X² <span>+ 11x + 7
because 7 is a prime number, this doesn't factor prettily. you'll want to use the quadratic formula; if you aren't familiar with it, i'd either research it or look it up in your textbook, because it's clunky and not easily understood in this format:
(-b </span>± √((b)² - 4ac))/(2a)
in your equation x² + 11x + 7 ... a = 1, b = 11, and c = 7. what you do is you take the coefficients of every term, then plug it into your equation:
(-11 ± √((11)² - 4(1)(7))/(2(1))
not pretty, i know. but, regardless, you can simplify it:
(-11 ± √((11)² - 4(1)(7))/(2(1))
(-11 ± √(121 - 28))/2
(-11 ± √93)/2
and you can't simplify it further. -11 isn't divisible by 2, and 93 doesn't have a perfect square that you can take out from beneath the radical. the ± plus/minus symbol indicates that you have 2 answers, so you can write them out separately:
(x - (-11 - √93)/2) and (x + (-11 - √93)/2)
they look confusing, but those are your two factors. they can be simplified just slightly by changing the signs in the middle due to the -11:
(x + (11 + √93)/2) (x - (11 - √93)/2)
and how these would read, just in case the formatting is too confusing for you: x plus the fraction 11 + root 93 divided by 2. the 11s and root 93s are your numerator, 2s are your denominator.
Answer:
Step 1: Solve one of the equations for one of the variables. Let's solve the first equation for x
Thus, option A) is true.
The solution to the system of equations be:
Step-by-step explanation:
It is important to remember that when we solve the system of equations, the first step we need to do is to solve one of the equations for one of the variables.
Given the system of equations
Step 1: Solve one of the equations for one of the variables. Let's solve the first equation for x
Add y to both sides
Thus, option A) is true.
<u>NOW LET US SOLVE THE REMAINING PORTION</u>
to solve for y
For x = -1 + y
substitute y = 5
Thus, the solution to the system of equations be:
Answer:
Increased.
Step-by-step explanation:
In March 2007, the unemployment rate was 4.4 percent. In August 2008 was 6.1 percent. We need to remember that the unemployment rate equals the number of unemployed people divided by the people in the labor force.
Now, if we consider that the labor force remained constant during this period of time (according to the problem) then this would mean that the number of unemployed people actually increased during this period of 17 months.
Answer:
64 sodas and 32 hot dogs
Step-by-step explanation:
192 divide by 2 = 96. 96 divide by 3 = 32. 32 +32 =64 because there was 2 times as many sodas sold.64 +32=96.
