What do 3x+2x+y+2y-3 equals in combining like terms
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9514 1404 393
Answer:
Each term in the pattern will be odd.
Step-by-step explanation:
The first differences are ...
7 -3 = 4
15 -7 = 8
These differ by 4, and the second is double the first.
These relationships between the first differences give rise to two possible sequences: a) an exponential sequence; b) a quadratic sequence. We can use a graphing calculator to find the coefficients of each of the patterns.
<u>Exponential Sequence</u>
a[n] = 2·2^n -1
The sequence is 3, 7, 15, 31, 63, 127, 255, 511, 1023, 2047.
The 10th term is 2047.
<u>Quadratic Sequence</u>
a[n] = 2n^2 -2n +3
The sequence is 3, 7, 15, 27, 43, 63, 87, 115, 147, 183.
The 10th term is 183.
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Based on the above, the only thing we can say about these sequences is that they are all odd numbers.
Clearly, the 10th term is not 30. 7 is not a multiple of 3, so that observation fails immediately. 15 is not prime, so that observation also fails immediately.
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<em>Additional comment</em>
The differences of first differences are called "second differences". The differences of those are "third differences". and so on. If you keep taking differences of a sequence described by a polynomial, the n-th differences being constant means the sequence is described by an n-th degree polynomial.
Here, if we assume the 2nd differences are constant at 4, then the sequence is described by a 2nd-degree polynomial. (Similarly, constant first-differences are described by a 1st-degree polynomial--a linear function.)
If sequential levels of differences are all exponential sequences, then the sequence itself is an exponential sequence. As here, it may have a vertical offset. The base of the exponential will be the common ratio of the differences. (Here, the first differences have a ratio of 8/4 = 2, so the sequence could be exponential with a base of 2.)
The equation of the line that passes through the point (-6,3) and has a slope of -4/3 is y=(-4/3)x-5.
<h3>What is the equation of a line?</h3>A line is a one-dimensional shape that is straight, has no thickness, and extends in both directions indefinitely. The equation of a line is given by,
y =mx + c
where,
x is the coordinate of the x-axis,
y is the coordinate of the y-axis,
m is the slope of the line, and
c is constant.
Given the slope of the line is -4/3, also, the line passes through the point (-6,3). Therefore, when the values are substituted in the general equation of a line to get the value of the constant, we will get,
y = mx + c
3 = (-4/3)(-6)+c
3 = 8 + c
c = -5
Thus, the equation can be written as y=(-4/3)x-5.
Hence, the equation of the line that passes through the point (-6,3) and has a slope of -4/3 is y=(-4/3)x-5.
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The equation of the parabola is
None of the given options is correct
Given:
Focus: (0, 3)
Directrix: y = -3
Note that:
f - k = k - (-3)
f - 3 = 3 + 3
f = 6 + 3
f = 9
The equation of the parabola is of the form:
Substitute f = 9, k = 3, h = 0 into the equation
The equation of the parabola is
Learn more on equation of a parabola here: brainly.com/question/4061870
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