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a. Okay. So for questions like these, we have to combine like terms and solve this answer out. The problem would look like this: 10x - 6 = 24 + 9x. First, subtract 9x from both sides to get x - 6 = 24. Now, add 6 to both sides and you get x = 30. There is one solution and the equation is neither.
b. Repeat the same thing in this equation. 25 - 4x = 25 - 4x. First, add 4x to both sides to get 25 = 25. There are in infinite number of solutions and the equation is an identity.
c. 4x + 8 = 4x - 13. okay, subtract 4x from both sides, and you get 8 = 13, which is not a true statement. This problem has no solutions and is a contradiction.
Basically, to solve these problems, you have to add or subtract the "x" from the right side first to get the whole number by itself, and then if needed, add or subtract the whole number from the left side. Then, divide each side by the number the "x" is beside to isolate the "x". If the number is a positive, you subtract. If a number is negative, you add. If the number beside the "x" is negative and you have to divide, just divide by the negative. An identity equation has an infinite number of solutions, a contradiction equation has no solutions, and neither just simply means it's not an identity nor contradiction.
<span>Part I: Taylor should deposit her money in a fix deposit account. This is because at the age of 35, she might be having responsibilities. So unless she commits herself, she may end up saving nothing.
Part II: I would state saving for my retirement immediately i start earning. Preferably at my 20s.
Part III: If I am saving for my retirement i would invest in a fixed deposit account. This way my money would be increasing with interest and still getting the dividends at the end of every year. </span>
Answer:
8 Liters
Step-by-step explanation:
Percentage of Alcohol in water= 2L X 0 =0
Percentage of Alcohol to be added = xL X 0.9 =0.9x
- New Volume =(x+2) Liters
- Desired Concentration = 0.72%
Therefore:
0+0.9x=0.72(x+2)
0.9x=0.72x+1.44
Collect like terms
0.9x-0.72x=1.44
0.18x=1.44
Divide both sides by 1.44
x=8 Liters
Therefore, Shanice must add 8 Liters of 90% alcohol solution to create the desired mixture
Answer:
12) ![y = -x - 5](https://tex.z-dn.net/?f=%20y%20%3D%20-x%20-%205%20)
Step-by-step explanation:
![y - y_1 = \dfrac{y_2 - y_1}{x_2 - x_1}(x - x_1)](https://tex.z-dn.net/?f=%20y%20-%20y_1%20%3D%20%5Cdfrac%7By_2%20-%20y_1%7D%7Bx_2%20-%20x_1%7D%28x%20-%20x_1%29%20)
12) (0, -5), (-1, -4)
![y - (-5) = \dfrac{-4 - (-5)}{-1 - 0}(x - 0)](https://tex.z-dn.net/?f=%20y%20-%20%28-5%29%20%3D%20%5Cdfrac%7B-4%20-%20%28-5%29%7D%7B-1%20-%200%7D%28x%20-%200%29%20)
![y + 5 = \dfrac{-4 + 5}{-1}(x)](https://tex.z-dn.net/?f=%20y%20%2B%205%20%3D%20%5Cdfrac%7B-4%20%2B%205%7D%7B-1%7D%28x%29%20)
![y + 5 = \dfrac{1}{-1}(x)](https://tex.z-dn.net/?f=%20y%20%2B%205%20%3D%20%5Cdfrac%7B1%7D%7B-1%7D%28x%29%20)
![y = -x - 5](https://tex.z-dn.net/?f=%20y%20%3D%20-x%20-%205%20)
F(x) = -(x + 8)² - 1
<span>The function (not its graph) decreases on interval [-8, ∞). It is a quadratic function in vertex form. That form makes it easy to pick out the one extremum, where x equals -8. The leading coefficient is negative, so the extremum must be a maximum. The function decreases as x increases from there. </span>
<span>Notice that I include the value -8 in the interval. The function does not have instantaneous decrease at that value, but that is not what it means for a function to be decreasing over an interval. </span>
<span>Let a and b be any two values on [-8, ∞), such that a < b. </span>
<span>-8 ≤ a < b </span>
<span>Then f(a) > f(b). Therefore, function f is decreasing on interval [-8, ∞).</span>