12/2=6.
6X0.5=3
so the scale drawing is 3 inches long
10/2=5
5X0.5=2.5
so the width of the scale drawing is 2.5 inches
3+3+2.5+2.5=11
So average is of the first 6 tests is 82 well that means
(test1 + test2+ test3+ test4 + test5+test6)/6 = 82
so now let do some cross multiplliying
test1 + test2 + test3 + test 4 + test5 +test6 = 82*6
test1 + test2 + test3 + test 4 + test5 +test6 = 492
now lets see if we can find that 7th test score
(test1 + test2 + test3 + test4 + test5 +test6 + test7)/7 = 80.5
So look we found test1 + test2 + test3 + test4 + test5 +test6 to be 492 so lets substitute.
(492 + test7 )/7 = 80.5
test7 = (80.5*7)-492 = 71.5
Answer:
Center (6 , -5) and radius = 3
Step-by-step explanation:
The Standard equation of circle can be written as
(x - a)² + (y - b)² = r²
with center (a , b) and radius = r
Now from given circle equation
(x - 6)² + (y +5)² = 9
so, from here center of circle (6 , -5) and radius = 3
Using polynomial long division, we get
3x^3+6x^2+11x
_____________
(x+2) | 3x^4-x^2+cx-2
-(3x^4+6x^3)
____________
6x^3-x^2+cx-2
- (6x^3+12x^2)
_____________
11x^2+cx-2
-(11x^2+22x)
__________
(22+c)x-2.
If you're wondering how I did the long division, what I essentially did was get the first value (at the start, it was 3x^4) and divided it by the first value of the divisor (which in x+2 was x) to get 3x^3 in our example. I then subtracted the polynomial by the whole divisor multiplied by, for example, 3x^3 and repeated the process.
For this to be a perfect factor, (x+2)*something must be equal to (22+c)x-2. Focusing on how to cancel out the 2, we have to add 2 to it. To add 2 to it, we have to multiply (x+2) by 1. However, there's a catch, which is that we subtract whatever we multiply (x+2) by, so we have to multiply it by -1 instead. We still need to cross out (22+c)x. Multiplying (x+2) by -1, we get
(-x-2) but by subtracting the whole thing from something means that we have to add -(-x-2)=x+2 to something to get 0. x+2-x-2=0, xo (22+c)x-2 must equal -x-2, meaning that (22+c)=-1 and c=-23
