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3 years ago

Solve the system of equations using linear combination method or substitution method. Show all steps.

Mathematics

1 answer:

Korvikt [17]3 years ago

7 0

Answer:

{x,y} = {19/12,5/6}

Step-by-step explanation:

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You go shopping at a local department store with your friend and cousin. You buy one pair of jeans, four pairs of shorts, and tw

VashaNatasha [74]

Answer: Cost per pair of jeans = $ 20

Cost per pair of shorts = $12

Cost per shirt = $8

Step-by-step explanation:

Let x= cost per pair of jeans

y = Cost per pair of shorts

z= cost per shirt.

For you, total cost = x+4y+2z= 84

For your friend, total cost = 2x+y+3z=76

For cousin, total cost = x+2y+z= 52

Required system:

$x+4y+2z=84\ (i)\\ 2x+y+3z=76\ (ii)\\ x+2y+z=52\ (iii)$

from (i), $x=84-4y-2z$ (*)

put this in (ii) and (iii) we get

$2\left(84-4y-2z\right)+y+3z=76\\\Rightarrow\ -7y-z+168=76\ (iv)\\\\ 84-4y-2z+2y+z=52\\\Rightarrow\ -2y-z+84=52 \ (v)$

from (iv), $y=-\frac{z-92}{7}\ (vi)$

$\mathrm{Subsititute\:}y=-\frac{z-92}{7}\ \text{in}\ (v)$

$-2\left(-\frac{z-92}{7}\right)-z+84=52\\\\\Rightarrow\ -2\left(-\frac{z-92}{7}\right)-z=-32\\\\\Rightarrow\ -\frac{5z}{7}-\frac{184}{7}=-32\\\\\Rightarrow\ -5z-184=-224\\\\\Rightarrow\ -5z=-40\\\\\Rightarrow\ z=8$

$\mathrm{Subsititute\:}z=8\text{ in (vi)}$

$y=-\frac{8-92}{7}\\\\\Rightarrow \ y=12$

$\mathrm{Subsititute\:}z=8,\:y=12\text{ in (*)}$

$x=84-4\cdot \:12-2\cdot \:8\\\\\Rightarrow\ x= 20$

Hence, x= 20, y= 12 , z=8

So, Cost per pair of jeans = $ 20

Cost per pair of shorts = $12

Cost per shirt = $8

7 0

3 years ago

What is the volume of this sphere <br> Use π=3.14 and round your answer to the nearest hundredth

Alina [70]

The answer is 523.6 and all you have to do is round it to the nearest hundredth

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2 years ago

Which show the factored form of x^2-12x-45

slavikrds [6]

Answer:

$x^{2} -12x-45\\=(x-15)(x+3)$

Step-by-step explanation:

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3 years ago

a chicken needs cooking for 2 hours 20 min it needs to be cooked at 1pm what time do i need to start cooking

castortr0y [4]

So it cooks for 2 hrs and 20 minutes......and it has to be done by 1 pm.

so from 1 p.m. - 2 hrs = 11 a.m........- 20 minutes = 10:40 a.m

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2 years ago

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morpeh [17]

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3 years ago

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