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2 years ago

Determine if the sequence below is arithmetic or geometric and determine the

Mathematics

1 answer:

algol132 years ago

4 0

9514 1404 393

Answer:

r = 2

Step-by-step explanation:

The first differences between successive terms are ...

10 -5 = 5

20 -10 = 10

The differences are not constant, so the sequence is NOT arithmetic.

The ratios of successive terms are ...

10/5 = 2

20/10 = 2

The ratios are constant, so the sequence is ...

geometric with a common ratio of 2.

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Match each point with one of the following fractions: 5/6, 7/12, 1/8, 5/16

Anton [14]

Answer is B. second one

A = 1/8, B = 5/16, C = 7/12, D = 5/6
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2 years ago

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Which equation represents a parabola that opens upward, has a minimum at x = 3, and has a line of symmetry at x = 3?

densk [106]

Answer:

$A.\ y = x^2 - 6x + 13$ is the correct answer.

Step-by-step explanation:

We know that vertex equation of a parabola is given as:

$y = a(x-h)^2+k$

where $(h,k)$ is the vertex of the parabola and

$(x,y)$ are the coordinate of points on parabola.

As per the question statement:

The parabola opens upwards that means coefficient of $x^{2}$ is positive.

Let $a = +1$

Minimum of parabola is at x = 3.

The vertex is at the minimum point of a parabola that opens upwards.

$\therefore$ $h = 3$

Putting value of a and h in the equation:

$y = 1(x-3)^2+k\\\Rightarrow y = (x-3)^2+k\\\Rightarrow y = x^2-6x+9+k$

Formula used: $(a-b)^2=a^{2} +b^{2} -2\times a \times b$

Comparing the equation formulated above with the options given we can observe that the equation formulated above is most similar to option A.

Comparing $y = x^2 - 6x + 13$ and $y = x^2-6x+9+k$

13 = 9+k

k = 4

Please refer to the graph attached.

Hence, correct option is $A.\ y = x^2 - 6x + 13$

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2 years ago

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Solve for x in the following system<br><br> 6x + 6y = -2<br> y = -x

klasskru [66]

6x + 6(-x) = - 2
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2 years ago

The functions r and s are defined as follows.

irina1246 [14]

Answer:

r(s(-2)) = -2

Step-by-step explanation:

We are given these following functions:

$r(x) = -2x + 2$

$s(x) = x^2 - 2$

Find the value of r(s (-2)).

First we find the composition of r and s functions. It is:

$r(s(x)) = r(x^2-2) = -2(x^2-2) + 2 = -2x^2 + 6$

At x = -2

$r(s(-2)) = -2(-2)^2 + 6 = -8 + 6 = -2$

r(s(-2)) = -2

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2 years ago

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aleksandrvk [35]

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