Answer:
- Find the coefficients using ax^2 + bx + c = 0
a = 4
b = 7
c = 0
- Make the coefficient equal 1. But how do we do that? Division.
4n² + 7n = 0
4/4n² + 7n/4 = 0/4
= n² + 7/4n = 0
a = 1
b = 7/4
c = 0
- Complete the square using b/2².
b = 7/4
(b/2)² = (7/4 ÷ 2)²
Use fraction rule.
7/4 ÷ 2² = 7/4² / 2²
<em>square the numbers</em>
7/4² / 2² = 49/16 ÷ 4
49/16 ÷ 4 = 49/16 × 1/4
49/16 × 1/4 = 49/64
Add to both sides of the equation using 49/64
b = 7/4
b/2 = 7/4 ÷ 2
<em>simplify</em>
b/2 = 7 ÷ (4 × 2)
<em>simplify(arithmetic)</em>
b/2 = 7/8
n² + 7/4n + 49/64 = 49/64
(n + 7/8)² = 49/64
![(n+\frac{7}{8})^2=\frac{49}{64}\\\sqrt{(n+\frac{7}{8})^2}=\sqrt{\frac{49}{64}}\\](https://tex.z-dn.net/?f=%28n%2B%5Cfrac%7B7%7D%7B8%7D%29%5E2%3D%5Cfrac%7B49%7D%7B64%7D%5C%5C%5Csqrt%7B%28n%2B%5Cfrac%7B7%7D%7B8%7D%29%5E2%7D%3D%5Csqrt%7B%5Cfrac%7B49%7D%7B64%7D%7D%5C%5C)
Next, cancel out the square on the left side.
![n+\frac{7}{8}=+/-\sqrt{\frac{49}{64}}](https://tex.z-dn.net/?f=n%2B%5Cfrac%7B7%7D%7B8%7D%3D%2B%2F-%5Csqrt%7B%5Cfrac%7B49%7D%7B64%7D%7D)
Subtract 7/8 from both of the sides.
![n+\frac{7}{8}-\frac{7}{8}=-\frac{7}{8}+/-\sqrt{\frac{49}{64}}](https://tex.z-dn.net/?f=n%2B%5Cfrac%7B7%7D%7B8%7D-%5Cfrac%7B7%7D%7B8%7D%3D-%5Cfrac%7B7%7D%7B8%7D%2B%2F-%5Csqrt%7B%5Cfrac%7B49%7D%7B64%7D%7D)
Simplify the left side.
![n=-\frac{7}{8}+/-\sqrt{\frac{49}{64}}\\n=-\frac{7}{8}+/-\frac{\sqrt{49}}{\sqrt{64}}\\n=-\frac{7}{8}+/-\frac{7}{8}\\n_1=0\\n_2=-\frac{7}{4}](https://tex.z-dn.net/?f=n%3D-%5Cfrac%7B7%7D%7B8%7D%2B%2F-%5Csqrt%7B%5Cfrac%7B49%7D%7B64%7D%7D%5C%5Cn%3D-%5Cfrac%7B7%7D%7B8%7D%2B%2F-%5Cfrac%7B%5Csqrt%7B49%7D%7D%7B%5Csqrt%7B64%7D%7D%5C%5Cn%3D-%5Cfrac%7B7%7D%7B8%7D%2B%2F-%5Cfrac%7B7%7D%7B8%7D%5C%5Cn_1%3D0%5C%5Cn_2%3D-%5Cfrac%7B7%7D%7B4%7D)
<em>That wraps it up for this equation. Hope it helped!</em>
It is is y = -3
Good luck!!
The problem above is modelled in diagram below
We use the trigonometry ratio to solve length DE
![tan(x)= \frac{DE}{FE}](https://tex.z-dn.net/?f=tan%28x%29%3D%20%5Cfrac%7BDE%7D%7BFE%7D%20)
![tan(40)= \frac{DE}{14}](https://tex.z-dn.net/?f=tan%2840%29%3D%20%5Cfrac%7BDE%7D%7B14%7D%20)
![14tan(40)=DE](https://tex.z-dn.net/?f=14tan%2840%29%3DDE)
DE=3.36
Answer:
a) $7.50
b) 10 miles
Step-by-step explanation:
a)
y=mx+b
y=$29.50
x=8
m=$2.75
b=unknown
29.50=2.75(8)+b
29.50-22=22-22+b
7.50=b
Check:
2.75(8)+7.50=29.50
b)
y=$35
x=unknown
m=2.75
b=7.50
35-7.50=2.75x+7.50-7.50
27.5/2.75=2.75/2.75x
10=x
It should be perpendicular