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andreev551 [17]
2 years ago
14

Find the 78th term of the arithmetic sequence 14,5, -4, ...

Mathematics
2 answers:
BigorU [14]2 years ago
8 0

answer

the formula is a+(n-1)d

a: the first term

d:the 2nd term -the first term

iren2701 [21]2 years ago
7 0

Answer:

-679

Step-by-step explanation:

14, 5, -4, ...

a = 14

d = 5 - 14 = -9

nth term = a + (n - 1) d

n(78) = 14 + (78 - 1) * -9

= 14 + 77(-9)

= 14 -693

= -679

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Answer:

The line of symmetry is x = -3

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In this problem, we have:

y=-x^2-6x-13

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x_v=-\frac{-6}{2(-1)}=-\frac{-6}{-2}=-\frac{6}{2}=-3

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For this part, we need to find the x-intercepts. This is, when y = 0:

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And solve:

x_{1,2}=\frac{6\pm\sqrt{36-52}}{-2}x_{1,2}=\frac{-6\pm\sqrt{-16}}{2}

Since there is no solution to the square root of a negative number, the function does not have any x-intercept. The correct option is ZERO x-intercepts.

Part 4:

To find the y intercept, we need to find the value of y when x = 0:

y=-0^2-6\cdot0-13=-13

The y-intercept is at (0, -13)

Part 5:

Now we need to find two points in the parabola. Let-s evaluate the function when x = 1 and x = -1:

x=1\Rightarrow y=-1^2-6\cdot1-13=-1-6-13=-20x=-1\Rightarrow y=-(-1)^2-6\cdot(-1)-13=-1+6-13=-8

The two points are:

(1, -20)

(-1, -8)

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Now, we can use 3 points to find the graph of the parabola.

We can locate (1, -20) and (-1, -8)

The third could be the vertex. We need to find the y-coordinate of the vertex. We know that the x-coordinate of the vertex is x = -3

Then, y-coordinate of the vertex is:

y=-(-3)^2-6(-3)-13=-9+18-13=-4

The third point we can use is (-3, -4)

Now we can locate them in the cartesian plane:

And that's enough to get the full graph:

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1 year ago
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The answer is point S

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