Answer:
Step-by-step explanation:
Cross multiply, isolate the variable, and divide by the coefficient to solve.
Plug back in to check.
A basket contains 6 pieces of paper numbered from 1 to 6. A hat contains the letters A, B, and C. If a blindfolded person picks
1 answer:
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An arithmetic sequence can be expressed as explicitly or recursively
The explicit formula of the sequence is
The recursive formula is given as:
Substitute 2 for n in
This gives
Calculate the common difference (d)
The explicit formula is then calculated as:
This gives
Expand
Hence, the explicit formula of the sequence is
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The vertex-form of the equation of a parabola is 
,
where (h, k) is the vertex point.
We are given that 9 is the maximum point, and that the axis of symmetry is the line x=-5.
The axis of symmetry passes through the vertex, so the x-coordinate of the vertex is -5. The maximum height is 9 means that the y-coordinate of the vertex is 9.
So: (h, k)=(-5, 9).
Substituting in the vertex-form, now we have:
.
We also know that (-7, 1) is a point of the parabola, so this point is an (x, y) which satisfies the equation. That is:
Now we have all the constants h, k and a, so we are able to write the equation:
.
Answer:.
where (h, k) is the vertex point.
We are given that 9 is the maximum point, and that the axis of symmetry is the line x=-5.
The axis of symmetry passes through the vertex, so the x-coordinate of the vertex is -5. The maximum height is 9 means that the y-coordinate of the vertex is 9.
So: (h, k)=(-5, 9).
Substituting in the vertex-form, now we have:
We also know that (-7, 1) is a point of the parabola, so this point is an (x, y) which satisfies the equation. That is:
Now we have all the constants h, k and a, so we are able to write the equation:
Answer: