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3 years ago

The first term in this sequence is -1. Write the function that represents the sequence

Mathematics

1 answer:

sattari [20]3 years ago

3 0

Answer:

$a_{n}$ = 2n - 3

Step-by-step explanation:

Note the difference in consecutive terms is constant, that is

1 - (- 1) = 3 - 1 = 5 - 3 = 7 - 5 = 2

This indicates that the terms are an arithmetic sequence with

$a_{n}$ = a₁ + (n - 1)d

where a₁ is the first term and d the common difference

Here a₁ = - 1 and d = 2, thus

$a_{n}$ = - 1 + 2(n - 1) = - 1 + 2n - 2 = 2n - 3

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Let G denote the centroid of triangle ABC. If triangle ABG is equilateral with side length 2, then determine the perimeter of tr

zhannawk [14.2K]

We know from Euclidean Geometry and the properties of a centroid that GC=2GM. Now GM=sin60*GA= $\sqrt{3}$ . Hence CM=GC+GM=3* $\sqrt{3} /$ . Now, since GM is normal to AB, we have by the pythagoeran theorem that:
$AC^2=AM^2+GM^2=BM^2+GM^2=BC^2$
Hence, we calculate from this that AC^2= 28, hence AC=2* $\sqrt{7}$ =BC. Thus, the perimeter of the triangle is 2+4* $\sqrt{7}$ .

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3 years ago

Use the guess and check method to solve for the equation : 4(x+2)+2=14 please help need answer

TiliK225 [7]

4(x+2)+2=14

4x+8+2=14

4x+10=14

Subtract 10 from both sides

4x=4

Divide by 4 on both sides

x=1

4 0

4 years ago

Question 2 of 10

DiKsa [7]

Answer:

y=2x-3

Step-by-step explanation:

First we find the y-intercept of this graph whic in this case is -3. Then we plot two pints on the graph and caculate the rise over run which is 2/1=2. Finally, we get the equation- y=2x-3.

5 0

3 years ago

Jerome found the lengths of each side of triangle QRS as shown, but did not simplify his answers. Simplify the lengths of each s

tankabanditka [31]

Answer:

D. Triangle QRS is an isosceles triangle because QR = RS.

Step-by-step explanation:

Find the length of each side of the triangle using the formula for calculating the distance between two points.

D = √(x2-x1)²+(y2-y1)²

For side RS

R(0,0) and S(5, -3.322)

RS = √(5-0)²+(-3.322-0)²

RS = √25+11.035684

RS = √36.035684

RS = 6.0029

For side RQ

R(0,0) and Q(-3, -5.2)

RQ = √(-3-0)²+(-5.2-0)²

RQ = √9+27.04

RQ = √36.04

RQ = 6.0033

For side QS

Q(-3,-5.2) and S(5, -3.322)

QS = √(5+3)²+(-3.322+5.2)²

QS = √64+3.526884

QS = √67.526884

QS = 8.22

From the calculation it can be seen that RS=QR

Since the two sides f the triangle are equal, hence the triangle is an isosceles triangle. An isosceles triangle is a triangle that has two of its sides equal

7 0

3 years ago

there are five bells which ring at interval of 4,5,12 and 15 minutes respectively at what minute those bells ring at the same ti

Rus_ich [418]

<h3>Answer: 60 minutes</h3>

=====================================================

Explanation:

Let's find the LCM of 4 and 5, which are the first two items of the list.

multiples of 4 are: 4,8,12,16,20,24,...
multiples of 5 are: 5,10,15,20,25,...

The smallest item in each list is 20, so the LCM of 4 and 5 is 20.

We can replace the "4,5" in the list "4,5,12,15" with "20". So our new list would be "20,12,15".

We then repeat the process of finding the LCM of the first two items

multiples of 20 are: 20,40,60,80,...
multiples of 12 are: 12,24,36,48,60,72,...

LCM of 20 and 12 is 60.

The list "20,12,15" condenses to "60,15".

Repeat this process of finding the LCM once more and you'll find the overall LCM is 60.

Therefore, the LCM of the entire set {4,5,12,15} is 60. This is the smallest multiple shared by all four values. Interestingly enough, the outer values pair up to multiply to 60, and so do the inner values.

4*15 = 60

5*12 = 60

The bells ring together every <u>60 minutes</u>

In other words, all of the bells ring together at the same time every hour (perhaps at the top of every hour; eg at 7:00 pm and at 8:00 pm, etc).

8 0

2 years ago