Hello!
log₃(x) + log₃(x - 6) = log₃(7) <=>
<=> log₃(x * (x - 6)) = log₃(7) <=>
<=> log₃(x² - 6x) = log₃(7) <=>
<=> x² - 6x = 7 <=>
<=> x² - 6x - 7 = 0 <=>
<=> x² + x - 7x - 7 = 0 <=>
<=> x * (x + 1) - 7 * (x + 1) = 0 <=>
<=> (x + 1) * (x - 7) = 0 <=>
<=> x + 1 = 0 and x - 7 = 0 <=>
<=> x = -1 and x = 7, x ∈ { 6; +∞ } <=>
<=> x = 7
Good luck! :)
Answer: the blue and the pink
Area = perimeter + 132.
Let each side of the city be x miles long, then:-
x^2 = 4x + 132
x^2 - 4x - 132 = 0
x = [-(-4) +/- sqrt((-4)^2 - 4 * 1 *-132)] / 2
x = 13.66, -9.66 We ignore the negative
So the city has dimension of 13.66 * 13.66
13.7 * 13.7 to nearest 10th
Answer: 34.2 pounds
Step-by-step explanation:
First, convert 15 4/5 into an improper fraction. You should get 79/5. Then, convert 50 into a fraction that has a denominator of 5. Right now, 50= 50/1 so just multiply the top and bottom by 5 to make it 250/5. Then, subtract 79/5 from 250/5. You should get 171/5. Lastly, simplify. You should get 34.2 pounds as your final answer. Hope this helps!
Step-by-step explanation: When an equation has a squared term in it
such as x² - 2x - 63 = 0, it's called a polynomial equation.
The rule for solving a polynomial equation is
to first set it equal to 0, them factor.
Since this equation is already set equal to 0, we can factor the left side.
To factor x² - 2x - 63, look for factors of -63 that add to -2.
In this case, these factors are -9 and +7.
So we have (x - 9)(x + 7) = 0.
When two terms are multiplying together to equal 0,
either one term or the other must equal 0.
So x - 9 = 0 or x + 7 = 0.
Solving for x in each equation, we get x = 9 or x = -7.
So this equation has two solutions and we write out answer
in set notation which looks like this {9, -7}.
