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slava [35]
2 years ago
11

Geometry help please!! 20 points

Mathematics
1 answer:
vekshin12 years ago
6 0

Answer:

Step-by-step explanation:

Opposite angles of a cyclic quadrilateral are supplementary, so <u>(6x+72)+3x=180</u>

<u />(6x+72)+3x=180\\9x+72=180\\9x=108\\x=12

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In Exercises 40-43, for what value(s) of k, if any, will the systems have (a) no solution, (b) a unique solution, and (c) infini
svet-max [94.6K]

Answer:

If k = −1 then the system has no solutions.

If k = 2 then the system has infinitely many solutions.

The system cannot have unique solution.

Step-by-step explanation:

We have the following system of equations

x - 2y +3z = 2\\x + y + z = k\\2x - y + 4z = k^2

The augmented matrix is

\left[\begin{array}{cccc}1&-2&3&2\\1&1&1&k\\2&-1&4&k^2\end{array}\right]

The reduction of this matrix to row-echelon form is outlined below.

R_2\rightarrow R_2-R_1

\left[\begin{array}{cccc}1&-2&3&2\\0&3&-2&k-2\\2&-1&4&k^2\end{array}\right]

R_3\rightarrow R_3-2R_1

\left[\begin{array}{cccc}1&-2&3&2\\0&3&-2&k-2\\0&3&-2&k^2-4\end{array}\right]

R_3\rightarrow R_3-R_2

\left[\begin{array}{cccc}1&-2&3&2\\0&3&-2&k-2\\0&0&0&k^2-k-2\end{array}\right]

The last row determines, if there are solutions or not. To be consistent, we must have k such that

k^2-k-2=0

\left(k+1\right)\left(k-2\right)=0\\k=-1,\:k=2

Case k = −1:

\left[\begin{array}{ccc|c}1&-2&3&2\\0&3&-2&-1-2\\0&0&0&(-1)^2-(-1)-2\end{array}\right] \rightarrow \left[\begin{array}{ccc|c}1&-2&3&2\\0&3&-2&-3\\0&0&0&-2\end{array}\right]

If k = −1 then the last equation becomes 0 = −2 which is impossible.Therefore, the system has no solutions.

Case k = 2:

\left[\begin{array}{ccc|c}1&-2&3&2\\0&3&-2&2-2\\0&0&0&(2)^2-(2)-2\end{array}\right] \rightarrow \left[\begin{array}{ccc|c}1&-2&3&2\\0&3&-2&0\\0&0&0&0\end{array}\right]

This gives the infinite many solution.

5 0
3 years ago
The price of a computer was decreased by 30% to £147. What was the price before the decrease?
Sunny_sXe [5.5K]

Answer:

£210

Step-by-step explanation:

A decrease of 30% represents 70% of the original cost.

100% represents the original cost

Divide the price by 70 to find 1% then multiply by 100 for original cost

original cost = \frac{147}{70} × 100 = 2.1 × 100 = £210

4 0
3 years ago
Read 2 more answers
If ADEF is reflected over the x-axis, what would be the coordinates of point F?
Brut [27]

Answer:

Please check the explanation.

Step-by-step explanation:

Let the coordinates of the point F be (x, y).

When a point F(x, y) is reflected over the x-axis, the x-coordinate of the point F remains the same, and the y-coordinate of the point reverses the sign.

Thus, the rule of reflection over the x-axis:

F(x, y)   →    F'(x, -y)

Here,

F'(x, -y) would be coordinates of point F after the reflection over the x-axis.

Let say, the point F(1, 2).

The coordinate of the point F after the reflection over the x-axis would be:

F(1, 2)   →    F'(1, -2)

Thus, F'(1, -2) would be the coordinates of point F after the reflection over the x-axis.

6 0
3 years ago
2,776,714 rounded to the greatest place value is?How many zeros are in the rounded number?The estimated speed of light using a p
Simora [160]

Answer:

3,000,000. 6 Zeros. 898,752,432,640

299,792 kilometers per second is the speed of light normally

Step-by-step explanation:

7 0
3 years ago
3 is less than w, and 8 is greater than w
eduard

Answer:

Whats the question?

Step-by-step explanation:

Srry i couldnt help

3 0
3 years ago
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