Answer:
The radius of the tree trunk is 7 inches.
Step-by-step explanation:
circumference = 2(3.14)radius
43.96 = 2(3.14) r
43.96 = 6.28r
7 = r
Answer:
The value of x = 109°
angle PQS = 24°
Step-by-step explanation:
24° + 47° + x = 180° { angles on straight line }
=> 71 ° + x = 180°
=> x = 180° - 71°
=> x = 109°
Now,
Angle PQS = 24°
angle PQS = angle QSR { alternative angle }
Let's use f(x) for the first one and g(x) for the second.
n is the number of songs downloaded, t is the time in years, and m is the time in months.
f(x) = 125t + 10m
g(x) = 50 + n
For 2, substitute 1 for t and 12 for m.
For 4, solve f(x) = g(x).
For 5, solve g(x) for n=(14*12). Compare it to the value of f(x) for t=1 and 12=m.
A quadratic in vertex form reads as
(<em>x</em> - <em>a</em>)² + <em>b</em>
where (<em>a</em>, <em>b</em>) is the vertex.
To get the given quadratic in this form, complete the square:
<em>x</em>² - 6<em>x</em> - 40 = <em>x</em>² - 6<em>x</em> + 9 - 49 = (<em>x</em> - 3)² - 49
Or, work backwards by expanding the vertex form and solving for <em>a</em> and <em>b</em> :
(<em>x</em> - <em>a</em>)² + <em>b</em> = <em>x</em>² - 2<em>ax</em> + <em>a</em>² + <em>b</em>
So if
<em>x</em>² - 6<em>x</em> - 40 = <em>x</em>² - 2<em>ax</em> + <em>a</em>² + <em>b</em>,
then
-2<em>a</em> = -6 → <em>a</em> = 3
<em>a</em>² + <em>b</em> = -40 → <em>b</em> = -49
The answer is (2.5, 2.5) and (2, 0)
