Use a basic fact and a pattern to find the product 5,000 x 80
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In the United States, 13 out of every 20 cans are recycled. What percent of cans are recycled?
How do you solve polynomial equation by factoring2x^3 - 12x^2 = 32x - 192
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Answer:
Step-by-step explanation:
We have been given that the amount of a persons paycheck p varies directly with the numbers of hours worked t.
Since we know that the equation for direct variation is in form: , where, k represents the constant of variation.
We are also told that for 16 hours of work, the paycheck is $124.00. We can represent our given information as:
Upon substituting p=124 and t=16 in directly proportional equation we will get,
Let us divide both sides of our equation by 16 to solve for k.
Upon substituting the value of constant of variation in our equation we will get,
Therefore, the equation represents the relationship between hours of work and pay.
Let t = number of hours worked
Let p = money in the paycheck
And the relationship between the two variables varies DIRECTLY, thus they are equated with one another.
Well anyway, you can write this simple equation for their relationship:
16t=124p
Then you derive if you want to get the number of hours or the amount paid:
1) 16t/16= 124p
t = 124p/16
t=7.75p
or
2) 124p=16t
124p/124= 16t/124
p = 0.129t
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26 ÷ 4 = 6 2/4
6 2/4 = 6 1/2
Your answer is 6 1/2
b) Use the Quadratic Formula to solve the equation. Write the solution in terms of i.
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From their sum, the numbers are ' x ' and ' 8 - x ' .
From their product, x(8 - x) = 80 .
When you massage and manipulate this equation into the standard
quadratic form, you have
x² - 8x + 80 = 0 .
Applying the quadratic formula to tease out the solutions of this equation,
we find that they are
x = 4 + 64 i
and
x = 4 - 64 i
Final answer:
The two numbers are represented by x and 8 - x. By setting x * (8 - x) = 80, we obtain a quadratic equation which can be solved using the Quadratic formula to find x = 2 and x = -40. However, we ignore the negative solution as we're dealing with positive numbers, resulting in 2 and 6 as the two numbers.
Explanation:
First, let's identify the two numbers. Let's let x represent one of these numbers. Because we're told that the sum of the two numbers is 8, we can express the second number as 8 - x.
Next, let's use this information to write our equation. We're told that the product of our two numbers is 80. In terms of x, we can write this as: x * (8 - x) = 80. Simplify this to obtain the quadratic equation: -x^2 + 8x - 80 = 0.
From this, we can apply the Quadratic Formula, which is x = [-b ± sqrt(b^2 - 4ac)] / (2a). Substituting a = -1, b = 8, and c = -80 into the formula, we find the solutions are x = 2 and x = -40. However, since we're dealing with positive numbers here, we can ignore the negative solution, leaving us with the two numbers as 2 and 6.
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