Let's try to divide the sentence into multiple parts and then combine it one by one to make it easier to understand.
1. True
2 times y and 6 -------->(2y+6)
the square of the sum of "2 times y and 6" -------->(2y+6)^2
8 times "the square of the sum of 2 times y and 6"------> 8(2y+6)^2
2. True
the difference of x and 7 -------->(x-7)
9 and x -------->(9 + x)
2 times the product of the sum of
"9 and x" and "the difference of x and 7"-------> 2(9 + x) (x-7)
3. True
difference of 5 times x and 3 -------->(5x-3)
the square of the difference of 5 times x and 3------->(5x-3)^2
4. False
The description should be: the product of 7 and the square of x
the product of 7 and x -------->(7x)
the square of the product of 7 and x -------->(7x)^2
5. True
This one should be clear as it was one sentences
the sum of y squared(y^2) and three times y(3y) minus 4-------->y^2+ 3y -4
6. False
The description should be: the product of 5 and 8 times the square of x plus the sum of 20x and 8
the sum of 20x and 8 -------->20x+8
8 plus the square of x plus the sum of 20x and 8-------->8+ x^2 +20x+8
the product of 5 and.... ------->(5)(........
the product of 5 and
8 plus the square of x plus the sum of 20x and 8---->(5)(8+ x^2 +20x+8)
Answer:
Let us say the domain in the first case, has the numbers. And the co-domain has the students, .
Now for a relation to be a function, the input should have exactly one output, which is true in this case because each number is associated (picked up by) with only one student.
The second condition is that no element in the domain should be left without an output. This is taken care by the equal number of students and the cards. 25 cards and 25 students. And they pick exactly one card. So all the cards get picked.
Note that this function is one-one and onto in the sense that each input has different outputs and no element in the co domain is left without an image in the domain. Since this is an one-one onto function inverse should exist. If the inverse exists, then the domain and co domain can be interchanged. i.e., Students become the domain and the cards co-domain, exactly like Mario claimed. So, both are correct!
Answer:
x = 65
Step-by-step explanation:
using the Altitude- on- Hypotenuse theorem
(leg of big Δ )² = (part of hypotenuse below it ) × (whole hypotenuse)
x² = 25 × 169 = 4225 ( take square root of both sides )
x = 
= 65
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