Answer:
The coordinates for the vertex are ( -6 , 1 )
Because this is a positive parabola, it opens upwards, like a cup, and the vertex dictates what the minimum value of the function is. In order to determine the vertex, I recommend completing the square. Do that by first setting the function equal to 0 and then moving the 9 to the other side by subtraction. So far:
. Now, to complete the square, take half the linear term, square it, and add that number to both sides. Our linear term is 6. Half of 6 is 3 and 3 squared is 9. So add 9 to both sides.
. The right side reduces to 0, and the left side simplifies to the perfect square binomial we created while completing this process.
. Move the 0 back over and the vertex is clear now. It is (-3, 0). Therefore, 0 is the minimum point on your graph. The first choice above is the one you want.
Answer:
x=21
Step-by-step explanation:
x-7=14
add 7 to both sides
x=21
It is usual to represent ratios in their simplest form so that we are not operating with large numbers. Reducing ratios to their simplest form is directly linked to equivalent fractions.
For example: On a farm there are 4 Bulls and 200 Cows. Write this as a ratio in its simplest form.
Bulls <span>: </span>Cows
4 <span>: </span>200
If we halve the number of bulls then we must halve the number of cows so that the relationship between the bulls and cows stays constant. This gives us:
Bulls <span>: </span>Cows
2 <span>: </span>100
Halving again gives us
1 <span>: </span>50
So the ratio of Bulls to Cows equals 1 : 50. The ratio is now represented in its simplest form.
An example where we have 3 quantities.
On the farm there are 24 ducks, 36 geese and 48 hens.
Ratio of ducks <span>: </span>geese <span>: </span>hens
24 <span>: </span>36 <span>: </span>48
Dividing each quantity by 12 gives us
2 <span>: </span>3 : 4
So the ratio of ducks to geese to hens equals 2 : 3 : 4 which is the simplest form since we can find no further common factor.
Y=24x+48
24 per hour (x) plus the 48 she already made would equal a total (y).
