Step-by-step explanation:
rules of the logarithm :
e.g.
log(a×b) = log(a) + log(b)
log10(9) = log10(3×3) = log10(3) + log10(3) =
= 0.4771 + 0.4771 = 0.9542
log10(49) = log10(7×7) = log10(7) + log10(7) =
= 0.8451 + 0.8451 = 1.6902
Answer
Find out the solution to the system of equations .
To prove
As the equations are
y = x – 10 , 4 = 2xy
in the equation y = x – 10
Than the equation becomes
2x² - 20x - 4 = 0
Taking 2 as common
x² - 10x - 2 = 0
Now using the discriment formula
Here a = 1 , b = -10 , c = -2
Put in the above
Thus the solution are
Put in the 4 = 2xy
When
Put in the 4 = 2xy
Hello there! I can help you! 58,500 female doctors makes up 17.9% of all registered doctors. To find the total amount of registered doctors, we can write and solve a proportion. Set it up like this:
58,500/x = 17.9/100
This is because 58,500 is part of the whole, which is represented by x. 17.9% is part of 100%. Let's cross multiply the values. 58,500 * 100 is 5,850,000. 17.9x * x is 17.9x. That makes 5,850,000 = 17.9x. Now, divide each side by 17.9 to isolate the x. 17.9x/17.9 cancels out. 5,850,000/17.9 is 326,815.6425 or 326,816 when rounded to the nearest whole number. Let's check this. 326,816 * 17.9% (0.179) is 58,500.064, which is a little off, but is very close to 58,500, and rounds off to that. x = 326,816. There are about 326,816 registered doctors in a recent year.
Answer:
Yes, we can find a unique price for an apple and an orange.
Step-by-step explanation:
Let x be the price of one apple and y be the price of one orange.
We have been given that a fruit stand has to decide what to charge for their produce. They need $5.30 for 1 apple and 1 orange.
We can represent this information in an equation as:
They also need $7.30 for 1 apple and 2 oranges.
Upon substituting our given information we formed a system of equations. Let us see if this system is solvable or not.
For a unique solution , where and are constant of x and y variables of 1st equation respectively. and are constant of x and y variables of 2nd equation respectively.
Let us check our system of equations for unique solution.
We can clearly see that 1 is not equal to half, therefore, we can find a unique price for an apple and orange using our system of equations.
Upon subtracting our 1st equation from 2nd equation we will get,
Therefore, price of one orange is $2.
Upon substituting y=2 in equation 1 we will get,
Therefore, price of one apple is $3.30.