Hello,
The line passes through (-1,3) and (9,11)
slope=(11-3)/(9+1)=8/10=4/5
y-3=4/5(x+1)
==>y=4/5 *x +19/5
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.
answer
10
step-by-step explanation
the equation given is sin(x) = cos(y) with x = 2k + 3 and y = 6k + 7
substitute in 2k+ 3 for x in sin(x) and substitute in 6k + 7 for y in cos(y)
sin(x) = cos(y)
sin(2k + 3) = cos(6k + 7)
we know that sin(x) = cos(90 -x)
sin(2k + 3)
= cos(90 - (2k + 3) )
= cos(90 - 2k - 3)
= cos(87 - 2k)
substitute this into the equation sin(2k + 3) = cos(6k + 7)
sin(2k + 3) = cos(6k + 7)
cos(87 - 2k) = cos(6k + 7)
87 - 2k = 6k +7
80 = 8k
k = 10
Answer:
6 hours
Step-by-step explanation:
Given that:
Time taken by Sam = 3 hours
Sam's rate = 1/3
Time taken : Sam + Laura = 2 hours
Sam's rate + Laura's rate = 1/2
Let time taken by Laura = x
1/3 + 1/x = 1/2
1/x = 1/2 - 1/3
1/x = (3 - 2) / 6
1/x = 1 /6
x = 6
Hencw, it will take 6 hours for Laura alone to rake leaves
1/4=4/16 so the can has 3 servings and a some leftovers that are smaller than a serving. I think the answer is 3.
