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3 years ago

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A sequence of 7 numbers starts with 8. The second number in the sequence is unknown and may be positive or negative. The third t

hrough seventh numbers are the sum of the previous two numbers in the sequence, and the seventh number is 0. What is the sum of the 7 numbers?

1 answer:

scoray [572]3 years ago

8 0

Answer:

4

Explanation:

$a_1=8,a_7=0$

Since the third term is the sum of the two previous terms

$a_3=a_2+a_1$

$a_7=a_6+a_5$

$a_7=a_5+a_4+a_4+a_3$

Continuing in like manner

$a_7=5a_3+3a_2$

Since $a_3=a_2+a_1$

$a_7=5(a_2+a_1+3a_2$

$a_7=5a_2+5a_1+3a_2$

$a_7=8a_2+5a_1$

Recall: $a_1=8,a_7=0$

$0=8a_2+5*8$

$8a_2=-40$

$a_2=-5$

The sequence is therefore:

8,-5,3,-2,1,-1,0

The sum of the seven numbers is 4.

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Give two different sequences of three transformations that would map PQR onto EFG given that PQR=EFG.

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Answer:

Translate P to E; rotate ∆PQR about E until Q is coincident with F; reflect ∆PQR across EF
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Step-by-step explanation:

The orientations of the triangles are opposite, so a reflection is involved. The various segments are not at right angles to each other, so a rotation other than some multiple of 90° is involved. A translation is needed in order to align the vertices on top of one another.

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<em>Additional comment</em>

The mapping can be done in two transformations: translate a ∆PQR vertex to its corresponding ∆EFG point; reflect across the line that bisects the angle made at that vertex by corresponding sides.

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2 years ago

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A bridge in the shape of an arch connects two cities separated by a river. The two ends of the bridge are located at (–7, –13) a

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Answer:

$y=-\dfrac{13}{49}x^2$

Step-by-step explanation:

The shape of an arch corresponds to a parabola.

the general equation for a parabola is:

$y=ax^2+bx+c$

we're given three coordinates: (-7,-13),(7,-13) and (0,0)

so we can plug these values in the general equation to make 3 separate equations:

(x,y) = (-7,-13)

$-13=a(-7)^2+b(-7)+c$

$49a-7b+c=-13$

(x,y) = (7,-13)

$-13=a(7)^2+b(7)+c$

$49a+7b+c=-13$

(x,y) = (0,0)

$0=a(0)^2+b(7)+c$

$c=0$

so we have three equations. and we can solve them simultaneously to find the values of a,b, and c.

we've already found c = 0, let's use substitute it to other equations.

$49a-7b+c=-13\quad\Rightarrow\quad49a-7b=-13$

$49a+7b+c=-13\quad\Rightarrow\quad49a+7b=-13$

we can solve these two equation using the elimination method, by simply adding the two equations

$\quad\quad49a-7b=-13\\+\quad49a+7b=-13$

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

$\quad\quad 98a=-26$

$\quad\quad a=-\dfrac{13}{49}$

Now we can plug this value of a in any of the two equations.

$49a-7b=-13$

$49\left(-\dfrac{13}{49}\right)-7b=-13$

$-13-7b=-13$

$-7b=0$

$b=0$

We have the values of a,b, and c. We can plug them in the general equation to find the equation of the arch.

$y=\left(-\dfrac{13}{49}\right)x^2+0x+0$

$y=-\dfrac{13}{49}x^2$

$49y=-13x^2$

This our equation of the arch!

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3 years ago

Can someone please give me a scenario of this please Y=3x + 2

Deffense [45]

Ahhh I think that is cheating?

Soz I know the anaswer but I cant tell you have to do by your self to learn you can't always ask for answers :<

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