Determine a and k so the given points are on the graph of the function. (1,18), (2,3); y= a(x + 1)2 +k

Step-by-step explanation:

Explanation:

Because

(2,6) is in the function, we can plug

6 as y

and

2 as x.

From that we get

6=a(2−1)2+k

6=a+k

Same for the next point:

12=a(3−1)2+k

12=22a+k

12=4a+k

Now we have this system of equations to solve:

a+k=6

4a+k=12

Solving it leads to the conclusion that

a=2,k=4 .

$53.50

step-by-step explanation:

you have to subtract the amount of money chuck earned ($72.50) by the cost of the gas for the mower ($11.25) and the new string for the trimmer he bought ($7.75).

72.50-11.25=61.25

and then subtract $61.25 by the second thing he bought (the new string for the trimmer)

61.25-7.75=53.5

so in total it's $53.50 (53 dollars and 50 cents)

answer: option a.

step-by-step explanation:

you know that the quadrilateral opqr ( a four sided figure) is inscribed in circle. this means that all its vertices are on the circle.

then, by definition, the opposite angles of the quadrilateral are supplementary, this means that the sum of their measures is 180 degrees.

you can observe in the figure that the angles ∠opq   and the angle ∠orq   are opposite, therefore:

then, can be used to d to calculate the measure of ∠opq