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3 years ago

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

1 answer:

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

p ⇒ q

¬q ⇒ ¬p

In this case, the contrapositive claims that

"If there are no scalars α and β such that c = αa + βb, then a₁b₂ - a₂b₁ = 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

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

and this is what we wanted to prove. QED

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

Read 2 more answers

Which equation can be used to solve for x in the parallelogram below?

densk [106]

Answer:

B. (3x - 12)° = (2x + 8)°

Step-by-step explanation:

This equation can be used to solve x.

3x - 12 = 2x + 8

3x - 2x = 12 + 8

x = 20°

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

Verification:

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

60 - 12 = 40 + 8

48° = 48°

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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:

go in ur mirror and look at the time did it somehow get darker or lighter???

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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:
V = (w) * (l) * (h)
Where,
w: width
l: long
h: height.
We have then:
V = (w) * (l) * (h) = 48 in ^ 3
The volume of a similar box is:
V = (w * (2/3)) * (l * (2/3)) * (h * (2/3))
We rewrite:
V = ((w) * (l) * (h)) * ((2/3) * (2/3) * (2/3))
V = (w) * (l) * (h) * ((2/3) ^ 3)
V = 48 * ((2/3) ^ 3)
V = 14.22222222 in ^ 3
Answer:
the volume of a similar box that is smaller by a scale factor of 2/3 is:
V = 14.22222222 in ^ 3

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3 years ago