Completing the square worksheet

Let H represent the number of horses and C represent the number of chickens. Since there are 32 legs altogether this means that on equation to use would be given by:

2C + 4 H = 32 (Eq. 1)

Another equation can be made from the fact that there are 11 heads or 11 animals altogether which can be written as:

C + H = 11 (Eq. 2)

From Eq. 2, solve for the number of chickens:

C + H = 11

C = 11 - H (Eq. 3)

Substituting Eq. 3 in Eq. 1, the number of horses can be determined:

2 C + 4 H = 32

2 ( 11 − H ) + 4 H = 32

22 − 2 H + 4 H = 32

2H = 32 − 22

2 H = 10

H = 5 Eq.4

Putting Eq.4 in Eq.1

2C + 4*5 = 32

2C = 32 - 20

2C = 12

C = 12/2

C = 6

8 0

3 years ago

Which equation represents an exponential function that passes through the point (2, 80)?

Sloan [31]

The equation is y=mx+c where m is the gradient and c is the y-intercept

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3 years ago

Read 2 more answers

2. Solve the system of equations. Write your answer in parametric vector notation. X, +5x2 + 4x3 + 3x4 +9xs = 18 2x, +6x2 + 4x3

ratelena [41]

Answer:

The system is inconsistent.

Step-by-step explanation:

The system is

$x_1+5x_2+4x_3+3x_4+9x_5=18\\2x_1+6x_2+4x_3+6x_4+6x_5=28\\3x_1+7x_2+4x_3+10x_4+x_5=41\\4x_1+6x_2+2x_3+7x_4+4x_5=29$

The associated matrix to the system is

$\left[\begin{array}{cccccc}1&5&4&3&9&18\\2&6&4&6&6&28\\3&7&4&10&1&41\\4&6&2&7&4&29\end{array}\right]$

Now we use row operations to find the echelon form of the matrix:

1. We substract to row 2, two times the row 1.

We substract to row 3, three times the row 1.

We substract to row 4, four times the row 1 and obtain the matrix

$\left[\begin{array}{cccccc}1&5&4&3&9&18\\0&-4&-4&0&-12&-8\\0&-8&-8&1&-26&-13\\0&-14&-14&-5&-32&-43\end{array}\right]$

2. We multiply the second row of the preview step by -1/4. We obtain the matrix

$\left[\begin{array}{cccccc}1&5&4&3&9&18\\0&1&1&0&3&2\\0&-8&-8&1&-26&-13\\0&-14&-14&-5&-32&-43\end{array}\right]$

3.

We add to row 3, eight times the row 2.

We add to row 4, fourtheen times the row 2 and obtain the matrix

$\left[\begin{array}{cccccc}1&5&4&3&9&18\\0&1&1&0&3&2\\0&0&0&1&-2&3\\0&0&0&-5&10&-155\end{array}\right]$

4. We add to row 4 of the preview step, five times the row 3 and obtain the matrix

$\left[\begin{array}{cccccc}1&5&4&3&9&18\\0&1&1&0&3&2\\0&0&0&1&-2&3\\0&0&0&0&0&-140\end{array}\right]$

Using backward substitution we have that

$0x_5=-140$ , then $0=-140$ and this is absurd. Then The system is inconsistent.

4 0

3 years ago