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2 years ago

Solve the system of equations

Mathematics

2 answers:

Illusion [34]2 years ago

5 0

Answer:

x=-8, y=2

Step-by-step explanation:

if 1/2x+6y=12 then 1/2x+y=2 and x+y=1 and y=1-x..if y=1-x then 1-x=x=15 and 2x=16 so x=8 if x=8 then 1/2(8) +6y=12 or 4=6y=12.. then 2y=4 and y=2

kaheart [24]2 years ago

3 0

Answer:

x=-12,y=3

Step-by-step explanation:

1/2x+6y=12

y=x+15

since y=x+15

substitute y in first equation, we have

1/2x+6(x+15)=12

open the bracket

1/2x+6x+90=12

1/2x+6x=12-90

x/2+6x= -78

13x/2=-78

13x=2×-78

x=-12

Now x=-12, put x=-12 in the second equation, we have

y=x+15

y=-12+15

y=3

hope it helps

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adoni [48]

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3 years ago

Find the first 4 terms in each sequence

koban [17]

Answer:

a₁ = -21 (Given)

a₂ = -28

a₃ = -35

a₄ = -42

Step-by-step explanation:

First term a₁ = -21 (Given)

…………………………………

Second term a₂ :

a₂ = $a_{2-1} - 7\\a_{1} - 7\\a_{1} = -21\\-21 - 7 = -28$

…………………………………

Third term a₃ :

a₃ = $a_{3-1} - 7\\a_{2} - 7\\a_{2} = -28\\-28 - 7 = -35$

…………………………………

Fourth term a₄ :

a₄ = $a_{4-1} - 7\\a_{3} - 7\\a_{3} = -35\\-35 - 7 = -42$

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2 years ago

Ernie bought 3 12-packs of regular cola, 4 12-packs of diet cola, and 2 6-packs of orange soda. How many cans did he buy? 3. Dra

Feliz [49]

$(3 \times 12) + (4 \times 12) +(2 \times 6) \\ 36 + 48 + 12 = 96$

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3 years ago

An icicle with a diameter of 15.5 centimeters at the top, tapers down in the shape of a cone with a length of

Helga [31]

Answer:

Step-by-step explanation:

Note: I will leave the answers as fraction and in terms of pi unless the question states rounding conditions to ensure maximum precision.

From the question, we can tell it is a inversed-cone (upside down)

Volume of Cone = $\pi r^{2} \frac{h}{3}$

a) Given Diameter , d = 15.5cm and Length , h = 350cm,

we first find the radius.

$r = \frac{d}{2} \\=\frac{15.5}{2} \\=7.75cm$

We will now find the volume of the cone.

Volume of cone $\pi (7.75)^{2} \frac{350}{3} \\= \frac{168175\pi }{24}$

We know the density of ice is 0.93 grams per $1cm^{3}$

$1cm^{3} =0.93g\\\frac{168175\pi }{24} cm^{3} =0.93(\frac{168175\pi }{24} )\\= 20473 g$ (Nearest Gram)

b) After 1 hour, we know that the new radius = 7.75cm - 0.35cm = 7.4cm

and the new length, h = 350cm - 15cm = 335cm

Now we will find the volume of this newly-shaped cone.

Volume of cone = $\pi (7.4)^{2} \frac{335}{3} \\= \frac{91723\pi }{15} cm^{3}$

Volume of cone being melted = New Volume - Original volume

= $\frac{168175\pi }{24} -\frac{91723\pi }{15} \\= \frac{35697\pi }{40} cm^{3}$

c) Lets take the bucket as a round cylinder.

Given radius of bucket, r = 12.5cm (Half of Diameter) and h , height = 30cm.

Volume of cylinder = $\pi r^{2} h\\=\pi (12.5)^{2} (30)\\=\frac{9375\pi }{2} cm^{3}$

To overflow the bucket, the volume of ice melted must be more than the bucket volume.

Volume of ice melted after 5 hours = $5(\frac{35697\pi }{40} )\\=\frac{35697\pi }{8} cm^{3}$

See, from here of course you are unable to tell whether the bucket will overflow as all are in fractions, but fret not, we can just find the difference.

Volume of bucket - Volume of ice melted after 5 hours

= $\frac{9375\pi }{2} -\frac{35697\pi }{8 } \\=\frac{1803\pi }{8}cm^{3}$

from we can see the bucket can still hold more melted ice even after 5 hours therefore it will not overflow.

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madreJ [45]

Answer:

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Step-by-step explanation:

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