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kolezko [41]
2 years ago
15

The first five terms of a quadratic sequence are 3, 12, 25, 42, 63.

Mathematics
1 answer:
skad [1K]2 years ago
7 0

Since we know the sequence is quadratic, we expect the n-th term to have the general form

x_n = an^2 + bn + c

Plug in the first 3 known values of the sequence to form a system of equations.

x_1 = 3 = a + b + c

x_2 = 12 = 4a + 2b + c

x_3 = 25 = 9a + 3b + c

Eliminating c gives

(4a + 2b + c) - (a + b + c) = 12 - 3 \implies 3a + b = 9

(9a + 3b + c) - (a + b + c) = 25 - 3 \implies 8a + 2b = 22 \implies 4a + b = 11

Eliminating b gives

(4a + b) - (3a + b) = 11 - 9 \implies a = 2

Solving for b,c, we get

4a + b = 11 \implies b = 11-4\cdot2 = 3

a+b+c=3 \implies c=3-2-3 = -2

So, the n-th term of the sequence is

x_n = \boxed{2n^2 + 3n - 2}

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Which function f (x) , graphed below, or g (x) , whose equation is g (x) = 3 cos 1/4 (x + x/3) + 2, has the largest maximum and
Leya [2.2K]

Answer:

g(x), and the maximum is 5

Step-by-step explanation:

for given function f(x), the maximum can be seen from the shown graph i.e. 2

But for the function g(x), maximum needs to be calculated.

Given function :

g (x) = 3 cos 1/4 (x + x/3) + 2

let x=0 (as cosine is a periodic function and has maximum value of 1 at 0 angle)

g(x)= 3 cos1/4(0 + 0) +2

    = 3cos0 +2

     = 3(1) +2

     = 3 +2

     = 5 !

7 0
3 years ago
A box of baseball cards is $25.00 with %15 off. What is the sale price of the box of cards? In other words, how much is it after
yan [13]

Answer:

21.25

Step-by-step explanation:

you would multiply 25 by 0.15 to get the percent being taken off then subtract that from your original price

8 0
3 years ago
True or false: Every sequence is either arithmetic or geometric. If this is true, explain. If false,
tiny-mole [99]

In an arithmetic sequence, the difference between consecutive terms is constant. In formulas, there exists a number r such that

a_{n+1}-a_n=r\quad \forall n\geq 1

In an geometric sequence, the ratio between consecutive terms is constant. In formulas, there exists a number r such that

\dfrac{a_{n+1}}{a_n}=r\quad \forall n\geq 1

So, there exists infinite sequences that are not arithmetic nor geometric. Simply choose a sequence where neither the difference nor the ratio between consecutive terms is constant.

For example, any sequence starting with

1, 15, -3,\ldots

Won't be arithmetic nor geometric. It's not arithmetic (no matter how you continue it, indefinitely), because the difference between the first two numbers is 14, and between the second and the third is -18, and thus it's not constant. It's not geometric either, because the ratio between the first two numbers is 15, and between the second and the third is -1/5, and thus it's not constant.

5 0
3 years ago
consider the line y= 2/3x-0. Find the equation of the line that is parallel to this line and passes through the point (8, 4).
tresset_1 [31]
Point-slope form of a line: we need a point (x₀,y₀) and the slope "m".
y-y₀=m(x-x₀)

slope intercept form :
y=m+b

m=slope

If the line is parallel to y=2/3 x-0, the line will have the same slope, therefore the slope will be: 2/3.

Data:
(8,4)
m=2/3

y-y₀=m(x-x₀)
y-4=2/3(x-8)
y-4=2/3 x-16/3
y=2/3 x-16/3+4
y=2/3 x-4/3  (slope intercept form)

Answer: The equation of the line would be: y=2/3 x-4/3.


if we have the next slope "m",then the perendicular slope will be:
m´=-1/m

We have this equation: y=2/3 x+0; the slope is: m=2/3.

The perpendicular slope will be: m`=-1/(2/3)=-3/2

And the equation of the perpendicular line to : y=2/3 x+0, given the point (8,4) will be:

y-y₀=m(x-x₀)
y-4=-3/2 (x-8)
y-4=-3/2 x+12
y=-3/2x + 12+4
y=-3/2x+16

answer: the perpendicular line to y=2/3 x+0 , given the point (8,4) will be:
y=-3/2 x+16
3 0
3 years ago
What is 23d=109<br> pls answer
grandymaker [24]

Answer:

what kinda... what do they give yall these days but anyways,

Step-by-step explanation:

Divide each term by

23 and simplify.

Exact Form:

d=109/23

Decimal Form:

d=4.73913043

um…

Mixed Number Form:

d=4 17/23

5 0
3 years ago
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