Answer:
- 10 - (-20 + 5)
Step-by-step explanation:
- 10 - (-20 + 5)
- 10 - (-15) = -10 + 15
-10 + 15 = 5
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To solve the equation using complete square method we proceed:
z^2-19z=66
but
c=(-b/2a)^2
c=(-19/2)^2
c=361/4
thus:
z^2-19z+361/4=66+361/4
factoring the LHS we get:
1/4(2z-19)^2=625/4
(2z-19)^2=625
getting the square root of both sides we get:
2z-19=+/-25
2z=+/-25+19
2z=44 or -6
z=22 or -3
Answer: z=22 or z=-3
By applying the law of sines, the length of side PQ is equal to 7.1 units.
<h3>What is the law of sines?</h3>
The law of sines is also referred to as sine law and it can be defined as an equation that relates the side lengths of a triangle to the sines of its angles.
<h3>How to calculate the length of PQ?</h3>
Mathematically, the law of sines is given by this equation:
![\frac{sinA}{a} =\frac{sinB}{b} =\frac{sinC}{c}](https://tex.z-dn.net/?f=%5Cfrac%7BsinA%7D%7Ba%7D%20%3D%5Cfrac%7BsinB%7D%7Bb%7D%20%3D%5Cfrac%7BsinC%7D%7Bc%7D)
Substituting the given parameters into the formula, we have;
![\frac{sin80}{PQ} =\frac{sin42}{4.8} \\\\\frac{0.9848}{PQ} =\frac{0.6691}{4.8}\\\\0.6691PQ = 4.7270\\\\PQ = 4.7270/0.6691](https://tex.z-dn.net/?f=%5Cfrac%7Bsin80%7D%7BPQ%7D%20%3D%5Cfrac%7Bsin42%7D%7B4.8%7D%20%5C%5C%5C%5C%5Cfrac%7B0.9848%7D%7BPQ%7D%20%3D%5Cfrac%7B0.6691%7D%7B4.8%7D%5C%5C%5C%5C0.6691PQ%20%3D%204.7270%5C%5C%5C%5CPQ%20%3D%204.7270%2F0.6691)
PQ = 7.1 units.
Read more on law of sines here: brainly.com/question/7922954
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33 dollars. The tip is 3 dollars, and that to 30 dollar dinner bill and the whole bill will be $33.