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3 years ago

Can somebody help me with number 7? Please explain as well! :)

Mathematics

1 answer:

gayaneshka [121]3 years ago

4 0

To factor number 7 :
3x^2-12
3x^2+3×-4
3*1, -4:2*-2
3(x^2-2^2)
use difference of square formula ((a^2+b^2=(a+b)(a-b))
3(x+2)(x-2)

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Help I need it now!!<br> T14= 46, and t20= 100, find t3, t7, and tn

Vinil7 [7]

Answer:

$t_3 = -53\\\\\\t_7 = -17\\t_n= -80 +9n$

Step-by-step explanation:

Arithmetic sequence:

$\sf \boxed{t_n=a+(n-1)d}$

Here a is the first term and d is the common difference.

$t_{14}= 6$ ⇒ $\sf a + 13 d = 46$ ------------(I)

$\sf t_{20} = 100$ ⇒ a + 19d = 100 ---------(II)

Subtract equation (I) from (II)

(I1) a + 19d = 100

(II) a + 13d = 46

6d = 54

d = 54 ÷ 6

$\sf \boxed{d = 9}$

Substitute d = 9 in equation(I) and find 'a',

a + 13*9= 46

a + 117 = 46

a = 46 - 117

a = -71

$\sf t_3 = -71 + 2*9$

= -71 + 18

= -53

$\sf t_7 = -71 + 6*9$

= -71 + 54

= -17

$\sf t_n= -71 + (n-1)*9$

= -71 + 9*n - 1 *9

= -71 + 9n - 9

= -71 - 9 + 9n

= - 80 + 9n

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