Answer:
36
Step-by-step explanation:
first, see the formula in the attached picture.
now, by applying that formula we get :
the coefficient of the x7y2 is :
9C7 = 36 (you can either use a calculator or just the algebraic formula)
Help with inequalities
1 answer:
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Question:
The numerator and denominator of a fraction are in the ratio of 3 to 5. If the numerator and denominator are both decreased by 2, the fraction is now equal to .
If n = the numerator and d = the denominator, which of the following systems of equations could be used to solve the problem?
5n = 3d and n - 2 = 2d - 4
5n = 3d and 2n - 4 = d - 2
3n = 5d and 2n - 4 = d - 2
Answer:
5n = 3d and 2n – 4 = d – 2
Solution:
Let n be the numerator of the fraction and d be the denominator of the fraction.
Given the numerator and denominator of a fraction are in the ratio of 3 to 5.
This can be written as n : d = 3 : 5.
⇒ – – – – (1)
Do cross multiplication, we get
⇒ 5n = 3d
When the numerator and denominator are decreased by 2, the fraction is equal to .
⇒
Do cross multiplication, we get
⇒ 2(n –2)=1(d – 2)
⇒ 2n – 4 = d – 2
Hence, 5n = 3d and 2n – 4 = d – 2 can be used to solve the problem.
Answer:
The lengths of the sides of the playground are 14 feet, 6 feet, 7 feet
Step-by-step explanation:
At first, let us find the perimeter of the playground
∵ Perimeter of a triangle is P = S1 + S2 + S3
∵ The sides of the triangular playground are (2x) ft, (x - 1) ft, and x ft
∴ S1 = 2x, S2 = x - 1, S3 = x
→ Substitute them in the rule of the perimeter above
∵ P = 2x + x - 1 + x
→ Add the like terms
∴ P = (2x + x + x) - 1
∴ P = 4x - 1
∵ The perimeter of this playground is 27 feet
∴ P = 27
→ Equate the two values of P
∴ 4x - 1 = 27
→ Add 1 to both sides
∴ 4x - 1 + 1 = 27 + 1
∴ 4x = 28
→ Divide both sides by 4
∵ =
∴ x = 7
→ Substitute the value of x in each side to find their lengths
∵ S1 = 2(7)
∴ S1 = 14 feet
∵ S2 = 7 - 1
∴ S2 = 6 feet
∵ S3 = 7 feet
∴ The lengths of the sides of the playground are 14 feet, 6 feet, 7 feet