Solve the quadratic equation: -x^2+8x=7
1 answer:
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Answer:
x = 2
Step-by-step explanation:
In an equation our aim is to find the value of what we are looking for as well as keeping the equation balanced. For example if we divided by 2 only from one side then the equation would change so it's an important rule to keep in mind when solving equations, that you need to keep both sides of the equation the same.
→ Expand the brackets
→ Multiply everything by 12 to make solving the equation easier
6x - 6 - 2x - 2 = 0
→ Simplify equation
4x - 8 = 0
→ Add 8 to both sides to isolate 4x
4x = 8
→ Divide by 4 on both sides to isolate x
x = 2
⇒ We can substitute x = 2 back into the equation to see if the solution is correct, if we get 0 on both sides then x = 2 is correct
⇒ Substitute in the values
⇒ Simplify
⇒ Simplify further
0 = 0
The solution x = 2 is correct
To answer this question, we will use the sine law which is illustrated in the attached image.
We are given that:
The distance from school to library = a
∠A = 32
∠B = 110
b = 2.2
Substitute with the givens in the relation of the sine law to get a as follows:
(sin 32) / (a) = (sin 110) / (2.2)
a = (2.2 sin 32) / (sin 110)
distance from school to library = a = 1.2406 mi
Based on the above calculations, the best choice would be:
B. 1.2 mi
We are given that:
The distance from school to library = a
∠A = 32
∠B = 110
b = 2.2
Substitute with the givens in the relation of the sine law to get a as follows:
(sin 32) / (a) = (sin 110) / (2.2)
a = (2.2 sin 32) / (sin 110)
distance from school to library = a = 1.2406 mi
Based on the above calculations, the best choice would be:
B. 1.2 mi