Step-by-step answer:
Given:
A triangle
Perimeter = 60 cm
longest side = 4* shortest side (x)
Solution:
longest side = 4x
shortest side = x
third (intermediate side = 60 -x -4x = 60-5x
The triangle inequality specifies that the sum of the two shorter sides must be greater than the longest side to form a triangle. Hence
x + y > 4x
x + 60-5x > 4x
60 - 4x > 4x
8x < 60
x < 60/8 = 7.5, or
x < 7.5
Therefore to form a triangle, x (shortest side) must be less than 7.5 cm.
Examine the options: both 7 and 5 are both less than 7.5 cm.
40, 30 and 25 all have a problem because the longest side (4 times longer) will exceed the perimeter of 60.
Now also examine cases where 4x is NOT the longest side, in which case we need
4x>=y
or
4x >= 60-5x
9x >=60
x >= 6.67
so x=5 will not qualify, because 4x will no longer be the longest side.
The only valid option is x=7 cm
The side lengths for x=7 and x=5 are, respectively,
(7, 25, 28)
5, 20, 35 (in which case, the longest side is no longer 4x=20, so eliminated)
Answer:
b. Nolinear Positive association
Step-by-step explanation:
have a nice day! ^w^
Answer:
x = 1/8
Step-by-step explanation:
- 24x = - 3
Divide both sides by - 24
x = -3/-24
x = 1/8
Answer:it will take 5 months for the cumulative costs of the plans to be equal and the total cos is $200
Step-by-step explanation:
Let x represent the number of months that for which the cumulative costs of the plans will be equal.
Let y represent the total cost of using plan A for x months.
Let z represent the total cost of using plan B for x months.
He can either pay a $150 joining fee and a $10 monthly fee. This means that the total cost of using plan A would be
y = 150 + 10x
For plan B, he can pay a $50 joining fee and a $30 monthly fee. This means that the total cost of using plan B would be
y = 50 + 30x
To determine the number of hours for which the cumulative costs of the plans will be equal, we would equate y to z. It becomes
150 + 10x = 50 + 30x
30x - 10x = 150 - 50
20x = 100
x = 100/20 = 5 months
The total cost would be
150 + 10 × 5 = 150 + 50 = $200
