The correct answers are :
(5x)² ≥ 46
x² + 5x ≤ 46
5x² > 46
<h3>
What is Inequalities?</h3>
A statement of an order relationship—greater than, greater than or equal to, less than, or less than or equal to—between two numbers or algebraic expressions.
Here, Suppose number is x
1) The square of the product of 5 and a number is not less than 46.
Step 1
Product of 5
5x
Step 2
Square of product of 5
(5x)²
Step 3
A number is not less than 46
(5x)² ≥ 46
2) The sum of square of a number and five times that number is not more than 46
Step 1
Square of a number
x²
Step 2
Five times that number
5x
Step 3
The sum = x² + 5x
Step 4
Is not more than 46
x² + 5x ≤ 46
3) The product of 5 and the square of a number is greater than 46
Step 1
The square of a number
x²
Step 2
The product of 5
5x²
Step 3
Is greater than 46
5x² > 46
Thus, The correct answers are :
(5x)² ≥ 46
x² + 5x ≤ 46
5x² > 46
Learn more about Inequality from:
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Answer:
The pints of each of the two existing types of drinks are 22 and 88 respectively.
Step-by-step explanation:
We are given that the Royal Fruit Company produces two types of fruit drinks. The first type is 70% pure fruit juice, and the second type is 95% pure fruit juice. The company is attempting to produce a fruit drink that contains 90% pure fruit juice.
Let the first type of fruit drink pints in the mixture be 'x' and the second type of fruit drink pints in the mixture be 'y'.
So, according to the question;
- <u>The first condition</u> states that we have to make 110 pints of a mixture of two types that is pure fruit juice, that means;
x + y = 110
x = 110 - y ---------------- [equation 1]
- <u>The second condition</u> states that the first type is 70% pure fruit juice, and the second type is 95% pure fruit juice, that means;
![0.70x+0.95y=0.90\times 110](https://tex.z-dn.net/?f=0.70x%2B0.95y%3D0.90%5Ctimes%20110)
![70x+95y=9900](https://tex.z-dn.net/?f=70x%2B95y%3D9900)
![70(110-y)+95y=9900](https://tex.z-dn.net/?f=70%28110-y%29%2B95y%3D9900)
![7700-70y+95y=9900](https://tex.z-dn.net/?f=7700-70y%2B95y%3D9900)
![25y=9900-7700](https://tex.z-dn.net/?f=25y%3D9900-7700)
![y=\frac{2200}{25}](https://tex.z-dn.net/?f=y%3D%5Cfrac%7B2200%7D%7B25%7D)
y = 88
Now, putting the value of y in equation 1 we get;
x = 110 - y
x = 110 - 88 = 22
Hence, the pints of each of the two existing types of drinks are 22 and 88 respectively.
Answer:
b=20 yards
Step-by-step explanation:
15^2+x^2=25^2
225+x^2=625
x^2=400
x=20