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stealth61 [152]

3 years ago

15

Joan bought a soft drink for 3 dollars and 8 candy bars. She spent a total of 43 dollars. How much did each candy bar cost? Whic

h equation matches this problem?

1 answer:

Oksana_A [137]3 years ago

8 0

Answer:

each candy bar cost 5 dollars

Step-by-step explanation:

first the drink cost 3 dollars so take that away from the total and you have 40. then do 40 divided by the 8 candy bars and you get 5. Which means that each candy bar cost 5 dollars

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14, 16, and 20 using elimination method showing work. Thanks so much

Nady [450]

14) x=0, y=3, z=-2

Solution Set (0,3,-2)

16) x=1, y=1 and z=1

Solution set = (1,1,1)

20) x = -263/31, y=164/31 ,z=122/31

Solution set (-263/31, 164/31 ,122/31)

Step-by-step explanation:

14)

$x-y+2z=-7\\y+z=1\\x=2y+3z$

Rearranging and solving:

$x-y+2z=-7\,\,\,eq(1)\\y+z=1\,\,\,eq(2)\\x-2y-3z=0\,\,\,eq(3)$

Eliminate y:

Adding eq(1) and eq(2)

$x-y+2z=-7\,\,\,eq(1)\\ 0x+y+z=1\,\,\,eq(2)\\-------\\x+3z=-6\,\,\,eq(4)$

Multiply eq(2) with 2 and add with eq(3)

$0x+2y+2z=2\,\,\,eq(2)\\\\x-2y-3z=0\,\,\,eq(3)\\--------\\x-z=2\,\,\,eq(5)$

Eliminate x:

Subtract eq(4) and eq(5)

$x+3z=-6\,\,\,eq(4)\\x-z=2\,\,\,eq(5)\\-\,\,\,+\,\,\,\,\,\,-\\---------\\4z=-8\\z= -2$

So, value of z = -2

Now putting value of z in eq(2)

$y+z=1\\y+(-2)=1\\y-2=1\\y=1+2\\y=3$

So, value of y = 3

Now, putting value of z and y in eq(1)

$x-y+2z=-7\\x-(3)+2(-2)=-7\\x-3-4=-7\\x-7=-7\\x=-7+7\\x=0$

So, value of x = 0

So, x=0, y=3, z=-2

S.S(0,3,-2)

16)

$3x-y+z=3\\\x+y+2z=4\\x+2y+z=4$

Let:

$3x-y+z=3\,\,\,eq(1)\\x+y+2z=4\,\,\,eq(2)\\x+2y+z=4\,\,\,eq(3)$

Eliminating y:

Adding eq(1) and (2)

$3x-y+z=3\,\,\,eq(1)\\x+y+2z=4\,\,\,eq(2)\\---------\\4x+3z=7\,\,\,eq(4)$

Multiply eq(1) by 2 and add with eq(3)

$6x-2y+2z=6\,\,\,eq(1)\\x+2y+z=4\,\,\,eq(3)\\---------\\7x+3z=10\,\,\,eq(5)$

Now eliminating z in eq(4) and eq(5) to find value of x

Subtracting eq(4) and eq(5)

$4x+3z=7\,\,\,eq(4)\\7x+3z=10\,\,\,eq(5)\\-\,\,\,-\,\,\,\,\,\,\,\,\,\,-\\-----------\\-3x=-3\\x=-3/-3\\x=1$

So, value of x = 1

Putting value of x in eq(4) to find value of x:

$4x+3z=7\\4(1)+3z=7\\4+3z=7\\3z=7-4\\z=3/3\\z=1$

So, value of z = 1

Putting value of x and z in eq(2) to find value of y:

$x+y+2z=4\\1+y+2(1)=4\\1+y+2=4\\y+3=4\\y=4-3\\y=1$

So, x=1, y=1 and z=1

Solution set = (1,1,1)

20)

$x+4y-5z=-7\\3x+2y+2z=-7\\2x+y+5z=8$

Let:

$x+4y-5z=-7\,\,\,eq(1)\\3x+2y+2z=-7\,\,\,eq(2)\\2x+y+5z=8\,\,\,eq(3)$

Solving:

Eliminating z :

Adding eq(1) and eq(3)

$x+4y-5z=-7\,\,\,eq(1)\\2x+y+5z=8\,\,\,eq(3)\\---------\\3x+5y=1\,\,\,eq(4)$

Multiply eq(1) with 2 and eq(2) with 5 and add:

$2x+8y-10z=-14\,\,\,eq(1)\\15x+10y+10z=-35\,\,\,eq(2)\\----------\\17x+18y=-49\,\,\,eq(5)$

Eliminate y:

Multiply eq(4) with 18 and eq(5) with 5 and subtract:

$54x+90y=18\\85x+90y=-245\\-\,\,\,-\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,+\\-------\\-31x=158\\x=-\frac{263}{31}$

So, value of x = -263/31

Putting value of x in eq(4)

$3x+5y=1\\3(-\frac{263}{31})+5y=1\\-\frac{789}{31}+5y=1 \\5y=1+\frac{789}{31}\\5y=\frac{820}{31}\\y=\frac{820}{31*5}\\y=\frac{164}{31}$

Now putting x = -263/31 and y=164/31 in eq(1) and finding z:

We get z=122/31

So, x = -263/31, y=164/31 ,z=122/31

Solution set (-263/31, 164/31 ,122/31)

Keywords: Solving system of Equations

Learn more about Solving system of Equations at:

#learnwithBrainly

4 0

2 years ago

I will give you extra point and mark you braniest if you give me an explanation on how to find the answer.

EastWind [94]

Answer:

Step-by-step explanation:

The surface area of a cylinder is 2pi *rh + 2pir^2, where r and h are radius and height, respectively. (If you want me to explain this, comment down below). Anyways, we can simply plug in 11 and 8 in the formula, so 2* 8*11*pi + 2* pi * 8^2=304pi. Thus, we do 304 * 3.14=954.56.

4 0

3 years ago

Read 2 more answers

PR and os are diameters of circle T. What is the

____ [38]

Answer:

100degrees

Step-by-step explanation:

Find the diagram attached

From the diagram

<PQT =<TRS = 40

Since the triangle STR is isosceles, here,

<TSR =<TRS = 40

Also the sum of angle in a triangle is 189, hence:

Arc SR+<TSR +<TRS = 18₩

ArcSR +40+40=180

ArcSR +80=180

ArcSR = 180-80

ArcSR = 100degrees

Hence the measure of SR is 100degrees

8 0

3 years ago

Select from the drop - down menus to correctly complete each statement

Stels [109]

In a flowchart proof, <u>statements</u> and <u>conclusions</u> are connected with arrows.

In terms of mathematics, a statement is simply any sentence in which it can be verifiably true or false. A statement cannot be a subjective opinion. It must be an objective fact and there must not be any ambiguity involved. A conclusion is also a statement that derives from the first statement made.

As an example, you can have the simple argument "if it rains, then it gets wet outside". So the box on the left would be "it rains" and the box on the right would be "it gets wet outside". An arrow connecting the two shows the logical flow of how the argument is set up.

See the diagram below.

Side note: the box on the left is also considered the antecedent because it comes before the conclusion.

5 0

3 years ago

If Victoria earns $216.30 for working $6 hours in a day, how much does she earn per hour?

geniusboy [140]

Answer:

$36.05

Step-by-step explanation:

Do 216.30 then divide that by 6. With that you get 36.05; the amount she makes per hour.

5 0

3 years ago