There are 4 doughnuts in 1/3 of a dozen
Answer:
1.
-3x + 8y = -5
6x + 2y = -8
Set the equations to a common variable.
-3x + 8y = -5 → 8y = 3x - 5 → y = 3/8x - 5/8
6x + 2y = -8 → 2y = -6x - 8 → y = -3x - 4
Set the equations equal to each other.
3/8x - 5/8 = -3x - 4
Combine like terms.
3x + 3/8x = -4 + 5/8
3.375x = -3.375
Divide by 3.375
x = -1
Plug x back in to find y.
-3x + 8y = -5
-3(-1) + 8y = -5
3 + 8y = -5
8y = -8
y = -1
answer: (-1, -1)
2.
3x + 2y = -16
-3x - 8y = 46
Set the equations to a common variable.
3x + 2y = -16 → 2y = -3x - 16 → y = -3/2x - 8
-3x - 8y = 46 → -8y = 3x + 46 → y = -3/8x - 23/4
Set the equations equal to each other.
-3/2x - 8 = -3/8x - 23/4
Combine like terms.
-9/8x = 9/4
or
-1.125x = 2.25
Divide by -1.125
x = -2
Plug x back in to find y.
3(-2) + 2y = -16
-6 + 2y = -16
2y = -10
y = -5
answer: (-2, -5)
Without needing fancy formulas, we can conclude that after 10 years, half of the substance will be left. So, we can make our own formula:
amount remaining = 1 / 2^(years/10)
So, after 5 years
amount remaining = 1 / 2^(5/10)
amount remaining = 1 / 2^(.5)
amount remaining = 1 /
<span>
<span>
<span>
1.414213562
</span>
</span></span><span>amount remaining = 0.70711 * 20 grams
</span><span><span><span><span>amount remaining = </span>14.1421356237 grams
</span></span></span>
Answer:
400cm²
Step-by-step explanation:
Total surface area of a prism includes the area of the top and bottom triangle sides of the prism, plus the area of all 3 rectangular sides.
Base & Bottom triangle area: 2 x [(8 x 15)/2] = 120cm²
Side triangle area: 17 x 7 + 8 x 7 + 15 x 7 = 280cm²
Total surface area = 280 + 120 = 400cm²
6-z
Z-6 would be wrong because the question said start with 6
