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3 years ago

7

Please do this will give brainiest HELPPPPPP

1 answer:

asambeis [7]3 years ago

6 0

Step-by-step explanation:

1. 6(9+3)=57

2. 3(12+6)+2(4)=29

3. 5(3-16)=65

(3×4+12(4)=48

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The first five terms of a quadratic sequence are 3, 12, 25, 42, 63.

skad [1K]

Since we know the sequence is quadratic, we expect the $n$ -th term to have the general form

$x_n = an^2 + bn + c$

Plug in the first 3 known values of the sequence to form a system of equations.

$x_1 = 3 = a + b + c$

$x_2 = 12 = 4a + 2b + c$

$x_3 = 25 = 9a + 3b + c$

Eliminating $c$ gives

$(4a + 2b + c) - (a + b + c) = 12 - 3 \implies 3a + b = 9$

$(9a + 3b + c) - (a + b + c) = 25 - 3 \implies 8a + 2b = 22 \implies 4a + b = 11$

Eliminating $b$ gives

$(4a + b) - (3a + b) = 11 - 9 \implies a = 2$

Solving for $b,c$ , we get

$4a + b = 11 \implies b = 11-4\cdot2 = 3$

$a+b+c=3 \implies c=3-2-3 = -2$

So, the $n$ -th term of the sequence is

$x_n = \boxed{2n^2 + 3n - 2}$

7 0

2 years ago

Find the distance and midpoint between the points (7, 3) and (-2,-5).

pochemuha

(7,3)
(-2,-5)

Distance:-

$\\ \rm\Rrightarrow \sqrt{(7+2)^2+(3+5)^2}$

$\\ \rm\Rrightarrow \sqrt{9^2+8^2}$

$\\ \rm\Rrightarrow \sqrt{81+64}]/tex][tex]\\ \rm\Rrightarrow \sqrt{145}$

$\\ \rm\Rrightarrow 12(approx)$

Midpoint

$\\ \rm\Rrightarrow \left(\dfrac{7-2}{2},\dfrac{3-5}{2}\right)$

$\\ \rm\Rrightarrow \left(\dfrac{5}{2},\dfrac{-2}{2}\right)$

$\\ \rm\Rrightarrow \left(\dfrac{5}{2},-1\right)$

#TMB

4 0

2 years ago

How does writing equivalent equations help you solve a system of equations?

Alexus [3.1K]

Writing equivalent equations help you solve system of equations because it sets it up for being broken down part by part.

3 0

3 years ago

(GIVING BRAINILEST) The dot plots show the number of crackers per box for two different brands Which of he following statements

Tema [17]

Answer:

A

Step-by-step explanation:

6 0

3 years ago

4 (2x + 3) = 4x + 24 + 6x – 6

omeli [17]

Answer:

-3 = x

Step-by-step explanation:

4 (2x + 3) = 4x + 24 + 6x – 6

8x + 12 = 10x + 18

12 = 2x + 18

-6 = 2x

-3 = x

5 0

4 years ago