Answer:
66°
Step-by-step explanation:
<em>See attached picture.</em>
<em>When an angle intercepts an arc, </em><em>ARC AC</em><em>, and forms in the </em><em>center [central angle]</em><em>, the angle has </em><em>SAME</em><em> measure as the ARC AC </em><em>[denoted by x]</em><em>. When the angle formed is on the opposite side, it has a measure </em><em>HALF</em><em> of that ARC AC </em><em>[denoted 
]</em>
If you look at the problem given, ∠DBC is intercepted by ARC DC and falls in the opposite side of the circle, NOT in the CENTER. <em>Hence </em><em>∠DBC</em><em> has a measure that is </em><em>HALF of ARC DC</em><em>.</em>
<em>There are </em><em>360 degrees in a circle.</em><em> </em><em>ARC DB</em><em> has 2 endpoints that are the diameter of the circle, so </em><em>ARC DB</em><em> has a measure of </em><em>180 degrees</em><em>. </em>Also,
ARC DB = ARC DC + ARC CB
ARC DB = ARC DC + 48
180 = ARC DC + 48
ARC DC = 180 - 48 = 132
Since, ∠DBC = 0.5 * ARC DC, we have:
∠DBC = 0.5 * (132)
∠DBC = 66
Our answer is the second choice of 66°.
Answer:
$13,304
-We use the compound interest function to determine the rate of growth.
-Given that the amount doubles in 13 years, the annual growth rate is calculated as:
We now substitute this value of i in the compound interest formula equation to solve for future value:
Hence, the future value to the nearest dollar is $13,304
*You can alternatively use the exponential growth function:
This is slightly off by just $1
Step-by-step explanation:
Answer:
65
Step-by-step explanation:
They are vertical angles; so angles are congruent
*<em>Vertical angles are always congruent*</em>
<em>Congruent means equal or same.</em>
1) Since they are congruent, you form an equation.
<h2>
145 = 2x + 15</h2>
2) Solve by subtracting 15 from both sides.
<h2>
145 = 2x + 15</h2><h2>
- 15 -15</h2><h2>
----------------------</h2><h2>
130 = 2x</h2>
3) Solve by dividing 2 from both sides
<h2>
130/2 = 2x/2</h2>
4) Simplify
x = 65
Ayanna is 17 and Brittany is 14.
To find this, let's write two equations using the given information.
a = b + 3
3b + 2a = 76
Now, just substitute the first equation into the second and solve.
3b + 2(b + 3) = 76
3b + 2b + 6 = 76
5b = 70
b = 14
If Brittany is 14, then Ayanna is 3 years older at 17.
