• Angles DXC and AXB form a vertical pair, so they are congruent and have the same measure.
• ∆ABD is isosceles, since it's given that AD and BD are congruent. This means the "base angles" BAD and ABD have the same measure; call this measure <em>x</em>.
• The measure of angle ADB can be computed by using the inscribed angle theorem, which says
m∠ADB = 1/2 (100°) = 50°
(that is, it's half the measure of the subtended arc AB whose measure is 100°)
• The interior angle to any triangle sum to 180° in measure. So we have in ∆ABD,
m∠ADB + 2<em>x</em> = 180°
Solve for <em>x</em> :
50° + 2<em>x</em> = 180°
2<em>x</em> = 130°
<em>x</em> = 65°
• Use the inscribed angle theorem again to find the measure of angle BAC. This will be half the measure of the subtended arc BC, so
m∠BAC = 1/2 (50°) = 25°
• Now in ∆ABX, we have
m∠AXB + 25° + 65° = 180°
m∠AXB = 90°
Hence m∠DXC = 90°.
Answer:
1 1/5 miles per hour
Step-by-step explanation:
49 and 5/8. 100-50=50-3/8 is going to be 49 and 5/8.
Answer:
9 TV ads and 20 radio ads
Step-by-step explanation:
He has $37,000 to spend. He has to sum that amount of money between the TV and radio ads. Each TV ad costs $3000 while each radio ad costs $500, so the equation that represents that is 37000 = 3000x + 500y
The same happens with the amount of voters he needs to reach, the equation is 130000 = 10000x + 2000y
The system that represents this is

And the augmented matrix is
![\left[\begin{array}{cc|c}3000&500&37000\\10000&2000&130000\end{array}\right]](https://tex.z-dn.net/?f=%5Cleft%5B%5Cbegin%7Barray%7D%7Bcc%7Cc%7D3000%26500%2637000%5C%5C10000%262000%26130000%5Cend%7Barray%7D%5Cright%5D)
First we divide the first row by 3000 and the second by 10000:
![\left[\begin{array}{cc|c}1&1/6&37/3\\1&1/5&13\end{array}\right]](https://tex.z-dn.net/?f=%5Cleft%5B%5Cbegin%7Barray%7D%7Bcc%7Cc%7D1%261%2F6%2637%2F3%5C%5C1%261%2F5%2613%5Cend%7Barray%7D%5Cright%5D)
Then we multiply the second row by (-1) and we add the first row:
![\left[\begin{array}{cc|c}1&1/6&37/3\\0&-1/30&-2/3\end{array}\right]](https://tex.z-dn.net/?f=%5Cleft%5B%5Cbegin%7Barray%7D%7Bcc%7Cc%7D1%261%2F6%2637%2F3%5C%5C0%26-1%2F30%26-2%2F3%5Cend%7Barray%7D%5Cright%5D)
Now we multiply the second row by -30:
![\left[\begin{array}{cc|c}1&1/6&37/3\\0&1&20\end{array}\right]](https://tex.z-dn.net/?f=%5Cleft%5B%5Cbegin%7Barray%7D%7Bcc%7Cc%7D1%261%2F6%2637%2F3%5C%5C0%261%2620%5Cend%7Barray%7D%5Cright%5D)
Finally, to the first row we add the second one multiply by (-1/6):
![\left[\begin{array}{cc|c}1&0&9\\0&1&20\end{array}\right]](https://tex.z-dn.net/?f=%5Cleft%5B%5Cbegin%7Barray%7D%7Bcc%7Cc%7D1%260%269%5C%5C0%261%2620%5Cend%7Barray%7D%5Cright%5D)
So, x = 9 and y = 20
That means 9 TV and 20 radio ads will contact 130,000 voters using the allocated funds