Distribute 1/2 to <span>(n – 4):
</span>
![\frac{1}{2} \times n = \frac{1}{2}n](https://tex.z-dn.net/?f=%5Cfrac%7B1%7D%7B2%7D%20%5Ctimes%20n%20%3D%20%5Cfrac%7B1%7D%7B2%7Dn)
![\frac{1}{2} \times -4 = -2](https://tex.z-dn.net/?f=%5Cfrac%7B1%7D%7B2%7D%20%5Ctimes%20-4%20%3D%20-2)
<span>
Subtract (2n + 3):
</span>
![- (2n + 3) = -2n -3](https://tex.z-dn.net/?f=-%20%282n%20%2B%203%29%20%3D%20-2n%20-3)
<span>
Your equation should now look like this:
</span>
![\frac{1}{2}n - 2 - 3 = 3 - 2n - 3](https://tex.z-dn.net/?f=%5Cfrac%7B1%7D%7B2%7Dn%20-%202%20-%203%20%3D%203%20-%202n%20-%203)
<span>
Combine like terms on both sides:
</span>
![-2 - 3 = -5](https://tex.z-dn.net/?f=-2%20-%203%20%3D%20-5)
![3 - 3 = 0](https://tex.z-dn.net/?f=3%20-%203%20%3D%200)
![\frac{1}{2}n - 5 = -2n](https://tex.z-dn.net/?f=%5Cfrac%7B1%7D%7B2%7Dn%20-%205%20%3D%20-2n)
<span>
Subtract 1/2n from both sides:
</span>
![-5 = -\frac{5}{2}n](https://tex.z-dn.net/?f=-5%20%3D%20-%5Cfrac%7B5%7D%7B2%7Dn)
<span>
Divide both sides by -5/2 to get n by itself:
</span>
![n = 2](https://tex.z-dn.net/?f=n%20%3D%202)
<span>
The value of n is
2.</span>
Answer:
1. Consulting (agricultural, environmental, public health, urban, food processing)
2. State and federal government agencies.
3. Conservation and environmental biology.
4. Pharmaceutical industry.
5. Natural resources management
Answer:
You can decide where to put the first digit because you know 153 doesn't fit into 6 or 61. But you know it can fit into 613. You put it there.
Answer:
p is equal to 8.125
Step-by-step explanation:
Direct proportion formula : Y = kx ,k is constant
p = x = 3.2
r = y = 4
4 = k * 3.2
k = 4/3.2 = 1.25
y = 1.25x
Now, substitute x = 6.5 and find y.
y = 1.25 * 6.5 = 8.125
Hence p is equal to 8.125
we have
![7=-2x^{2} +10x](https://tex.z-dn.net/?f=7%3D-2x%5E%7B2%7D%20%2B10x)
Factor the leading coefficient
![7=-2(x^{2} -5x)](https://tex.z-dn.net/?f=7%3D-2%28x%5E%7B2%7D%20-5x%29)
Complete the square. Remember to balance the equation by adding the same constants to each side
![7-12.50=-2(x^{2} -5x+2.5^{2})](https://tex.z-dn.net/?f=7-12.50%3D-2%28x%5E%7B2%7D%20-5x%2B2.5%5E%7B2%7D%29)
![-5.50=-2(x^{2} -5x+2.5^{2})](https://tex.z-dn.net/?f=-5.50%3D-2%28x%5E%7B2%7D%20-5x%2B2.5%5E%7B2%7D%29)
Divide both sides by ![-2](https://tex.z-dn.net/?f=-2)
![2.75=(x^{2} -5x+2.5^{2})](https://tex.z-dn.net/?f=2.75%3D%28x%5E%7B2%7D%20-5x%2B2.5%5E%7B2%7D%29)
Rewrite as perfect squares
![2.75=(x-2.5)^{2}](https://tex.z-dn.net/?f=2.75%3D%28x-2.5%29%5E%7B2%7D)
Taking the square roots of both sides (square root property of equality)
![x-2.5=(+/-)\sqrt{2.75}](https://tex.z-dn.net/?f=x-2.5%3D%28%2B%2F-%29%5Csqrt%7B2.75%7D)
Remember that
![\sqrt{2.75}=\sqrt{\frac{11}{4}}= \frac{\sqrt{11}}{2}](https://tex.z-dn.net/?f=%5Csqrt%7B2.75%7D%3D%5Csqrt%7B%5Cfrac%7B11%7D%7B4%7D%7D%3D%20%5Cfrac%7B%5Csqrt%7B11%7D%7D%7B2%7D)
![x-2.5=(+/-)\frac{\sqrt{11}}{2}](https://tex.z-dn.net/?f=x-2.5%3D%28%2B%2F-%29%5Cfrac%7B%5Csqrt%7B11%7D%7D%7B2%7D)
![x=2.5(+/-)\frac{\sqrt{11}}{2}](https://tex.z-dn.net/?f=x%3D2.5%28%2B%2F-%29%5Cfrac%7B%5Csqrt%7B11%7D%7D%7B2%7D)
![x=2.5+\frac{\sqrt{11}}{2}=\frac{5+\sqrt{11}}{2}](https://tex.z-dn.net/?f=x%3D2.5%2B%5Cfrac%7B%5Csqrt%7B11%7D%7D%7B2%7D%3D%5Cfrac%7B5%2B%5Csqrt%7B11%7D%7D%7B2%7D)
![x=2.5-\frac{\sqrt{11}}{2}=\frac{5-\sqrt{11}}{2}](https://tex.z-dn.net/?f=x%3D2.5-%5Cfrac%7B%5Csqrt%7B11%7D%7D%7B2%7D%3D%5Cfrac%7B5-%5Csqrt%7B11%7D%7D%7B2%7D)
<u>the answer is</u>
The solutions are
![x=\frac{5+\sqrt{11}}{2}](https://tex.z-dn.net/?f=x%3D%5Cfrac%7B5%2B%5Csqrt%7B11%7D%7D%7B2%7D)
![x=\frac{5-\sqrt{11}}{2}](https://tex.z-dn.net/?f=x%3D%5Cfrac%7B5-%5Csqrt%7B11%7D%7D%7B2%7D)