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3 years ago

Can you draw an isosceles triangle with only one 80 degree angle?

Mathematics

1 answer:

aev [14]3 years ago

6 0

Answer:

The triangle is 50,50 80

Step-by-step explanation:

The three angles of a triangle equal 180 degrees

We only want one 80 degree angle. That means the other two angles have to be the same, since it is an isosceles triangle. Call the other angle x

x+x+80 = 180

2x+80 =180

Subtract 80 from each side

2x+80-80=180-80

2x =100

Divide by 2

2x/2=100/2

x = 50

Each of the other angles in the triangle would have to equal 50 degrees

The triangle is 50,50 80

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Solve the system of equations by finding the reduced row echelon form of the augmented matrix. Write the solutions for x and y i

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Answer:

The solutions for the given system of equations are:

$\left \{ {{x=-5} \atop {y=12-4z}} \right.$

Step-by-step explanation:

Given the equation system:

$\left \{ {{3x+y+4z=-3} \atop {-x+y+4z=17}} \right.$

We obtain the following matrix:

$\left[\begin{array}{cccc}3&1&4&-3\\-1&1&4&17\end{array}\right]$

Step 1: Multiply the fisrt row by 1/3.

$\left[\begin{array}{cccc}1&\frac{1}{3} &\frac{4}{3}&-1\\-1&1&4&17\end{array}\right]$

Step 2: Sum the first row and the second row.

$\left[\begin{array}{cccc}1&\frac{1}{3} &\frac{4}{3}&-1\\0&\frac{4}{3} &\frac{16}{3}&16\end{array}\right]$

Step 3: Multiply the second row by 3/4.

$\left[\begin{array}{cccc}1&\frac{1}{3} &\frac{4}{3}&-1\\0&1 &4&12\end{array}\right]$

Step 4: Multiply the second row by -1/3 and sum the the first row.

$\left[\begin{array}{cccc}1&0 &0&-5\\0&1 &4&12\end{array}\right]$

The result of the reduced matrix is:

$\left \{ {{x=-5} \atop {y+4z=12}} \right.$

This is equal to:

$\left \{ {{x=-5} \atop {y=12-4z}} \right.$

These are the solutions for the system of equations in terms of z, where z can be any number.

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