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mixas84 [53]
3 years ago
9

What is the position number of the term 125 in the sequence f(n) = 2n+3?

Mathematics
1 answer:
spin [16.1K]3 years ago
8 0

Answer:

61st term in the sequence

Step-by-step explanation:

125 = 2n + 3

122 = 2n

n = 61

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12 is 80% of what number
nydimaria [60]
X - the number

80\%x=12 \\
\frac{80}{100}x=12 \\
\frac{4}{5}x=12 \\
x=12 \times \frac{5}{4} \\
x=3 \times 5 \\
x=15

12 is 80% of 15.
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aleksandrvk [35]
On what do u Need help on?
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3 years ago
The polynomial $f(x)$ has degree 3. If $f(-1) = 15$, $f(0)= 0$, $f(1) = -5$, and $f(2) = 12$, then what are the $x$-intercepts o
Alex_Xolod [135]

Your calculator's cubic regression function can tell you the equation is

... f(x) = 2x³ + 5x² -12x = x(x +4)(2x-3)

The x-intercepts are -4, 0, +1.5.

_____

If you want to solve this "by hand", you can first of all recognize that since there is an x-intercept at 0, the cubic will only have three coefficients. That is, you can write the equation as

... f(x) = ax³ + bx² + cx

Substituting the given points (except (0, 0)) gives three linear equations in a, b, c.

... -a +b -c = 15 . . . . . for x=-1

... a + b + c = -5 . . . . for x=1

... 8a +4b +2c = 12 . . for x=2

adding the first two equations gives 2b=10, or b=5. Now, you can reduce the system to

... a + c = -10

... 4a +c = -4

Subtracting the first of these equations from the second gives 3a=6, or a=2. That tells you c=-12 (from a+c=10).

Then your equation is

... f(x) = x(2x² +5x -12)

Factoring by any of the usual techniques, or graphing, or using the quadratic formula will tell you the zeros (x-intercepts) are as above.

_____

Since the input values are sequential, you can also develop the function from differences of the output values. Those are 15, 0, -5, 12. First differences are -15, -5, +17. Second differences are +10, +22. The third difference is 12. Using the first of these differences in appropriate places in the interpolating polynomial formula, we have

... f(x) = 15 + (x+1)(-15 + (x)/2·(10 + (x-1)/3·(12))) = 2x³ +5x² -12x . . . . as above

4 0
3 years ago
Which is the best way to solve the equation x2 = n?
Gnom [1K]

n - no solutions in real numbers

n=0 \Rightarrow x=0

n>0 \Rightarrow x=\sqrt n \vee x=-\sqrt n

7 0
3 years ago
1767tires each truck needs 6 tires how many can we get in all
vodomira [7]

Answer:

294

Step-by-step explanation:

It exactly 294.5 but a car cant function with just half of its tires :').  So in this case instead of rounding up we round down. They will just have extra tires.

6 0
3 years ago
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