4 + 1 = 17<br> What is the solutikn

Solve the system by substitution. <br> -5x+3y=2 <br> Y=2x

Volgvan

Answer:

2 is the required answer.

Step-by-step explanation:

<u>Solution:</u>

<u>Given</u><u>:</u>

-5x+3y=2..............(i)

Putting the value of y=2x in the equation (i); we get:

i.e -5x+3×2x=2

or, -5x+6x=2

or, x=2

i.e. x=2

y=2x=2×2=4

8 0

3 years ago

Which of the following geometric series converges?

Artist 52 [7]

All three series converge, so the answer is D.

The common ratios for each sequence are (I) -1/9, (II) -1/10, and (III) -1/3.

Consider a geometric sequence with the first term <em>a</em> and common ratio |<em>r</em>| < 1. Then the <em>n</em>-th partial sum (the sum of the first <em>n</em> terms) of the sequence is

$S_n=a+ar+ar^2+\cdots+ar^{n-2}+ar^{n-1}$

Multiply both sides by <em>r</em> :

$rS_n=ar+ar^2+ar^3+\cdots+ar^{n-1}+ar^n$

Subtract the latter sum from the first, which eliminates all but the first and last terms:

$S_n-rS_n=a-ar^n$

Solve for $S_n$ :

$(1-r)S_n=a(1-r^n)\implies S_n=\dfrac a{1-r}-\dfrac{ar^n}{1-r}$

Then as gets arbitrarily large, the term $r^n$ will converge to 0, leaving us with

$S=\displaystyle\lim_{n\to\infty}S_n=\frac a{1-r}$

So the given series converge to

(I) -243/(1 + 1/9) = -2187/10

(II) -1.1/(1 + 1/10) = -1

(III) 27/(1 + 1/3) = 18

8 0

3 years ago

A manager bought 12 pounds of peanuts for $30. He wants to mix $5 per pound cashews with the peanuts to get a batch of mixed nut

seraphim [82]

Answer:

18 pounds of cashews are needed.

Step-by-step explanation:

Given;

A manager bought 12 pounds of peanuts for $30.

Price of peanut per pound P = $30/12 = $2.5

Price of cashew per pound C = $5

Price of mixed nut per pound M = $4

Let x represent the proportion of peanut in the mixed nut.

The proportion of cashew will then be y = (1-x), so;

xP + (1-x)C = M

Substituting the values;

x(2.5) + (1-x)5 = 4

2.5x + 5 -5x = 4

2.5x - 5x = 4 -5

-2.5x = -1

x = 1/2.5 = 0.4

Proportion of cashew is;

y = 1-x = 1-0.4 = 0.6

For 12 pounds of peanut the corresponding pounds of cashew needed is;

A = 12/x × y

A = 12/0.4 × 0.6 = 18 pounds

18 pounds of cashews are needed.

4 0

3 years ago

The sum of two numbers is 0. Twice the smaller number subtracted from 3 times the larger number is 10. Let x represent the large

Bezzdna [24]

Answer:

x+y=0 and 3x-2y=10

Step-by-step explanation

Let the numbers be x and y.

The sum of the two numbers is 0

$\implies \: x + y =0$

Letting the smaller number be y and the

larger number be x:

twice the smaller number

$\implies \: 2y$

Also, 3 times the larger number

$\implies \: 3x$

Now ,twice the smaller number subtracted from 3 times the larger number is 10.

$\implies \: 3x - 2y = 10$

Therefore the equations are

$x + y =0$

and

$3x - 2y =10$

6 0

3 years ago

Sophia puts $250 in the bank with a 2.5% annual interest rate compounded monthly. If Sophia does not touch his money, how much m

Fittoniya [83]

Answer:

Step-by-step explanation:

Deposited amount initially (P) = $250.

Rate of interest(r) = 2.5% compounded monthly = 0.025

Number of years (t) = 4.

Number of months in an year (n) = 12.

Formula for compound interest:

$A=P(1+\frac{r}{n})^{nt}$ .

Plugging values in formula, we get

$A= 250(1+\frac{0.025}{12})^{12\times 4}$

$A= 250(1.00208)^{48}$

$A= 250\times \:1.10506$

A=276.26.

<h3>Therefore, correct option is D) $276.26.</h3>

7 0

3 years ago

4 + 1 = 17 What is the solutikn