Answer:
<u>Triangle ABC and triangle MNO</u> are congruent. A <u>Rotation</u> is a single rigid transformation that maps the two congruent triangles.
Step-by-step explanation:
ΔABC has vertices at A(12, 8), B(4,8), and C(4, 14).
- length of AB = √[(12-4)² + (8-8)²] = 8
- length of AC = √[(12-4)² + (8-14)²] = 10
- length of CB = √[(4-4)² + (8-14)²] = 6
ΔMNO has vertices at M(4, 16), N(4,8), and O(-2,8).
- length of MN = √[(4-4)² + (16-8)²] = 8
- length of MO = √[(4+2)² + (16-8)²] = 10
- length of NO = √[(4+2)² + (8-8)²] = 6
Therefore:
and ΔABC ≅ ΔMNO by SSS postulate.
In the picture attached, both triangles are shown. It can be seen that counterclockwise rotation of ΔABC around vertex B would map ΔABC into the ΔMNO.
Answer:
<em><u>263.76</u></em><em><u> </u></em><em><u>in</u></em><em><u>^</u></em><em><u>3</u></em>
VOLUME OF FIGURE=VOL.OF CONE+VOL.OF CYLINDER +VOL.OF HEMISPHERE
=(1/3×3.14×3×3×4)+(3.14×3×3×6)+(2/3×3.14×3×3×3)
=37.68+169.56+56.52
=263.76in^3
Answer:
$3.75
Step-by-step explanation:
5*0.75 = 3.75
Just multiply the two numbers together.
Answer:
$159.84
<u>What we know - 4 bags cost $39.96</u>
<u>What we need to know - How much 16 bags cost</u>
Step-by-step explanation:
We can solve this by simply knowing how many times 4 goes into 16. We can do this by writing the equation 16 ÷ 4 = 4. We now know that 4 goes into 16 4 times. By doing this we can now multiply $39.96 by 4 to get the cost of 16 bags which is $159.84.
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Answer:
They need to sell 9400 pies to reach the break-order point
Step-by-step explanation:
* Lets explain the break-order point
- The break-order point is the point at which total cost and total
revenue are equal
∴ The total cost = The total revenue
* Lets solve the problem
∵ The equation of the total cost is y = 0.65x + 1410
∵ The revenue equation is y = 0.8x
- To find the break-order point equate the two equations
∴ 0.65x + 1410 = 0.8x
- Subtract 0.65x from both sides
∴ 1410 = 0.8x - 0.65x
∴ 0.15x = 1410
- Divide both sides by 0.15
∴ x = 1410/0.15 = 9400
∵ x is the number of pies
* They need to sell 9400 pies to reach the break-order point