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3 years ago

Find the series shown.

Mathematics

1 answer:

solmaris [256]3 years ago

8 0

Answer:

C $11+13+15+17+...$

Step-by-step explanation:

Consider the series

$\sum\limits_{n=3}^{\infty}(2n+5)$

The nth term of series is $a_n=2n+5$

The bottom index tells you that n starts changing from 3, so

$a_3=2\cdor 3+5=11\\ \\a_4=2\cdot 4+5=13\\ \\a_5=2\cdot 5+5=15\\ \\a_6=2\cdot 6+5=17\\ \\...$

Thus, the sum of all terms is

$11+13+15+17+...$

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how would a enter a payment that was accepted with a 4 month, 8% note in a payment of a $4800.00 account

Anon25 [30]

Answer:

Enter a payment of 5192.52.

Step-by-step explanation:

Consider the provided information.

The payment is $4800 with a 4 month, 8% note.

The amount can be calculated as:

$Amount=p(1+\frac{r}{m})^{mt}$

Where p is money invested, r is annual interest rate, t is number of years and m is number of period.

Now substitute p = 4800 r = 0.08 and m = 4 in the above formula.

$Amount=4800(1+\frac{0.08}{4})^4$

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6 0

3 years ago

Find the measure of the the sides of DEF then classify it by it sides. D(8,-6) E(-1,-3) F(-2,5)

Mama L [17]

Answer:

Part a) The measure of the sides of triangle DEF are

$d_D_E=\sqrt{90}\ units$

$d_E_F=\sqrt{65}\ units$

$d_D_F=\sqrt{221}\ units$

Part b) Is a scalene triangle

Step-by-step explanation:

we know that

the formula to calculate the distance between two points is equal to

$d=\sqrt{(y2-y1)^{2}+(x2-x1)^{2}}$

we have the coordinates

D(8,-6) E(-1,-3) F(-2,5)

step 1

Find the length side DE

D(8,-6) E(-1,-3)

substitute in the formula

$d=\sqrt{(-3+6)^{2}+(-1-8)^{2}}$

$d=\sqrt{(3)^{2}+(9)^{2}}$

$d_D_E=\sqrt{90}\ units$

step 2

Find the length side EF

E(-1,-3) F(-2,5)

substitute in the formula

$d=\sqrt{(5+3)^{2}+(-2+1)^{2}}$

$d=\sqrt{(8)^{2}+(-1)^{2}}$

$d_E_F=\sqrt{65}\ units$

step 3

Find the length side DF

D(8,-6) F(-2,5)

substitute in the formula

$d=\sqrt{(5+6)^{2}+(-2-8)^{2}}$

$d=\sqrt{(11)^{2}+(-10)^{2}}$

$d_D_F=\sqrt{221}\ units$

step 4

Classify the triangle by the measure of its sides

we have

$d_D_E=\sqrt{90}\ units$

$d_E_F=\sqrt{65}\ units$

$d_D_F=\sqrt{221}\ units$

Is a scalene triangle, because is a triangle in which all three sides have different lengths.

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