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3 years ago

Complete the equivalent equation for -7x-60 =x^2 +10x

Mathematics

1 answer:

alex41 [277]3 years ago

6 0

Answer:

(x+12)(x+5)

Step-by-step explanation:

Formula use: a²+bx+c

Make one side equal to zero:

Original:

-7x-60 =x² +10x

New:

x² + 17x + 60

Multiply A with C

New:

(1)x x 60 = 60

Find factors of 60 that when added, equal to 17.

New:

10 × 6, 60 × 1, 20 × 3, <u>5 × 12</u>, 4 × 15

5 times 12 equal 60, but when added equal to 17.

Replace the 17 with 5 and 12

New:

x² + 5x + 12x + 60

Break them off into two equations

New:

x² + 5x l 12x + 60

Divide each equation into it's simpilest form. Make sure the numbers in the ( ) are the same.

New:

x(x + 5) l +12(x+5)

Answer: (x+12)(x+5)

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Hello!

You solve this algebraically

6(3 - 2x) = 54

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Subtract 18 from both sides

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Let’s pretend that we want to give our employees in total a28% raise in the next two years, but we want to spread out aconsisten

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Solution

- The solution steps are given below:

$\begin{gathered} \text{ Let the original amount be X} \\ \\ \text{ If we want a 28\% raise over the next two years, then it means that the amount will be:} \\ X+\frac{28}{100}X=1.28X \\ \\ \text{ If we want to give them a consistent raise each year, we can compute the scenario as follows:} \\ \text{ Let the percentage be }y \\ \\ X+y\%\text{ of }X=\text{ Salary after first year} \\ \\ (X+y\%\text{ of }X)+y\%\text{ of }(X+y\%\text{ of }X)\text{ = Salary after second year.} \\ \\ \text{ But we already know that the salary after second year is }1.28X \\ \text{ Thus, we can say:} \\ (X+y\%\text{ of }X)+y\%\text{ of }(X+y\%\text{ of }X)=1.28X \\ \\ \text{ Simplifying, we have:} \\ X+\frac{yX}{100}+\frac{y}{100}(X+\frac{yX}{100})=1.28X \\ \\ \text{ Divide through by }X \\ 1+\frac{y}{100}+\frac{y}{100}(1+\frac{y}{100})=1.28 \\ \\ \text{ Subtract 1 from both sides and expand the brackets} \\ \frac{y}{100}+\frac{y}{100}+(\frac{y}{100})^2=1.28-1=0.28 \\ \\ \frac{2y}{100}+(\frac{y}{100})^2=0.28 \\ \\ \text{ Multiply both sides by }100^2 \\ 200y+y^2=2800 \\ \\ \text{ Rewrite, we have:} \\ y^2+200y-2800=0 \\ \\ Solving\text{ the equation using the Quadratic formula, we have that:} \\ y=\frac{-200\pm\sqrt{200^2-4(-2800)}(1)}{2(1)} \\ \\ y=-213.137\text{ or }13.137 \\ \\ \text{ Since the change in salary is an increase, thus, the rate }y\text{ has to be positive.} \\ \text{ Thus, } \\ y=13.137\approx13.14\% \\ \\ \end{gathered}$

Final Answer

y = 13.14%

The screenshots of the solution are:

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