Answer:
George has 64 nickel and 32 dimes.
Step-by-step explanation:
Normally, we have:
One nickel = 5 cents
One dime = 10 cents
One dollar = 100 cents
Therefore, total number of cents that George has can be calculated as follows:
Total number of cents = $6.40 * 100 = 640 cents
Based on the above, we have:
640 cents = 640 / 5 = 128 nickel
640 cents = 640 / 10 = 64 dimes
Therefore, we have:
128 nickel = 64 dimes
Divide through by 2 in order to share 640 cents equally, we have:
128 nickel / 2 = 64 dimes / 2 => 64 nickel = 32 dimes
Since 64 minus 32 is equal to 32, it therefore implies that George has 64 nickel and 32 dimes.
Answer:
50 years
Step-by-step explanation:
Given data
Principal= $500
Rate= 6%
Amount = $2000
The simple interest expression is given as
A=P(1+rt)
Substitute
2000= 500(1+0.06*t)
open bracket
2000=500+ 30t
2000-500=30t
1500=30t
t= 1500/30
t= 50 years
Hence the time is 50 years
A system of equations with infinitely many solutions is a system where the two equations are identical. The lines coincide. Anything that is equal to
![3y=2x-9](https://tex.z-dn.net/?f=3y%3D2x-9)
will work. You could try multiply the entire equation by some number, or moving terms around, or adding terms to both sides, or any combination of operations that you apply to the entire equation.
You could multiply the whole thing by 4.5 to get
![13.5y=9x-40.5](https://tex.z-dn.net/?f=13.5y%3D9x-40.5)
. If you want, you could mix things up and write it in slope-intercept form:
![y= \frac{2}{3}x-3](https://tex.z-dn.net/?f=y%3D%20%5Cfrac%7B2%7D%7B3%7Dx-3)
. The point is, anything that is equivalent to the original equation will give infinitely many solutions x and y. You can test this by plugging in values x and y and seeing the answers!
The attached graph shows that four different equations are really the same.
Answer:
722.50
Step-by-step explanation:
not exactly sure its right but i did use a calculator so I'm pretty sure it's right
Look at the picture.
Use Pythagorean theorem:
![r^2+23^2=(r+10)^2\\\\use\ (a+b)^2=a^2+2ab+b^2\\\\r^2+529=r^2+2\cdot r\cdot10+10^2\\\\r^2+529=r^2+20r+100\ \ \ |subtract\ r^2\ from\ both\ sides\\\\529=20r+100\ \ \ \ |subtract\ 100\ from\ both\ sides\\\\20r=429\ \ \ |divide\ both\ sides\ by\ 20\\\\r=21.45](https://tex.z-dn.net/?f=r%5E2%2B23%5E2%3D%28r%2B10%29%5E2%5C%5C%5C%5Cuse%5C%20%28a%2Bb%29%5E2%3Da%5E2%2B2ab%2Bb%5E2%5C%5C%5C%5Cr%5E2%2B529%3Dr%5E2%2B2%5Ccdot%20r%5Ccdot10%2B10%5E2%5C%5C%5C%5Cr%5E2%2B529%3Dr%5E2%2B20r%2B100%5C%20%5C%20%5C%20%7Csubtract%5C%20r%5E2%5C%20from%5C%20both%5C%20sides%5C%5C%5C%5C529%3D20r%2B100%5C%20%5C%20%5C%20%5C%20%7Csubtract%5C%20100%5C%20from%5C%20both%5C%20sides%5C%5C%5C%5C20r%3D429%5C%20%5C%20%5C%20%7Cdivide%5C%20both%5C%20sides%5C%20by%5C%2020%5C%5C%5C%5Cr%3D21.45)
The diameter d = 2r, therefore