Answer: The volume is 33 cubic centimeters.
Step-by-step explanation:
First find the volume of the square pyramid on top of the cube. To find the volume of the square pyramid you use the volume a^2*h/3 a is the side length of the base of the square pyramid and h is the height all divide by 3.
So we can say that the side length of the base of the square pyramid is 3 because it has the same side length base as the cube.
V= 3^2 * 2 /3
V= 9 * 2 /3
V= 18/3
v= 6
So the volume of the square pyramid is 6 so now we need to find the volume of the cube and add them together.
Volume of the a cube uses the formula s^3 where s is the side length.
V= 3^3
v= 3*3*3
v= 27
The volume of the cube is 27.
Add 6 and 27 to find the total volume.
6 +27 = 33
1. 12000(1 - n/5) = 2,400
12000 - 2400n = 2400
- 2400n + 12000 - 12000 = 2400 - 12000
- 2400 = - 9600
n = 4, After 4 years the scanner will be replaced.
2. Let x represents Michael age in years now.
Now 4years later
Michael x x + 4
John x - 17 (x - 17) + 4
x + 4 + x - 17 + 4 = 49
x + 4 + x - 13 = 49
2x - 9 = 49
2x - 9 + 9 = 49 + 9
2x = 58
(1/2)(2x) = (1/2)(58)
x = 29, Michaels age is 29
3. Brady speed 1 Rate(mph) Time(hours) Distance(miles)
17 t 17 t
Brady speed 2 22 4 - t 22(4 - t)total distance
The total distance he rode 17t + 22(4 - t) = 70
The total distance = 70 miles
showing work:
17t + 22(4 - t) = 70
17t + 88 - 22t = 70
- 5t + 88 = 70
- 5t + 88 - 88 = 70 - 88
- 5t = - 18
t = 3.6, Brady rode 17(mph) for 3.6(hrs).
4. t = the price of 1 shirt
4t - 39.58 = 52.22
4t - 39.58 = 52.22 + 39.58
4t + 0 = 91.80
(1/4)(4t) = (1/4)(91.80)
t = 22.95, price of 1 shirt was $22.95
5. Let M represent number of months.
3.5m + 90 = 132
3.5m + 90 - 90 = 132 - 90
3.5m = 42
(1/3.5)(3.5m) = (1/3.5)(42)
m = 12, the boy will grow 132cm tall, 12 months from now
6. Let N represent given number
n + 1/6n + (2 1/2)n + 7 = 12 1/2
n ( 1 + 1/6 + 5/2) + 7 = 12 1/2
n(6/6 + 1/6 + 15/6) + 7 = 12 1/2
n(22/6 + 7 - 7 = 12 1/2
11/3n + 7 - 7 = 12 1/2 - 7
11/3n + 0 = 5 1/2
11/3n = 5 1/2
3/11.11/3 = 3/11.11/2
1n = 3/2
n = 1 1/2, is the number
7. let X represents the first number, then 33 - x represents the other # since their sum is 33
X - (33 - x) = 2
X + ( - (33 - x)) = 2
X + ( -33) + X = 2
2x + (- 33) = 2
2x + (- 33) + 33 = 2 + 33
2x + 0 = 35
1/2 * 2x = 1/2 * 35
1x = 35/2
x = 17 1/2
33 - x = 33 - (17 1/2) = 15 1/2
{17 1/2, 15 1/2}
8. Let T represents number of tokens in machine A. Then 1/2T represents the number of tokens in machine B, and 3/4T represents the number of tokens in machine C.
T + 1/2T + 3/4T = 18,324
9/4T = 18, 324
T = 8, 144
Machine A took 8,144T, Machine B 4,072T, Machine C 6,108T
9. Let Z represents the cost of a pencil in dollars. Then, the cost of a pen in dollars is Z + 0.11
250(Z + Z + 0.11) = 42.5
250(2Z + 0.11) = 42.5
500Z + 27.5 = 42.5
500Z + 27.5 + ( - 27.5) = 42.5 + ( -27.5)
500Z + 0 = 15
500Z = 15
500Z/500 + 15/500
Z = $0.03, a pencil costs, and a pens cost $0.14
10. Let R represents speed in mph of faster car, Then r - 7 represents speed in mph of slow car.
5 1/2(r) + 5 1/2(r - 7) = 599.5
5 1/2(r + r - 7) = 599.5
5 1/2(2r - 7) = 599.5
11/2 (2r - 7) = 599.5
2/11 * 11/2 (2r - 7) = 2/11 * 599.5
1 * (2r - 7) = 1199/11
2r - 7 = 109
2r - 7 + 7 = 109 + 7
2r + 0 = 116
2r = 116
1/2 * 2r = 1/2 * 116
1r = 58
r =58
Faster car average speed is 58mph
Slower car average speed is 51mph
Distance = rate * time
d = 51 * 5 1/2
d = 51 * 11/2
d = 280.5
Slower car travel 280.5 miles in 5 1/2hrs
d = 58 * 5 1/2
d = 58 * 11/2
d = 319 or 599.5 - 280.5 = 319
Faster car travel 319 miles in 5 1/2 hrs
The slower car travels 280.5 miles in 5 1/2hrs. remainder of trips for both vehicle is 38.5 miles, because, 319 - 280.5 = 38.5
distance = rate * time
38.5 = 51 (t)
1/51(38.5) = 1/51(51)(t)
38.5/51 = 1t
77/102 = t, This time is in hours. To convert to minutes, multiply by 60 minutes per hour
77/102 * 60 = 77/51 * 30 = 2310/51 = 45, The slower car will arrive at about 45 minutes after the first car.
Hope this helps!!!
Next time please ask for help in chunks!! Try for yourself.. this is a lot...
In the chart of the triangle it shows that the variable b is the base. It also give us the equation for area 1/2bh (half of base * height)
Now we just plug in the values we are given
1/2bh
1/2(10*13)
1/2(130)
65
The area of the triangle is 65 ft
K = 917 + 6(w + h - a)
k = 1925
w = 119
a = 25
1925 = 917 + 6(119 + h - 25) =
1925 = 917 + 6(h + 94)
1925 = 917 + 6h + 564
1925 = 1481 + 6h
1925 - 1481 = 6h
444 = 6h
444/6 = h
74 = h........she is 74 inches tall
Answer:
x⁷ = 60
Step-by-step explanation:
<u>Given</u><u> </u><u>:</u><u>-</u><u> </u>
<u>To </u><u>Find</u><u> </u><u>:</u><u>-</u><u> </u>
- The expotential equation .
<u>Solution</u><u> </u><u>:</u><u>-</u><u> </u>
Given logarithmic equation is ,
⇒ log x⁵ + log x ¹² = 7
⇒ log x ⁵ * ¹² = 7 [ log aⁿ + log aⁿ' = log aⁿ * ⁿ' ]
⇒log x ⁶⁰ = 7
In expotential form we can write it as ,
⇒ x⁷ = 60
