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3 years ago

If the 1st and 10th terms of geometric sequence are 4 and 100. Fine the nth term of the sequence

1 answer:

3 0

A(n)=ar^(n-1) so

100=4r^9

25=r^9

ln25=9lnr

ln25/9=lnr

r=e^(ln25/9)

a(n)=4e^((n-1)(ln25/9) if you wanted an approximation...

a(n)=4(1.43^(n-1))

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Lizzie has 30 coins that total $4.80. All of her coins are dimes, D, and quarters, Q. Algebraically determine how many of each t

Gnom [1K]

Lizzie has 18 dimes and 12 quarters

<em><u>Solution:</u></em>

Let "d" be the number of dimes

Let "q" be the number of quarters

We know that,

value of 1 dime = $ 0.10

value of 1 quarter = $ 0.25

Given that LIzzie has 30 coins

number of dimes + number of quarters = 30

d + q = 30 ---- eqn 1

Also given that the coins total $ 4.80

number of dimes x value of 1 dime + number of quarters x value of 1 quarter = 4.80

$d \times 0.10 + q \times 0.25 = 4.80$

0.1d + 0.25q = 4.8 ------ eqn 2

Let us solve eqn 1 and eqn 2

From eqn 1,

d = 30 - q ---- eqn 3

Substitute eqn 3 in eqn 2

0.1(30 - q) + 0.25q = 4.8

3 - 0.1q + 0.25q = 4.8

0.15q = 1.8

From eqn 3,

d = 30 - 12

Thus she has 18 dimes and 12 quarters

6 0

3 years ago

the home teams score exceeded 2 times the hosting teams score by 5 if the visiting teams score is x which expression represents

babunello [35]

Answer:

2x+5

Step-by-step explanation:

7 0

3 years ago

What is (3 + 12) - 3² + 8 · 2 ÷ 4 ?<br> (please show how/ show work)

lisov135 [29]

Answer:

Step-by-step explanation:

(3 + 12) - 3² + 8 · 2 ÷ 4

15 - 9 + 16 : 4

6 + 4

8 0

3 years ago

Evaluate each expression 9 cubed

Harrizon [31]

9 cubed would be 9×9×9=729

8 0

3 years ago

Read 2 more answers

Find a formula for the sum S of the solutions of the quadratic equation ax²+bx+c=0 .

Deffense [45]

Answer:

$S = -\frac{b}{a}$

Step-by-step explanation:

Given a second order polynomial expressed by the following equation:

$ax^{2} + bx + c, a\neq0$

This polynomial has roots $x_{1}, x_{2}$ such that $ax^{2} + bx + c = (x - x_{1})*(x - x_{2})$ , given by the following formulas:

$x_{1} = \frac{-b + \sqrt{\bigtriangleup}}{2*a}$

$x_{2} = \frac{-b - \sqrt{\bigtriangleup}}{2*a}$

$\bigtriangleup = b^{2} - 4ac$

In this problem, the sum S of the solutions of a quadratic equation is:

$S = x_{1} + x_{2}$

$S = \frac{-b + \sqrt{\bigtriangleup}}{2*a} + \frac{-b - \sqrt{\bigtriangleup}}{2*a}$

They have the same denominators, so we can keep the denominators and sum the numerators.

$S = \frac{-b + \sqrt{\bigtriangleup} - b - \sqrt{\bigtriangleup}}{2a}$

$S = \frac{-2b}{2a}$

$S = -\frac{b}{a}$

8 0

3 years ago