The kite is symmetric about line segment BD.
Therefore
AB = BC
3x + 1 = 22
3x = 22 - 1 = 21
x = 21/3 = 7
Similarly,
AD = CD by symmetry
Therefore
4x = CD
4*7 = CD
28 = CD, the required line segment
Answer: 28
Dependent hope this hepls with it
Answer:
a=2, b=5
Step-by-step explanation:
Let
n -----> the denominator
we have
![3.5*10^4=\frac{7*10^9}{n}](https://tex.z-dn.net/?f=3.5%2A10%5E4%3D%5Cfrac%7B7%2A10%5E9%7D%7Bn%7D)
Solve for n
That means -----> isolate the variable n
Multiply by n both sides
![3.5*10^4(n)=7*10^9](https://tex.z-dn.net/?f=3.5%2A10%5E4%28n%29%3D7%2A10%5E9)
Divide by 3.5*10^4 both sides
![n=\frac{7*10^9}{3.5*10^4}=(\frac{7}{3.5})(\frac{10^9}{10^4})=2*10^5](https://tex.z-dn.net/?f=n%3D%5Cfrac%7B7%2A10%5E9%7D%7B3.5%2A10%5E4%7D%3D%28%5Cfrac%7B7%7D%7B3.5%7D%29%28%5Cfrac%7B10%5E9%7D%7B10%5E4%7D%29%3D2%2A10%5E5)
therefore
a=2, b=5
Answer:
5400
Step-by-step explanation:
Let x represent the cost of a chair and y represent the cost of a table. We can use this to set up a system of equations:
7x=2y
6x+5y=10575
We can solve this system using substitution.
Start by rewriting the first equation in terms of x.
![7x=2y\\\text{Divide both sides by 7}\\x=\frac{2}{7}y](https://tex.z-dn.net/?f=7x%3D2y%5C%5C%5Ctext%7BDivide%20both%20sides%20by%207%7D%5C%5Cx%3D%5Cfrac%7B2%7D%7B7%7Dy)
Substitute this into the second equation:
![6(\frac{2}{7}y)+5y=10575\\\frac{12}{7}y+5y+10575\\\frac{12}{7}y+\frac{35}{7}y=10575\\\frac{47}{7}y=10575](https://tex.z-dn.net/?f=6%28%5Cfrac%7B2%7D%7B7%7Dy%29%2B5y%3D10575%5C%5C%5Cfrac%7B12%7D%7B7%7Dy%2B5y%2B10575%5C%5C%5Cfrac%7B12%7D%7B7%7Dy%2B%5Cfrac%7B35%7D%7B7%7Dy%3D10575%5C%5C%5Cfrac%7B47%7D%7B7%7Dy%3D10575)
Multiply both sides by 7
![47y=74025](https://tex.z-dn.net/?f=47y%3D74025)
Divide both sides by 47
![y=1575](https://tex.z-dn.net/?f=y%3D1575)
This means...
![7x=2(1575)\\7x=3150](https://tex.z-dn.net/?f=7x%3D2%281575%29%5C%5C7x%3D3150)
Divide both sides by 7
![x=450](https://tex.z-dn.net/?f=x%3D450)
One chair costs 450. Now, multiply this number by 12 to find the cost of 12 chairs.
![450*12=5400](https://tex.z-dn.net/?f=450%2A12%3D5400)
12 chairs cost 5400.