Answer:
m(∠C) = 18°
Step-by-step explanation:
From the picture attached,
m(arc BD) = 20°
m(arc DE) = 104°
Measure of the angle between secant and the tangent drawn from a point outside the circle is half the difference of the measures of intercepted arcs.
m(∠C) = ![\frac{1}{2}[\text{arc(EA)}-\text{arc(BD)}]](https://tex.z-dn.net/?f=%5Cfrac%7B1%7D%7B2%7D%5B%5Ctext%7Barc%28EA%29%7D-%5Ctext%7Barc%28BD%29%7D%5D)
Since, AB is a diameter,
m(arc BD) + m(arc DE) + m(arc EA) = 180°
20° + 104° + m(arc EA) = 180°
124° + m(arc EA) = 180°
m(arc EA) = 56°
Therefore, m(∠C) = ![\frac{1}{2}(56^{\circ}-20^{\circ})](https://tex.z-dn.net/?f=%5Cfrac%7B1%7D%7B2%7D%2856%5E%7B%5Ccirc%7D-20%5E%7B%5Ccirc%7D%29)
m(∠C) = 18°
Answer:
<h2>
£1,330.46</h2>
Step-by-step explanation:
Using the compound interest formula ![A = P(1+\frac{r}{n} )^{nt}](https://tex.z-dn.net/?f=A%20%3D%20P%281%2B%5Cfrac%7Br%7D%7Bn%7D%20%29%5E%7Bnt%7D)
A = amount compounded after n years
P = principal (amount invested)
r = rate (in %)
t = time (in years)
n = time used to compound the money
Given P = £1200., r = 3.5%, t = 3years, n = 1 year(compounded annually)
![A = 1200(1+0.035)^{3}\\ A = 1200(1.035)^{3}\\ A = 1200* 1.108717875\\A = 1,330.46](https://tex.z-dn.net/?f=A%20%3D%201200%281%2B0.035%29%5E%7B3%7D%5C%5C%20A%20%3D%201200%281.035%29%5E%7B3%7D%5C%5C%20A%20%3D%201200%2A%201.108717875%5C%5CA%20%3D%201%2C330.46)
Value of Charlie's investment after 3 years is £1,330.46
Answer:
(2.5, 4 )
Step-by-step explanation:
Using the midpoint formula
Given endpoints (x₁, y₁ ) and (x₂, y₂ ), then midpoint is
[0.5(x₁ + x₂ ), 0.5(y₁ + y₂ ) ]
Given
(0, 1) and (5, 7), then
midpoint = [ 0.5(0 + 5), 0.5(1 + 7) ] = (0.5(5), 0.5(8)) = (2.5, 4)
Answer:(x^5−4) and (x^10+4x^5+16)