X = 5
Move the variable then cells to like terms and simplify
Answer: Choice B) x < 10
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Explanation:
There's 300 square feet total (land+water). Of that, 100 sq ft is taken up by the pond, so we have 300-100 = 200 sq ft of dry land.
1 duck needs more than 20 sq ft of dry land
2 ducks need more than 40 sq ft of dry land (note how 2*20 = 40)
3 ducks need more than 60 sq ft of dry land (note how 3*20 = 60)
and so on...
In general,
x ducks need more than 20*x square feet of dry land
The max amount of dry land we have is 200 sq ft
The total amount of space the ducks take up must be less than 200 sq ft
In terms of symbols, we have
T = total space ducks take up on dry land
T = 20*x
T < 200
So we can arrive at this inequality
20*x < 200
after replacing the "T" with "20*x"
Afterward, divide both sides by 20
20*x < 200
20*x/20 < 200/20
x < 10
So we must have less than 10 ducks
If we had 10 ducks exactly, then they would take up more than 20*10 = 200 sq ft, but we only have 200 sq ft
The largest number of ducks we can have is 9 ducks.
So that's why we have a "less than" symbol instead of a "less than or equal to" symbol.
The scale has two sides:
The Left Hand Side (LHS) and the Right Hand Side (RHS).
Let the weight of the sphere be represented as s
Let the weight of the cube be represented as c
Let the LHS have the 5 spheres and 1 cube, represented as = (5s + 1c)
Let the RHS have the 2 spheres and 3 cubes, represented as = (2s + 3c)
If the cube c, weighs 150 gram, c = 150g
Since the scale is balanced, therefore the weights on the LHS would be equal to the weights on the RHS.
Therefore: (5s + 1c) = (2s + 3c), c = 150.
(5s + 1*150) = (2s + 3*150)
(5s + 150) = (2s + 450) collect like terms.
5s - 2s = 450 - 150
3s = 300 Divide both sides by 3
s = 300/3
s = 100
Therefore the sphere weighs 100 gram each.
Answer:
9. x = 7
10. x = 12
Step-by-step explanation:
Assume the two lines are parallel.
9. The corresponding angles are congruent.
9x - 3 = 7x + 11
2x = 14
x = 7
10. The alternate interior angles are congruent.
5x - 20 = 2x + 16
3x = 36
x = 12
Y= 6// 2(6+3)=18 because 6+ 3= 9 and 9x 2 = 18
