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3 years ago

Use the elimination method to solve the following system of equations.

1 answer:

3 0

The answer
2x - y + z = -3 (1)
2x + 2y + 3z = 2 (2)
3x - 3y - z = -4 (3)

 (1) - (2) 3y +2z =5
3 .(1) - 2.(2) 3y+5z = -1

let 's solve
3y +2z =5
3y+5z = -1
z= - 2, and 3y =5+4=9, y=3, so 2x - 3 -2 = -3 implies x= 1

finally x=1, y=3 and z= -2
proof
2x - y + z = -3?? 2.1 - 3 -2 = -3 (true)

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alina1380 [7]

The first one is 4
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2 years ago

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ryzh [129]

Answer:

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Step-by-step explanation:

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3 years ago

A city park commission received a donation of playground equipment from a parents' organization. The area of the playground need

dalvyx [7]

Answer:

Length = 20.49 yards and Width = 12.49 yards.

Step-by-step explanation:

The area of the rectangular playground is given by 256 yards square. It is also known that one of the sides of the playground is 8 yards longer than the other side. Therefore, let the smaller side by x yards. Then the longer side will be (x+8) yards. The area of the rectangle is given by:

Area of the rectangle = length * width.

256 = x*(x+8)

x^2 + 8x = 256. Applying the completing the square method gives:

(x)^2 + 2(x)(4) + (4)^2 = 256 + 16

(x+4)^2 = 272. Taking square root on both sides gives:

x+4 = 16.49 or x+4 = -16.49 (to the nearest 2 decimal places).

x = 12.49 or x = -20.49.

Since length cannot be negative, therefore x = 12.49 yards.

Since smaller side = x yards, thus smaller side = 12.49 yards.

Since larger side = (x+8) yards, thus larger side = 12.49+8 = 20.49 yards.

Thus, the length and the width to minimize the perimeter of fencing is 20.49 yards and 12.49 yards respectively!!!

7 0

3 years ago

A 14 gram sample of a substance that's used to preserve fruit and vegetables has a k-value of 0.1092. Find the substance's half-

nignag [31]

Answer:

t = 6.3

Step-by-step explanation:

N=Noe^(-kt)

No = 14 grams

k = .1092

We want to find t when N = 7 or 1/2 of 14

N=Noe^(-kt)

7 = 14 e ^ (-.1092t)

Divide each side by 14

1/2 = e ^ (-.1092t)

take the natural log of each side

ln (1/2) = ln e ^ (-.1092t)

ln (1/2) = -.1092t

Divide each side by -.1092

ln (1/2)/ -.1092 = t

t≈6.3475

Rounding to the nearest tenth

t = 6.3

5 0

3 years ago

Find sin(a+B)

diamong [38]

Answer:

Cos A=5/13

we have

Cos² A= $1-Sin ²A$

25/169=1-Sin²A

sin²A=1-25/169

sin²A=144/169

Sin A= $\sqrt{144/169}=12/13$

again

Tan B=4/3

P/b=4/3

p=4

b=3

h= $\sqrt{3²+4²}=5$

Now

Sin B=p/h=4/5

in IV quadrant sin angle is negative so

Sin B=-4/5

CosB=b/h=3/5

Now

Sin(A+B):sinAcosB+CosAsinB

now 

substitute value

Sin(A+B):12/13*3/5+5/13*(-4/5)=36/65-4/13

=16/65 is a required answer

6 0

2 years ago