Solve x (PLEASE HELP!!) (10x-4) ---------- = 20 5
2 answers:
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<h3>Answer: x = 7</h3>
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Explanation:
The largest rectangle (composed of the green and yellow sections combined) has area of 11*12 = 132 cm^2.
The yellow region takes up 112 of those 132 sq cm. This must mean the green region takes up 132-112 = 20 cm^2.
The horizontal portion of the green rectangle is 12-x cm. The vertical portion is 11-x cm. We can form the area of the green rectangle as an algebraic expression like so
area = length*width
area = (11-x)*(12-x)
area = 132 - 11x - 12x + x^2 .... apply the FOIL rule
area = x^2 - 23x + 132
Set this equal to the 20 cm^2 we found earlier.
x^2 - 23x + 132 = 20
x^2 - 23x + 132-20 = 0
x^2 - 23x + 112 = 0
We could factor or we could use the quadratic formula. I'll go with the second option.
We'll plug in a = 1, b = -23, c = 112
One of these solutions isn't feasible. Note how if x = 16, then this exceeds both the 11 cm and 12 cm sides. So this x value is not possible.
However, x = 7 is possible.
If x = 7, then the horizontal portion of the green rectangle is 12-x = 12-7 = 5 cm. Also, the vertical portion of the green rectangle would be 11-x = 11-7 = 4 cm. The area then is length*width = 5*4 = 20 cm^2 which matches up with what we got earlier. So the answer is confirmed.
Short answer: (-8)^2 + 8 x -8 = 0
Use PEMDAS
"Evaluate the expression" just means solve until you can't simplify anymore. You must solve it in a certain order according to PEMDAS: Parentheses, Exponents, Multiply, Divide, Add, Subtract.
What does the beginning of the expression look like? It is
.
According to PEMDAS, you must solve what is in the parentheses *first*. But, since there is only a number (-8), there is nothing to solve for and you can move on to exponents.
The squared symbol, the little 2, means you have to square what is *inside* the parentheses. = 64, because -8 times itself is 64.
Next comes multiplication. Remember, we are not working from left to right. We must multiply the values on the far right before we do any adding, because multiplication comes *before* addition.
(64) + (8 times -8)
(64) + (-64)
Finally, we can add. In this case, because we are adding a negative number, we are really subtracting. 64 + -64 equals 0.
Use PEMDAS
"Evaluate the expression" just means solve until you can't simplify anymore. You must solve it in a certain order according to PEMDAS: Parentheses, Exponents, Multiply, Divide, Add, Subtract.
What does the beginning of the expression look like? It is
According to PEMDAS, you must solve what is in the parentheses *first*. But, since there is only a number (-8), there is nothing to solve for and you can move on to exponents.
The squared symbol, the little 2, means you have to square what is *inside* the parentheses.
Next comes multiplication. Remember, we are not working from left to right. We must multiply the values on the far right before we do any adding, because multiplication comes *before* addition.
(64) + (8 times -8)
(64) + (-64)
Finally, we can add. In this case, because we are adding a negative number, we are really subtracting. 64 + -64 equals 0.