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lara [203]
3 years ago
13

The 50th term of an arithmetic sequence is 86 and the common difference is 2.  Find the first three terms of the sequence.

Mathematics
1 answer:
Nesterboy [21]3 years ago
6 0
a_n=a_{n-1}+d=a_{n-2}+2d=\cdots=a_1+(n-1)d

which means

a_{50}=86=a_1+49\times2\implies a_1=-12

which in turn means the next two terms are a_2=-10 and a_3=-8.
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let a = (a1, a2) and b = (b1, b2) and c = (c1,c2) be three non zero vectors. if a1b2 - a2b1 is not equal to 0. then show three a
Ksenya-84 [330]

Consider the contrapositive of the statement you want to prove.

The contrapositive of the logical statement

<em>p</em> ⇒ <em>q</em>

is

¬<em>q</em> ⇒ ¬<em>p</em>

In this case, the contrapositive claims that

"If there are no scalars <em>α</em> and <em>β</em> such that <em>c</em> = <em>α</em><em>a</em> + <em>β</em><em>b</em>, then <em>a₁b₂</em> - <em>a₂b₁</em> = 0."

The first equation is captured by a system of linear equations,

\begin{cases}c_1 = \alpha a_1 + \beta b_1\\ c_2 = \alpha a_2 + \beta b_2\end{cases}

or in matrix form,

\begin{pmatrix}c_1\\c_2\end{pmatrix} = \begin{pmatrix}a_1&b_1\\a_2&b_2\end{pmatrix}\begin{pmatrix}\alpha\\\beta\end{pmatrix}

If this system has no solution, then the coefficient matrix on the right side must be singular and its determinant would be

\begin{vmatrix}a_1&b_1\\a_2&b_2\end{vmatrix} = a_1b_2-a_2b_1 = 0

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3 0
3 years ago
The area of a rectangle is 51 square inches. If the width of the rectangle is 6 inches, what is the length?
Assoli18 [71]
The length of the rectangle is 8.5 inches.
3 0
2 years ago
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densk [106]

Answer:

B. (3x - 12)° = (2x + 8)°

Step-by-step explanation:

This equation can be used to solve x.

3x - 12 = 2x + 8

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x = 20°

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

Verification:

3(20) - 12 = 2(20) + 8

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6 0
3 years ago
. The time of a clock as seen in a mirror is 3:15. The correct time is​
Oksana_A [137]

Answer:

3:15 cause a mirror cant change time

Step-by-step explanation:

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8 0
3 years ago
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a box of crackers has a volume of 48 cubic inches. what is the volume of a similar box that is smaller by a scale factor of 2/3
earnstyle [38]
For this case what you need to know is that the original volume of the cookie box is:
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 h: height.
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 Answer:
 the volume of a similar box that is smaller by a scale factor of 2/3 is:
 V = 14.22222222 in ^ 3
6 0
3 years ago
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