4 + 2x = 7
2x = 7 - 4 = 3
x = 3/2 = 1.5 inches
The solution to the equation x(x+4) = 6 is x = -2 + √10 or x = -2 - √10 after solving with the quadratic formula.
<h3>What is a quadratic equation?</h3>
Any equation of the form
where x is variable and a, b, and c are any real numbers where a ≠ 0 is called a quadratic equation.
As we know, the formula for the roots of the quadratic equation is given by:
![\rm x = \dfrac{-b \pm\sqrt{b^2-4ac}}{2a}](https://tex.z-dn.net/?f=%5Crm%20x%20%3D%20%5Cdfrac%7B-b%20%5Cpm%5Csqrt%7Bb%5E2-4ac%7D%7D%7B2a%7D)
We have an equation:
x(x + 4) = 6
By distributive property:
x² + 4x = 6
x² + 4x - 6 = 0
a = 1, b = 4, c = -6
Plugging all the values in the formula:
![\rm x = \dfrac{-4 \pm\sqrt{4^2-4(1)(-6)}}{2(1)}](https://tex.z-dn.net/?f=%5Crm%20x%20%3D%20%5Cdfrac%7B-4%20%5Cpm%5Csqrt%7B4%5E2-4%281%29%28-6%29%7D%7D%7B2%281%29%7D)
After calculating:
![\rm x = \dfrac{-4 \pm\sqrt{40}}{2}](https://tex.z-dn.net/?f=%5Crm%20x%20%3D%20%5Cdfrac%7B-4%20%5Cpm%5Csqrt%7B40%7D%7D%7B2%7D)
![\rm x=-2+\sqrt{10},\ \ \ or \ \ \ x=-2-\sqrt{10}](https://tex.z-dn.net/?f=%5Crm%20x%3D-2%2B%5Csqrt%7B10%7D%2C%5C%20%5C%20%5C%20or%20%5C%20%5C%20%5C%20x%3D-2-%5Csqrt%7B10%7D)
Thus, the solution to the equation x(x+4) = 6 is x = -2 + √10 or x = -2 - √10 after solving with the quadratic formula.
Learn more about quadratic equations here:
brainly.com/question/2263981
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Answer:
0.6
Step-by-step explanation:
The x increases by 5, while y increases by 3
Lets use the method, which is
.
Keep in mind that x goes horizontally along the axis, while y goes vertically on the axis.
So plug the numbers in.
0.6
Hence, the constant proportionality is 0.6.
Multiply the equation:
![2x+2y=8 \mapsto 6x+6y=24](https://tex.z-dn.net/?f=%202x%2B2y%3D8%20%5Cmapsto%206x%2B6y%3D24%20)
The solution set is the same, because multiplying both sides of an equation by a non-zero number doesn't change the solution set. In fact, if you rewrite the equation as
![2x+2y-8=0](https://tex.z-dn.net/?f=%202x%2B2y-8%3D0%20)
Multiplying this by 3 (or whatever number, for all it matters) gives
![3(2x+2y-8)=0](https://tex.z-dn.net/?f=%203%282x%2B2y-8%29%3D0%20)
Now, a product is zero if and only if at least one of the factor is zero. So, either
or ![2x+2y-8=0](https://tex.z-dn.net/?f=%202x%2B2y-8%3D0%20)
Since the first is clearly impossible, the second one must be true, which is the original equation.
So you have 3/4x2/3 because it's 2/3 of the bag left, so you find the least common denominator (bottom number of fraction), which in this case is 12, so you find how you get to 12 for each of the bottom numbers, so x3 on the first one, and x4 on the other one. then you multiply the top numbers by what you multiply the bottom ones by, so it would be 9/12x8/12 you then multiply both numbers so 72/144 and then you simplify that to 1/2 so it's 1/2lb.