All categories

3 years ago

What is the sum of the first 14 terms of the sequence -11+(-18)+(-25)+(-32)...

1 answer:

6 0

The difference between -11 and -18 is -7
the difference between -18 and -25 is -7
the difference between -25 and -32 is -7

therefore we can say that the difference between all of the terms will be -7.

the first term is -11 -> call this a
the difference is -7 -> call this d
the number of terms is 14 -> call this n

use the equation (sum of) $_{n}$ = $\frac{n}{2}$ (2a + (n-1)d)

(sum of) $_{n}$ = $\frac{14}{2}$ (2 x -11 + (14-1)-7)

= -7(-22 + (13 x -7))
= -7(-22 + -91)
= -7(-111)
= 777

You might be interested in

Simplify and then evaluate the equation when a= 2 and b = 4. b2 + 3(b – 62) – 2a= [?]

I am Lyosha [343]

Answer:

-170

Step-by-step explanation:

First, you would substitute 2 and 4 for a and b. 4 times 2 + 3(4 - 62) - 2 times 2 = ?

Then, do 4 times 2 (8), 3(4-62)=3(-58)

8 + -174 - 4 = -170

5 0

3 years ago

Factor the quadratic equation below to reveal the solutions. X^2+4x-21=-9

a_sh-v [17]

Answer:

x = 3 and x = -7

Step-by-step explanation:

The given quadratic equation is $x^2+4x-21=0$ . We need to find the solution of this equation.

If the equation is in the form of $ax^2+bx+c=0$ , then its solutions are given by :

$x=\dfrac{-b\pm \sqrt{b^2-4ac} }{2a}$

Here, a = 1, b = 4 and c = -21

Plugging all the values in the value of x, such that :

$x=\dfrac{-b+ \sqrt{b^2-4ac} }{2a},\dfrac{-b- \sqrt{b^2-4ac} }{2a}\\\\x=\dfrac{-4+ \sqrt{(4)^2-4\times 1\times (-21)} }{2(1)},\dfrac{-4- \sqrt{(4)^2-4\times 1\times (-21)} }{2(1)}\\\\x=3, -7$

So, the solutions of the quadratic equation are 3 and -7.

6 0

3 years ago

Is the Mandelbrot set locally connected?

MariettaO [177]

Answer:

Step-by-step explanation:

It is conjectured that the Mandelbrot set is locally connected. This famous conjecture is known as MLC (for Mandelbrot locally connected). By the work of Adrien Douady and John H. Hubbard, this conjecture would result in a simple abstract "pinched disk" model of the Mandelbrot set. In particular, it would imply the important hyperbolicity conjecture mentioned above.

The work of Jean-Christophe Yoccoz established local connectivity of the Mandelbrot set at all finitely renormalizable parameters; that is, roughly speaking those contained only in finitely many small Mandelbrot copies.[19] Since then, local connectivity has been proved at many other points of {\displaystyle M}M, but the full conjecture is still open.

5 0

3 years ago

Andy completes the square for the equation x2 + 6x - 8 = 0. Which of the following equations reveals the vertex of the parabola?

Stolb23 [73]

If the equation $x^2+6x-8$ has undergo completing the square, the answer would be:
$x^2+6x-8
$
$x^2+6x+9-8-9$
**In this example, since 6x is the middle term, what comes to my mind is the polynomial (x+3) because 2ab results into 6x. [from the special products lesson $(a+b)^2=a^2+2ab+b^2$ ]
$(x+3)^2 -17 = 0$
So if the equation is equal to y, then this equation's
$y+17=(x+3)^2$
The vertex would be on the point (-3, -17)

3 0

3 years ago

Read 2 more answers

Consider 6x2 + 6x + 1. Which term immediately tells you that this expression is NOT a perfect square trinomial? Justify your ans

oksian1 [2.3K]

Answer:

Step-by-step explanation:

The 6x^2 because 6 is not a perfect square.

4 0

4 years ago

Read 2 more answers