Answer:
(12, 11, 10)
(2, 3, 4)
(5, 7, 13)
(1, 1, 1)
(7, 10, 3)
(4, 6, 7)
(x, y, x + y) for any positive values of x and y
(x, y, x - y) if x is greater than y and x - y is greater than 0
(x, x, 2) for any positive value of x
Explanation:
The given equation is:
4a + 3 = 7a - 2
To solve for a, we can start by simplifying both sides of the equation. First, we can combine the constants on the right side:
4a + 3 = 7a - 2
4a + 5 = 7a
Next, we can isolate the variable terms on one side of the equation and the constant terms on the other side. Let's subtract 4a from both sides:
4a + 5 = 7a
5 = 3a
Finally, we can solve for a by dividing both sides by 3:
5 = 3a
5/3 = a
Therefore, the solution is:
a = 5/3
We can check this solution by substituting it back into the original equation:
4a + 3 = 7a - 2
4(5/3) + 3 = 7(5/3) - 2
20/3 + 3 = 35/3 - 2
29/3 = 29/3
Since both sides of the equation are equal when we substitute a = 5/3, we can confirm that this is the correct solution.
C 3) 1) 2) B. triangle and a (X) if it does not form a triangle. Which of the following could be the lengths of the sides of a triangle. Put a () if it is forms 12, 11, 10 2, 3, 4 3, 2, 1 4) 5) 6) 7) 7, 13, 7 8) 13, 12, 5 F 9) 3, 7, 10 10) 4, 6, 7 11) x, y, x + y 1 12) x, y, x-y 13) 1, 1, 2 nd all possible value of x.
To determine whether a set of lengths could form the sides of a triangle, we need to check if the sum of the two shorter sides is greater than the longest side. If it is, then the lengths can form a triangle; otherwise, they cannot.
Using this criterion, we can determine which sets of lengths form triangles:
(12, 11, 10) - (O) forms a triangle, since 10 + 11 > 12.
(2, 3, 4) - (O) forms a triangle, since 2 + 3 > 4.
(3, 2, 1) - (X) does not form a triangle, since 1 + 2 is not greater than 3.
(5, 7, 13) - (O) forms a triangle, since 5 + 7 > 13.
(1, 1, 1) - (O) forms a triangle, since all sides are equal.
(8, 8, 16) - (X) does not form a triangle, since 8 + 8 is not greater than 16.
(13, 12, 5) - (O) forms a triangle, since 5 + 12 > 13.
(7, 10, 3) - (X) does not form a triangle, since 3 + 7 is not greater than 10.
(4, 6, 7) - (O) forms a triangle, since 4 + 6 > 7.
(x, y, x + y) - (O) forms a triangle for any positive values of x and y, since x + y is always greater than x and y individually.
(x, y, x - y) - (O) forms a triangle if x is greater than y and x - y is greater than 0.
(1, 1, 2) - (X) does not form a triangle, since 1 + 1 is not greater than 2.
(x, x, 2) - (O) forms a triangle for any positive value of x, since x + x > 2.
Therefore, the sets of lengths that can form triangles are:
(12, 11, 10)
(2, 3, 4)
(5, 7, 13)
(1, 1, 1)
(7, 10, 3)
(4, 6, 7)
(x, y, x + y) for any positive values of x and y
(x, y, x - y) if x is greater than y and x - y is greater than 0
(x, x, 2) for any positive value of x