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Two numbers have a product of 80 their sum is 24?
Let's denote the two numbers as x and y. We know that xy = 80 and x + y = 24. We can solve this system of equations by substituting one equation into the other. By substituting y = 24 - x into the first equation, we get x(24 - x) = 80. Simplifying this equation gives us a quadratic equation: x^2 - 24x + 80 = 0. Solving this quadratic equation will give us the values of x and y.
Find the equation of the line that has the slope of 7 an y-intercept of 4?
3
What is a reasonable first step in solving this problem?
The first step is to show us the problem.
What two integers added together equal 15 but when multiplied together equal 36?
(Solving with algebra)Lets call the two numbers x and y.We want to find x and y so that x + y = 15 and xy = 36.First, solve one equation for x or y. Here we will solve the first equation for x:x = 15 - yBecause we know that 15 - y = x, we can plug it into the second equation:(15 - y)(y) = 36.Solving the above equation will give us one of the numbers:Distribute: y^2 - 15y + 36 = 0Factor: (x - 12)(x - 3) = 0We can see here that the numbers are 12 and 3 (by solving for x).The numbers in this problem are simple enough that you can use guess and check.Start at a number (1, for example), and find the other number that would add to 15. If the numbers multiply to 36, then you found the two numbers. If not, try another one.The two numbers are 12 and 3.
A line whose slope equals 9 and passes through point zero and negative 5?
Linear equations can be written in the following form: y = mx + b where m = slope and b = y-intercept In this case we are given the slope (m=9) so: y = 9x + b We are also given a single point (0, -5). Because this point gives us a value of x and y that are on the line, we can substitute those values into our equation to get b. y = 9x + b and x = 0 and y = -5 -5 = 9(0) + b -5 = b Substitute this value back into our equation to get the equation of the line y = 9x - 5
