the sequence is adding 2 to each last number
5 + 2 = 7
7 +2 = 9
9 + 2 = 11
11 + 2 = 13
13 + 2 = 15
the answer is D. 15
Arc length is angle times radius. The unit circle has radius 1, so the arc length is just π/3
The equation given is
![x^{2} =a](https://tex.z-dn.net/?f=%20x%5E%7B2%7D%20%3Da)
where a is some number.
We can solve for x by taking the square root of both sides.
Now let's think through what happens for various values of a.
TWO SOLUTIONS
If a is a positive number the above yields two solutions. Take for example:
![x^{2} =49 \sqrt{49}=7 or -7](https://tex.z-dn.net/?f=%20x%5E%7B2%7D%20%3D49%0A%20%5Csqrt%7B49%7D%3D7%20or%20-7%20)
There will be two solutions (one positive and one negative) as there are two numbers (here -7 and +7) that when multiplied by themselves give 49. That is,
![7^{2} =49](https://tex.z-dn.net/?f=%207%5E%7B2%7D%20%3D49)
and
![(-7)^{2}=49](https://tex.z-dn.net/?f=%20%28-7%29%5E%7B2%7D%3D49%20)
. The positive root is called the principal root and the negative root is called the secondary root. This will be the case anytime we take the root of a positive number.
ONE SOLUTION
If a = 0 there is only one solution. That is because
![x^{2} =0](https://tex.z-dn.net/?f=x%5E%7B2%7D%20%3D0%20)
and
![x= \sqrt{0}](https://tex.z-dn.net/?f=x%3D%20%5Csqrt%7B0%7D%20)
. Zero is neither positive nor negative and it has only one root which is 0 itself. So in this case there is only one solution and it is 0.
NO (REAL) SOLUTIONS
If a is negative we would be taking the square root of a negative number. There is no (real) number that when multiplied by itself gives a negative number. Take for example
![x^{2} =-49](https://tex.z-dn.net/?f=%20x%5E%7B2%7D%20%3D-49)
which gives us
![x= \sqrt{-49}](https://tex.z-dn.net/?f=x%3D%20%5Csqrt%7B-49%7D%20)
. The square root of -49 is not 7 because (7)(7)=49 which is positive. The square root of -49 is not -7 because (-7)(-7)=49 which is also positive. There is no real number that gives -49 when multiplied by itself. I say "real" numbers because there do exist imaginary/complex numbers but because of the way the questions was asked I imagine you may not know about these yet.
So the scale in part a would be 72 miles/6 inches = x miles/ 1 inch. Cross multiply and you get 6x= 72, so x = 12 miles. Now you now that 1 inch equals 12 miles.
Part B tells you that Foston is 4 inches from Liberty, and asks you to figure out how far it is from West Quail. The WHOLE distance is 6 inches ( Liberty to West Quail) so the distance from Foston to West Quail is 6-4= 2 inches.
Remember 1 inch equals 12 miles, so 2 inches will equal 24 miles
Erica earned a total of $50,450 last year from her two jobs. The amount she earned from her job at the store was $1,250 more than four times the amount she earned from her job at the college.
Lets x be the amount she earned from here job at college
amount she earned at the store = 4 * amount earned at college + 1250
= 4x + 1250
Amount earned at college + amount earned at store = 50450
x + 4x + 1250 = 50450
5x + 1250 = 50450
Subtract 1250 from both sides
5x = 49200 (divide by 5)
x = 9840
she earn $9840 from her job at the college