<h3>
Answer: Yes</h3>
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Explanation
The ratio 8:10 simplifies to 4:5 when you divide both parts by 2.
The ratio 16:20 simplifies to 4:5 when you divide both parts by 4
Therefore the two ratios 8:10 and 16:20 are both equal 4:5, so they are equal to one another.
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Put another way,
(8 large)/(10 small) = (16 large)/(20 small)
8/10 = 16/20
8*20 = 10*16 ... cross multiply
160 = 160
We get a true equation, so the first equation is true as well.
This shows the ratios are equivalent.
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Or you could have...
(8 large)/(16 large) = (10 small)/(20 small)
8/16 = 10/20
8*20 = 16*10
160 = 160
We get the same conclusion as before.
Hello from MrBillDoesMath!
Answer: factor = 4
Discussion:
Look at the sequence of numbers
1/64, 1/16, 1/4, 1, 4
It's seems clear that multiplying a term by 4 gives the next term in the sequence.
Thank you,
MrB
Answer:
5 units (you are right!)
Step-by-step explanation:
The triangles ABD and BCD are similar.
Therefore,
![\frac{x}{10}=\frac{10}{4x} \\4x^{2}=100\\x^{2}=25\\x=5](https://tex.z-dn.net/?f=%5Cfrac%7Bx%7D%7B10%7D%3D%5Cfrac%7B10%7D%7B4x%7D%20%5C%5C4x%5E%7B2%7D%3D100%5C%5Cx%5E%7B2%7D%3D25%5C%5Cx%3D5)
I hope this helped!
ANSWER
![x = - 2 \pm i](https://tex.z-dn.net/?f=x%20%3D%20-%202%20%5Cpm%20i)
EXPLANATION
We use the method of completing the squares.
The equation is
![3 {x}^{2} = - 12x - 15](https://tex.z-dn.net/?f=3%20%7Bx%7D%5E%7B2%7D%20%3D%20-%2012x%20-%2015)
We rewrite the above equation to obtain;
![3 {x}^{2} + 12x = - 15](https://tex.z-dn.net/?f=3%20%7Bx%7D%5E%7B2%7D%20%2B%2012x%20%3D%20-%2015)
We divide through by 3 to obtain;
![{x}^{2} + 4x = - 5](https://tex.z-dn.net/?f=%20%7Bx%7D%5E%7B2%7D%20%2B%204x%20%3D%20-%205)
We add half the coefficient of
![x](https://tex.z-dn.net/?f=x)
to both sides of the equation to get,
![{x}^{2} + 4x + {2}^{2} = - 5 + {2}^{2}](https://tex.z-dn.net/?f=%20%7Bx%7D%5E%7B2%7D%20%2B%204x%20%2B%20%7B2%7D%5E%7B2%7D%20%3D%20-%205%20%2B%20%7B2%7D%5E%7B2%7D%20)
The right hand side is now a perfect square.
![{(x + 2)}^{2} = - 1](https://tex.z-dn.net/?f=%7B%28x%20%2B%202%29%7D%5E%7B2%7D%20%3D%20-%201)
We now take square root of both sides to get;
![x + 2 = \pm \sqrt{ - 1}](https://tex.z-dn.net/?f=x%20%2B%202%20%3D%20%5Cpm%20%5Csqrt%7B%20-%201%7D%20)
We add -2 to both sides,
![x = - 2 \pm \sqrt{ - 1}](https://tex.z-dn.net/?f=x%20%3D%20-%202%20%5Cpm%20%5Csqrt%7B%20-%201%7D%20)
We simplify to obtain,
Answer:
87 cent?......................
Step-by-step explanation:
^^