When the equation is squared, you have to foil (8x+5), so it becomes
(8x+5)(8x+5)=63
then you use the distributive property, so it become 64x^2 +40x +40x +25, and you simplify that into 64x^2+80x+25=63
next you subtract 63 from the left, sso it becomes 64x^2+80x-38=0
then you use the quadratic formula -b+/- (root b^2-4ac )/2a to solve for the zeros or x-values
Answer:
See below
Step-by-step explanation:
a)
<u>Day 1</u>
- 70 min for 10 km
- Rate = 70/10 = 7 min/km
<u>Day 10</u>
- 2h40 min for 20 km
- 2*60+40 = 160 min for 20 km
- Rate = 160/20 = 8 min/km
<u>Day 20</u>
- 4 h 15 min for 30 km
- 4*60 + 15 = 255 min for 30 km
- Rate = 255/30 = 8.5 min / km
b)
<u>From the rate change we see:</u>
- 1 min increase when the distance increases from 10 km to 20 km
- 0.5 min increase when distance increases from 20 km to 30 km
So we see 1 min increase per twice the distance increase
- With the same rate increase we can expect 1 min increase from 20 km to 40 km, which gives us the rate of 9 min/km
- With same logic we get 9.055 km/min rate for 44 km distance
<u>Total time it takes:</u>
- 9.055*44 = 398.42 min = 398.42*1/60 min = 6 h and 38.42 min
To find the GCF of 66 and 91 you have to find the factors of each:
66 = 1, 2, 3, 6, 11, 22, 33, 66
91 = 1, 7, 13, 91
So the only, and therefore greatest, common factor is 1.
Now we do the same with 84 and 92:
84 = 1, 2, 3, 4<span>, 6, 7, 12, 14, 21, 28, 42, 84
92 = </span>1, 2, 4<span>, 23, 46, 92
This time we have multiple common factors but the greatest common factor is 4.
Now 51 and 75:
51 = </span>1, 3<span>, 17, 51
75 = </span>1, 3<span>, 5, 15, 25, 75
The GCF is 3
Now 64 and 72:
64 = 1, </span>2, 4, 8<span>, 16, 32, 64
72 = </span>1, 2, 3, 4, 6, 8<span>, 9, 12, 18, 24, 36, 72
GCF is 8. You just look for the highest number that is the same.
Finally, 99 and 66:
99 = </span><span>1, 3, 9, 11, </span>33<span>, 99</span><span>
66 = </span>1, 2, 3, 6, 11, 22, 33, 66<span>
GCF is 33.
Hope this helps.</span>