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Genrish500 [490]
3 years ago
8

A recipe for chicken marinade says, ''Mix 3 parts oil with 2 parts soy sauce and 1 part orange juice. ''if you need 42 cups of m

arinade in all,how much of each ingredient should you see?
Mathematics
1 answer:
Alla [95]3 years ago
4 0

Answer:

Parts of oil in 42 cups of marinade = 21 cups

Parts of soy sauce in 42 cups of marinade = 14 cups

Parts of orange juice in 42 cups of marinade = 7 cups

Step-by-step explanation:

Given that:

Parts of oil = 3

Parts of soy sauce = 2

Part of orange juice = 1

Total cups of marinade = 42

To find:

How much of each ingredient should be there ?

Solution:

This problem can be solved by taking the ratio of ingredients into account.

The ratio is:

Oil : Soy Sauce : Orange Juice = 3 : 2 : 1

So, we can let the parts of oil = 3x

Parts of soy sauce = 2x

Parts of orange juice = x

As per the question statement:

3x+2x+x=42\\\Rightarrow 6x=42\\\Rightarrow x =7

So, parts of oil in 42 cups of marinade = 3 \times 7 = 21 cups

Parts of soy sauce in 42 cups of marinade = 2 \times 7 = 14 cups

Parts of orange juice in 42 cups of marinade = 7 cups

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AlladinOne [14]

Answer:

(a) The zeroes of f(x) are rational numbers

(b) The smallest integer value of a is 3

Step-by-step explanation:

In the quadratic function f(x) = ax² + bx + c, we can know the number and the types of its roots using the discriminant  Δ, where Δ = b² - 4ac

  • If Δ > 0, then the zeroes are two different real numbers
  • If Δ = 0, then the zeroes are the same real number
  • If Δ < 0, then the zeroes are imaginary numbers

Note: In the first case if Δ is a perfect square number then the zeroes are rational, if not then the zeroes are irrational

(a)

∵ The equation function is f(x) = ax² + 11x + 12

∵ a = 2

∴ a = 2, b = 11 and c = 12

→ Substitute them in the rule of Δ

∵ Δ = (11)² - 4(2)(12) = 121 - 96

∴ Δ = 25

∵ Δ > 0

∴ f(x) has two different real zeroes

∵ 25 is a perfect square number

→ That means the zeroes of the function are rational numbers

∴ The zeroes of f(x) are rational numbers

(b)

∵ f(x) ha imaginary zeroes

→ By using the third rule above

∴ Δ < 0

∵ a = a, b = 11 and c = 12

→ Substitute them in the rule of Δ

∴ (11)² - 4(a)(12) < 0

∴ 121 - 48a < 0

→ Add 48a to both sides

∵ 121 - 48a + 48a < 0 + 48a

∴ 121 < 48a

→ Divide both sides by 48

∴ 2.52083 < a

∴ a > 2.52083

∵ The smallest integer greater than 2.52083 is 3

∴ The smallest integer value of a is 3

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