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2 years ago

50 POINTS! The fifth term of an arithmetic sequence is 11 and the tenth term is 41. What is the first term?

Mathematics

2 answers:

marshall27 [118]2 years ago

8 0

Answer:

Step-by-step explanation:

The fifth term:

$a_5=a+4d = 11$

The 10th term:

$a_{10}=a+9d=41$

Subtract side-by-side and find d:

9d - 4d = 41 - 11
5d = 30
d = 6

Find the first term:

a = 11 - 4*6
a = 11 - 24
a = - 13

Oxana [17]2 years ago

4 0

The common difference d is

(41–11) / (10–5) = 6.

The first term is

11 - 6(5–1) = -13.

so , the first term is -13 

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Is this wrong?

sammy [17]

Step-by-step explanation:

The last step is a little wrong. Lemme show you:

x(x + 2) + (x + 2)

Imagine there is an invisible '1' infront of (x + 2) like this:

= x(x + 2) + 1(x + 2)

Now we can combine the like terms together:

= (x + 1)(x + 2)

This is the correct factorization.

4 0

2 years ago

15. A rectangle has a length of 2x - 1 and a width of 3x + 7. Find the perimeter of this rectangle.

andrew11 [14]

Answer:

10x + 12 and 6x² + 11x - 7

Step-by-step explanation:

The perimeter (P) of a rectangle is calculated as

P = 2l + 2w ( l is length and w is width )

= 2(2x - 1) + 2(3x + 7) ← distribute parenthesis

= 4x - 2 + 6x + 14 ← collect like terms

= 10x + 12

--------------------------------------------------

The area (A) of a rectangle is calculated as

A = lw

= (2x - 1)(3x + 7) ← expand using FOIL

= 6x² + 14x - 3x - 7 ← collect like terms

= 6x² + 11x - 7

7 0

2 years ago

For the function g(x)=3-8(1/4)^2-x

Reika [66]

Using function concepts, it is found that:

a) The y-intercept is y = 2.5.

b) The horizontal asymptote is x = 3.

c) The function is decreasing.

d) The domain is $(-\infty,\infty)$ and the range is $(-\infty,3)$ .
e) The graph is given at the end of the answer.

------------------------------------

The given function is:

$g(x) = 3 - 8\left(\frac{1}{4}\right)^{2-x}$

------------------------------------

Question a:

The y-intercept is g(0), thus:

$g(0) = 3 - 8\left(\frac{1}{4}\right)^{2-0} = 3 - 8\left(\frac{1}{4}\right)^{2} = 3 - \frac{8}{16} = 3 - 0.5 = 2.5$

The y-intercept is y = 2.5.

------------------------------------

Question b:

The horizontal asymptote is the limit of the function when x goes to infinity, if it exists.

$\lim_{x \rightarrow -\infty} g(x) = \lim_{x \rightarrow -\infty} 3 - 8\left(\frac{1}{4}\right)^{2-x} = 3 - 8\left(\frac{1}{4}\right)^{2+\infty} = 3 - 8\left(\frac{1}{4}\right)^{\infty} = 3 - 8\frac{1^{\infty}}{4^{\infty}} = 3 -0 = 3$

--------------------------------------------------

$\lim_{x \rightarrow \infty} g(x) = \lim_{x \rightarrow \infty} 3 - 8\left(\frac{1}{4}\right)^{2-x} = 3 - 8\left(\frac{1}{4}\right)^{2-\infty} = 3 - 8\left(\frac{1}{4}\right)^{-\infty} = 3 - 8\times 4^{\infty} = 3 - \infty = -\infty$

Thus, the horizontal asymptote is x = 3.

--------------------------------------------------

Question c:

The limit of x going to infinity of the function is negative infinity, which means that the function is decreasing.

--------------------------------------------------

Question d:

Exponential function has no restrictions in the domain, so it is all real values, that is $(-\infty,\infty)$ .
From the limits in item c, the range is: $(-\infty,3)$

--------------------------------------------------

The sketching of the graph is given appended at the end of this answer.

A similar problem is given at brainly.com/question/16533631