Answer:
Alternate Interior Angles
Step-by-step explanation:
The angles are on opposite sides of the transversal and are in between the parallel lines. This means they are alternate Interior Angles. Additionally, this means they are congruent, so 15x=12x+15, which gives us x=5, and the measurements of the angles are 75° each.
Answer:
The garden is 9 feet wide and 26 feet long.
Step-by-step explanation:
L = W+17
area = LW = 234
(W+17)W = 234
W²+17W-234 = 0
Quadratic formula
W = [-17 ± √(17² – 4·1(-234))] / [2·1]
= [-17 ± √1225] / 2
= [-17 ± 35] /2
= -26, 9
-26 is an extraneous solution
W = 9
L = W+17 = 26
The garden is 9 feet wide and 26 feet long.
9 9x5=45
5,10,15,20,25,30,35,40,45
9
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.
Answer: It would be 50,000
Step-by-step explanation: If it was 50,500 - 50,999 it would be : 51,000
Hope it helped out :)
