Posted by kathy on Monday, September 26, 2011 at 8:05pm.
1.the square og 2 is the same as two times the difference of g and 10.
2. the product of 3 and the square of g equals the sum of thirty and the product of nine and g.
i really need help on this i don't get it.
thanks
To solve these equations, let's break them down step by step:
1. "The square of 2 is the same as two times the difference of g and 10."
To translate this into an equation, you can start by representing "the square of 2" as 2 * 2 or 2^2. The "difference of g and 10" can be represented as g - 10. Putting it all together, the equation becomes:
2^2 = 2 * (g - 10)
Simplifying further:
4 = 2g - 20
Now, isolate the variable g by moving the constant term to the other side of the equation:
2g = 4 + 20
2g = 24
Finally, divide both sides of the equation by 2 to solve for g:
g = 12
2. "The product of 3 and the square of g equals the sum of thirty and the product of nine and g."
Similarly, start by representing "the square of g" as g^2. "The product of 3 and the square of g" can then be written as 3 * g^2. The "product of nine and g" can be represented as 9 * g. The equation becomes:
3 * g^2 = 30 + 9 * g
Simplifying further:
3g^2 = 30 + 9g
Now, bring all the terms to one side of the equation to form a quadratic equation:
3g^2 - 9g - 30 = 0
Next, try factoring or use the quadratic formula to solve for g. If factoring is not possible, you can use the quadratic formula:
g = (-b ± √(b^2 - 4ac)) / (2a)
For the equation 3g^2 - 9g - 30 = 0, a = 3, b = -9, and c = -30. Plugging these values into the quadratic formula:
g = (-(-9) ± √((-9)^2 - 4 * 3 * (-30))) / (2 * 3)
g = (9 ± √(81 + 360)) / 6
g = (9 ± √441) / 6
Finally, simplify the square root:
g = (9 ± 21) / 6
This gives two possible solutions for g:
g = (9 + 21) / 6 or g = (9 - 21) / 6
g = 30 / 6 or g = -12 / 6
g = 5 or g = -2
So the solutions for g are g = 5 or g = -2.