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3 years ago

3x + 5y = 7 -3x - 2y = -1

Mathematics

1 answer:

Oksanka [162]3 years ago

6 0

Answer:

(-1,2) y=2 x=-1

Step-by-step explanation:

This is a system of equations and in this you see there is 3x and negative three x. To solve this you need tp get rid of one of the variables. so we can add the two equations together to get 3y=6. This means that y=2 if we divide by 3 on both sides. Then we just plug 3 in for y and we get 3x+10=7. We subtract 10 on both sides to get 2x=-3 which means x=-1.

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Help please i need to pass

stellarik [79]

Answer:

hi! i dont have the answer because i suck at school lol XD but, i actually have the same question! do you know the answer yet?:] sorry to bother you if you dont.

Step-by-step explanation:

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3 years ago

Read 2 more answers

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Sveta_85 [38]

Something happened when you copy and pasted the question, was it important to the question?

8 0

3 years ago

The total cost (in hundreds of dollars) to produce x units of a product is c(x) = (3x-2) / (8x+1), find the average cost for eac

olya-2409 [2.1K]

Answer:

a) $\frac{74}{10025}$

b) $\frac{3x-2}{x(8x+1)}$

c) $\frac{-24x^2+32x-2}{(8x^2+x)^2}$

Step-by-step explanation:

For total cost function $c(x)$ , average cost is given by $\frac{c(x)}{x}$ i.e., total cost divided by number of units produced.

Marginal average cost function refers to derivative of the average cost function i.e., $\left ( \frac{c(x)}{x} \right )'$

Given: $c(x)=\frac{3x-2}{8x+1}$

Average cost = $\frac{c(x)}{x}=\frac{3x-2}{x(8x+1)}$

At x = 50 units,

$\frac{c(50)}{50}=\frac{150-2}{50(400+1)}=\frac{148}{50(401)}=\frac{74}{10025}$

Average cost = $\frac{c(x)}{x}=\frac{3x-2}{x(8x+1)}$

Marginal average cost:

Differentiate average cost with respect to $x$

Take $f=3x-2\,,\,g=8x^2+x$

using quotient rule, $\left ( \frac{f}{g} \right )'=\frac{f'g-fg'}{g^2}$

Therefore,

$\left ( \frac{c(x)}{x} \right )'=\left ( \frac{3x-2}{8x^2+x} \right )'\\=\left ( \frac{3(8x^2+x)-(16x+1)(3x-2)}{(8x^2+x)^2} \right )\\=\frac{24x^2+3x-48x^2-3x+32x+2}{(8x^2+x)^2}\\=\frac{-24x^2+32x-2}{(8x^2+x)^2}$

3 0

3 years ago

An architect plans to buy 5 stone spheres and 3 stone cylinders. For the same amount, she can buy 2 stone spheres and 6 stone c

Vedmedyk [2.9K]

The cost of each stone sphere is $ 36.81

Solution:

Given that,

An architect plans to buy 5 stone spheres and 3 stone cylinders

For the same amount, she can buy 2 stone spheres and 6 stone cylinders

Let "x" be that same amount

Let "a" be the cost of each stone sphere

Cost of each stone cylinder = $ 36.81

Therefore,

x = 5 stone spheres and 3 stone cylinders

x = 5a + 3(36.81)

Similarly,

x = 2 stone spheres and 6 stone cylinders

x = 2a + 6(36.81)

Equate both,

$5a + 3(36.81) = 2a + 6(36.81)\\\\5a + 110.43 = 2a + 220.86\\\\5a - 2a = 220.86 - 110.43\\\\3a = 110.43\\\\a = 36.81$

Thus cost of each stone sphere is $ 36.81

7 0

3 years ago

Find the remainder when 1 + 2 + 2^2 + 2^3 + ... + 2^100 is divided by 7. Thanks in advance!

Firlakuza [10]

Answer:

Step-by-step explanation:

This is a geometric series so the sum is:

a1 * r^n - 1 / (r - 1)

= 1 * (2^101 -1) / (2-1)

= 2^101 - 1.

Find the remainder when 2^101 is divided by 7:

Note that 101 = 14*7 + 3 so

2^101 = 2^(7*14 + 3) = 2^3 * (2^14)^7 = 8 * (2^14)^7.

By Fermat's Little Theorem (2^14) ^ 7 = 2^14 mod 7 = 4^7 mod 7.

So 2^101 mod 7 = (8 * 4^7) mod 7

= (8 * 4) mod 7

= 32 mod 7

= 4 = the remainder when 2^101 is divided by 7.

So the remainder when 2^101- 1 is divided by 7 is 4 - 1 = 3..

4 0

3 years ago