The salsa recipe uses green pepper, onion and tomato in the extended ration 3:7:11. How many green peppers are needed to make 18
2 answers:
Answer:
27 cups green pepper uses for making salsa .
Option (B) is correct .
Step-by-step explanation:
As given
The salsa recipe uses green pepper, onion and tomato in the extended ration 3:7:11.
Let us assume that the x be the scalar multiple .
Green pepper used for making salsa = 3x
Onion used for making salsa = 7x
Tomato used for making salsa = 11x
As given
green pepper, onion and tomato are used for making 189 cups of salsa .
Eqution becomes
3x + 7x + 11x = 189
21x = 189
x = 9
Thus
Green pepper used for making salsa = 3x
= 3 × 9
= 27 cups
Therefore 27 cups green pepper uses for making salsa .
Option (B) is correct .
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Answer: x = 5*sqrt(10)
"sqrt" stands for "square root"
-------------------------------------------------------
Refer to the attached image. The figure is not to scale. Notice how I've added in y and z (blue and red respectively)
The length y is the bottom horizontal leg for the triangle on the right.
The length z is the bottom horizontal leg for the triangle on the left.
To find x, we need to find y first, which will help us find z, and then we can finally get to x.
Let's find y first
To do this, we use the pythagorean theorem
a^2 + b^2 = c^2
y^2 + 9^2 = 15^2
y^2 + 81 = 225
y^2 + 81-81 = 225-81
y^2 = 144
sqrt(y^2) = sqrt(144)
y = 12 ... keep in mind that y is a length, so it needs to be positive
Notice how the y and z lengths combine to form a total length of 25 units
Therefore,
y+z = 25
12+z = 25
12+z-12 = 25-12
z = 13
Now that we know z = 13, we can find x. Again we use the pythagorean theorem one last time
a^2 + b^2 = c^2
z^2 + 9^2 = x^2
13^2 + 9^2 = x^2
169 + 81 = x^2
250 = x^2
x^2 = 250
sqrt(x^2) = sqrt(250)
x = sqrt(250)
x = sqrt(25*10)
x = sqrt(25)*sqrt(10)
x = 5*sqrt(10)
This is in simplest radical form as we can't factor 10 any further (there are no perfect square factors that go into 10). This is the exact length of side x
Note: using a calculator, 5*sqrt(10) = 15.8113883008419 approximately
"sqrt" stands for "square root"
-------------------------------------------------------
Refer to the attached image. The figure is not to scale. Notice how I've added in y and z (blue and red respectively)
The length y is the bottom horizontal leg for the triangle on the right.
The length z is the bottom horizontal leg for the triangle on the left.
To find x, we need to find y first, which will help us find z, and then we can finally get to x.
Let's find y first
To do this, we use the pythagorean theorem
a^2 + b^2 = c^2
y^2 + 9^2 = 15^2
y^2 + 81 = 225
y^2 + 81-81 = 225-81
y^2 = 144
sqrt(y^2) = sqrt(144)
y = 12 ... keep in mind that y is a length, so it needs to be positive
Notice how the y and z lengths combine to form a total length of 25 units
Therefore,
y+z = 25
12+z = 25
12+z-12 = 25-12
z = 13
Now that we know z = 13, we can find x. Again we use the pythagorean theorem one last time
a^2 + b^2 = c^2
z^2 + 9^2 = x^2
13^2 + 9^2 = x^2
169 + 81 = x^2
250 = x^2
x^2 = 250
sqrt(x^2) = sqrt(250)
x = sqrt(250)
x = sqrt(25*10)
x = sqrt(25)*sqrt(10)
x = 5*sqrt(10)
This is in simplest radical form as we can't factor 10 any further (there are no perfect square factors that go into 10). This is the exact length of side x
Note: using a calculator, 5*sqrt(10) = 15.8113883008419 approximately