15%=$2,411
Amount at 14%=$7,405
Step-by-step explanation:
let
x= the amount at 15% rate.
y=amount at 14% rate
y= x times 3 plus $172
y= 3x + $172 (1)
x times 15% plus y times 14% equals a return of $1,398.35 after one year
0.15x + 0.14y= $1,398.35 (2)
Recall,
y= 3x + $172
Substitute (1) into (2)
0.15x + 0.14y= $1,398.35
0.15x + 0.14(3x+172)=1398.35
0.15x + 0.42x + 24.08=1398.35
Collect like terms
0.15x + 0.42x=1398.35 - 24.08
0.57x=1374.27
Divide both sides by 0.57
x=2,411
x=$2,411
Find y
y= 3x + $172
=3(2,411) + 172
=7,233+172
=7,405
y=$7,405
Amount at 15%=$2,411
Amount at 14%=$7,405
Check:
$2,411*0.15=$361.65
$7,405*0.14=$1036.70
Total=$361.65 + $1036.70
=$1,398.35
<span> i only know PART B
____
I'm not sure how you were taught, so I'll show work for different methods to get the same answer.
____
Method 1: Solving for the lateral surface area of the triangular prism (not using volume)
Note that for the triangular prism:
**DON'T include the 2 triangular bases. DO include the 3 rectangular sides**
*lateral surface area does not include the area of the bases*
*lateral surface area just includes the lateral faces*
formula: (a + b + c)(h)
[a, b, c still using the values from PART A; h being your height from PART A]
Plug them into the above formula:
(10 + 13 + 13)(20) -> (10 + 26)(20) -> (36)(20) = 720
=> Your lateral surface area is 720.
(If you forget to exclude the area of the bases, you will get the surface area of 840)
___________________
Method 2: Solving for the lateral surface area of the triangular prism (using volume)
Note that we will be using surface area, height, and volume to find the lateral area this time.
formula: A - 2 (V/h)
[A is the surface area; V is the given volume; h is the height from PART A]
Before we can plug things into the above formula, we need to find the surface area.
Since we have already found the lateral surface area (the area of the 3 rectangular sides), we just have to solve for the area of the bases (the area of the 2 triangles).
(Area of a triangle = (1/2)b*h or (0.5)(b*h) -> one-half of the base times the height
We can do this 2 ways:
1) Using our base value from PART A which is 5, and our height from PART A
which is 12
1/2(5*12) -> 1/2(60) -> 30.
Because we split that triangle in half in PART A, there are 4 triangles (2 in
each base).
So 30(4) = 120.
2) Using the whole base of the triangle which is 10, and the height from PART A
which is 12
1/2(10*12) -> 1/2(120) -> 60.
Since this time we used each whole base, instead of splitting them, there are
only 2
triangles (1 per base).
So 60(2) = 120.
Both ways gave you the same answer of 120.
Now add the lateral surface area and the area of the bases.
720 + 120
720 + 120 = 840.
840 is your surface area.
With that, you can now plug things into the formula.
A - 2 (V/h) -> 840 - 2 (1200/20) = 720
=> Your lateral surface area is 720.
___________________
Both Method 1 & Method 2 get you a lateral surface area of 720.
___
The approx. amount of cardboard used for the sides (aka lateral faces[aka rectangular sides]) of the candy box is 720.</span>
When you multiply 12 strawberry pops by 4.54 each you get 54.48 and so on. In total Fred spent all together $364.17.
Answer:
Step-by-step explanation:
slant height=√(3²+1²)=√10
L.A=4×1/2×2×√10=4√10
