1) x = - 4, y = - 12; (- 4, - 12)
2) x = 34, y = 17; (34, 17)
3) x = 16, y = 7; (16, 7)
4) x = 7, y = - 4; (7, - 4)
5) x = - 4, y = 10; (- 4, 10)
6) x = 12, y = - 7; (12, - 7)
7) x = 5, y = 10; (5, 10)
8) x = 11, y = - 12; (11, - 12)
You would use the function root(Xsub2-Xsub1)^2+(Ysub2-Ysub1)^2.
Now plug in your numbers.
This gives you root(7-1)^2+(5-(-3))^2.
Simplify to root(6)^2+(8)^2. Simplify again to root36+64.
Simplify one more time to root 100. now solve.
Your answer is 10.
Let's look at each answer choice's words per minute:
A) 320/8 = 40
B) 600/12 = 50
C) 350/10 = 35
D) 225/5 = 45
The fastest is 50 words/min which is B
The vertex form of the function gives the vertex as (-6,48). The vertex of f(x)=x^2 is (0,0) so from this information, the vertex is moved LEFT 6 and UP 48. This cancels out two options. The coefficient -3 tells us that the graph is flipped or reflected over the x-axis (negative sign flips graph) and that all y-values will be 3 times as large. Larger y-values for the same x inputs makes the graph narrower.
Answer:
5.44 cm³
Step-by-step explanation:
The volume of the hexagonal nut can be found by multiplying the area of the end face by the length of the nut. The end face area is the difference between the area of the hexagon and the area of the hole.
The area of a hexagon with side length s is given by ...
A = (3/2)√3·s²
For s=1 cm, the area is ...
A = (3/2)√3(1 cm)² = (3/2)√3 cm²
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The area of a circle is given by ...
A = πr²
The radius of a circle with diameter 1 cm is 0.5 cm. Then the area of the hole is ...
A = π(0.5 cm)² = 0.25π cm²
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The volume is the face area multiplied by the length, so is ...
V = Bh = ((3/2)√3 -0.25π)(3) . . . . . cm³
V = (9/2)√3 -0.75π cm³ ≈ 5.44 cm³
The volume of the metal is about 5.44 cm³.
