Nine wholes with five twelves
9 5/12
9514 1404 393
Answer:
- 4
- -2
- 4
- 2
- -2±√2
Step-by-step explanation:
In order to fill the first blank, we need to look at the second line to see what the coefficient of x is.
1. x² +<u> </u><u>4 </u>x +2 = 0
The constant is subtracted from both sides to get the second line.
2. x² +4x = <u> -2 </u>
The value that is added on the third line is the square of half the x-coefficient: (4/2)² = 4
3. x² +4x +<u> 4 </u> = -2 +4
On the fourth line, the left side is written as a square, and the right side is simplified. The square root is taken of both sides.
4. √(x +2)² = ±√<u> 2 </u>
Finally, 2 is subtracted from both sides to find the values of x.
5. x = <u> -2 ±√2 </u>
Answer:
Both the boats will closet together at 2:21:36 pm.
Step-by-step explanation:
Given that - At 2 pm boat 1 leaves dock and heads south and boat 2 heads east towards the dock. Assume the dock is at origin (0,0).
Speed of boat 1 is 20 km/h so the position of boat 1 at any time (0,-20t),
Formula : d=v*t
at 2 pm boat 2 was 15 km due west of the dock because it took the boat 1 hour to reach there at 15 km/h, so the position of boat 2 at that time was (-15,0)
the position of boat 2 is changing towards east, so the position of boat 2 at any time (-15+15t,0)
Formula : D=
⇒ 
Now let 
∵ 
⇒ t= 450/1250
⇒ t= .36 hours
⇒ = 21 min 36 sec
Since F"(t)=0,
∴ This time gives us a minimum.
Thus, The two boats will closet together at 2:21:36 pm.
Answer:



Step-by-step explanation:








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Answer:
Answers are below in bold
Step-by-step explanation:
1) A = 1/2bh Use this equation to find the area of each triangular base
A = 1/2(8)(6) Multiply
A = 1/2(48) Multiply
A = 12cm² Area of each triangular base
2) A = L x W Use this equation to find the area of the bottom rectangular face
A = 20 x 8 Multiply
A = 160 cm² Area of the bottom rectangular face
3) A = L x W Use this equation to find the area of the back rectangular face
A = 20 x 6 Multiply
A = 120 cm² Area of the back rectangular face
4) A = L x W Use this equation to find the area of the sloped rectangular face
A = 20 x 10 Multiply
A = 200 cm² Area of the sloped rectangular face
5) To find the total surface area of the triangular prism, add together all of the numbers.
A = 12 + 12 + 160 + 120 + 200 Add
A = 504 cm² Total area of the triangular prism