Answer:
the third
Step-by-step explanation:
The length of AC is 16 km.
Solution:
Given data:
AB = c = 14 km, ∠A = 30° and ∠B = 89°
AC = b = ?
<u>Let us first find angle C:</u>
<em>Sum of all angles in a triangle = 180°</em>
m∠A+ m∠B + m∠C = 180°
30° + 89° + m∠C = 180°
119° + m∠C = 180°
Subtract 119° from both sides, we get
m∠C = 61°
<u>To find the length of AC:</u>
<em>Using sine formula:</em>
![$\frac{b}{\sin B } =\frac{c}{\sin C}](https://tex.z-dn.net/?f=%24%5Cfrac%7Bb%7D%7B%5Csin%20B%20%7D%20%3D%5Cfrac%7Bc%7D%7B%5Csin%20C%7D)
Substitute the given values in the formula.
![$\frac{b}{\sin 89^\circ } =\frac{14}{\sin 61^\circ }](https://tex.z-dn.net/?f=%24%5Cfrac%7Bb%7D%7B%5Csin%2089%5E%5Ccirc%20%7D%20%3D%5Cfrac%7B14%7D%7B%5Csin%2061%5E%5Ccirc%20%7D)
Multiply by sin 89° on both sides.
![$\sin 89^\circ \times \frac{b}{\sin 89^\circ } =\frac{14}{\sin 61^\circ } \times \sin 89^\circ](https://tex.z-dn.net/?f=%24%5Csin%2089%5E%5Ccirc%20%5Ctimes%20%5Cfrac%7Bb%7D%7B%5Csin%2089%5E%5Ccirc%20%7D%20%3D%5Cfrac%7B14%7D%7B%5Csin%2061%5E%5Ccirc%20%7D%20%5Ctimes%20%5Csin%2089%5E%5Ccirc)
![$b=\frac{14}{0.8746 } \times0.9998](https://tex.z-dn.net/?f=%24b%3D%5Cfrac%7B14%7D%7B0.8746%20%7D%20%5Ctimes0.9998)
![b=16](https://tex.z-dn.net/?f=b%3D16)
The length of AC is 16 km.
Step-by-step explanation:
Simplifying
3(3w + -5) = 12
Reorder the terms:
3(-5 + 3w) = 12
(-5 * 3 + 3w * 3) = 12
(-15 + 9w) = 12
Solving
-15 + 9w = 12
Solving for variable 'w'.
Move all terms containing w to the left, all other terms to the right.
Add '15' to each side of the equation.
-15 + 15 + 9w = 12 + 15
Combine like terms: -15 + 15 = 0
0 + 9w = 12 + 15
9w = 12 + 15
Combine like terms: 12 + 15 = 27
9w = 27
Divide each side by '9'.
w = 3
Simplifying
w = 3
Answer:
Answer: k must be 5/2 or 1
Step-by-step explanation:
![{ \tt{ - {2k}^{2} + 7k - 5 = 0}}](https://tex.z-dn.net/?f=%7B%20%5Ctt%7B%20-%20%20%7B2k%7D%5E%7B2%7D%20%20%2B%207k%20-%205%20%3D%200%7D%7D%20)
» Factorise the equation:
![{ \tt{ {2k}^{2} - 7k + 5 = 0 }} \\ { \tt{(2k - 5)(k - 1) = 0}} \\ \\ { \tt{k = \frac{5}{2} \: and \: 1 }}](https://tex.z-dn.net/?f=%7B%20%5Ctt%7B%20%7B2k%7D%5E%7B2%7D%20-%207k%20%2B%205%20%3D%200%20%7D%7D%20%5C%5C%20%20%20%7B%20%5Ctt%7B%282k%20-%205%29%28k%20-%201%29%20%3D%200%7D%7D%20%5C%5C%20%20%5C%5C%20%7B%20%5Ctt%7Bk%20%20%3D%20%20%5Cfrac%7B5%7D%7B2%7D%20%20%5C%3A%20and%20%5C%3A%201%20%7D%7D)
£30.08+£40
£70.08 is the answer.