You have a metal plate that you have drilled a hole into. The entire area enclosed by the metal plate is given by 5x^2 = 12x + 10 and the area of the hole is given by x^2+2. Write an expression for the area in factored form of the plate that is left after the hole is drilled.
To find the area of the plate left after the hole is drilled, we need to subtract the area of the hole from the entire area enclosed by the metal plate.
The entire area enclosed by the metal plate is given by 5x^2 = 12x + 10.
The area of the hole is given by x^2 + 2.
To find the area in factored form, we can factor each equation individually.
The equation for the entire area enclosed by the metal plate, 5x^2 = 12x + 10, can be rearranged to the form:
5x^2 - 12x - 10 = 0.
To factor this quadratic equation, we need to find two numbers whose product is (-10)(5) = -50 and whose sum is -12 (the coefficient of x). After simplifying several possibilities, the factored form of 5x^2 - 12x - 10 = 0 is:
(5x + 2)(x - 5) = 0.
The equation for the area of the hole, x^2 + 2, is already in its factored form.
To find the area of the plate left after the hole is drilled, we need to subtract the area of the hole from the entire area enclosed by the metal plate:
(5x + 2)(x - 5) - (x^2 + 2).
= 5x^2 - 25x + 2x - 10 - x^2 - 2.
= 4x^2 - 23x - 12.
Therefore, the expression for the area, in factored form, of the plate that is left after the hole is drilled is: 4x^2 - 23x - 12.
To find the expression for the area of the plate that is left after the hole is drilled, we will first find the equation for the area of the plate itself by subtracting the area of the hole from the total area.
The total area of the plate is given by the equation 5x^2 = 12x + 10, and the area of the hole is given by the equation x^2 + 2. To find the remaining area, we need to subtract the area of the hole from the total area.
So, the expression for the area of the plate that is left after the hole is drilled is:
5x^2 - (x^2 + 2)
Now, let's simplify this expression:
5x^2 - x^2 - 2
Combining like terms, we have:
4x^2 - 2
Therefore, the expression in factored form for the area of the plate that is left after the hole is drilled is:
2(2x^2 - 1)
The sentence "The entire area enclosed by the metal plate..." makes little sense. What is x? IF x is the area, then you have to solve for it in that equation, then subtract by something (if area is x, then you cant subtract x^2+2 from it.
I think someone goofed in constructing this problem.