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3 years ago

What is the solution of the system? y=x^2 + 6x + 9

Mathematics

1 answer:

Katyanochek1 [597]3 years ago

5 0

Because we have two values of x, we can set the two expressions equal to each-other.

x^2 + 6x + 9 = x + 3

Subtract x and 3 from both sides.

x^2 + 5x + 6 = 0

Now that we have all terms on one side, we can find the values of x.

Using the AC method, we can simplify this equation to (x + 2)(x + 3)

The solutions to the system of equations presented are:

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In the figure below

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Thus,

$\begin{gathered} \frac{4}{5}=\frac{6}{x} \\ \text{cross}-\text{multiply} \\ 4\times x=6\times5 \\ 4x=30 \\ \text{divide both sides by the coefficient of x, which is 4} \\ \text{thus,} \\ \frac{4x}{4}=\frac{30}{4} \\ x=7.5 \end{gathered}$

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In the above diagram,

$\begin{gathered} BC=BY+YC \\ \Rightarrow BC=15\text{ + y} \end{gathered}$

Thus, from the theorem of similar triangles,

$\begin{gathered} \frac{BX}{BA}=\frac{BY}{BC}=\frac{XY}{AC} \\ \frac{9}{15}=\frac{15}{15+y} \end{gathered}$

solving for y, we have

$\begin{gathered} \frac{9}{15}=\frac{15}{15+y} \\ \text{cross}-\text{multiply} \\ 9(15+y)=15(15) \\ \text{open brackets} \\ 135+9y=225 \\ \text{collect like terms} \\ 9y\text{ = 225}-135 \\ 9y=90 \\ \text{divide both sides by the coefficient of y, which is 9} \\ \text{thus,} \\ \frac{9y}{9}=\frac{90}{9} \\ \Rightarrow y=10 \end{gathered}$

thus, YC = 10.

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Answer:

Step-by-step explanation:

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