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3 years ago

Evaluate 2r +1 if r=3

Mathematics

1 answer:

Evgesh-ka [11]3 years ago

6 0

Answer:

Step-by-step explanation:

So, substitute in your 4 for r, 2(3) + 1. Multiply 2 and 3 to get 6 and then add a to get 7. I hope this helps :)

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How many is -10x divide by -10=

Norma-Jean [14]

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3 years ago

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4 years ago

Write the quadratic function in the form g(x)=a (x-h)2 +kThen, give the vertex of its graph. G(x) =2x2 +20x+49Writing in the for

Snezhnost [94]

The quadratic function given to us is:

$g(x)=2x^2+20x+49$

We are asked to find the vertex form of the function.

The general formula for the vertex form of a quadratic equation is:

$\begin{gathered} g(x)=a(x-h)^2+k \\ \text{where,} \\ (h,k)\text{ is the coordinate of the vertex} \end{gathered}$

In order to write the function in its vertex form, we need to perform a couple of operations on the function.

1. Add and subtract the square of the half of the coefficient of x to the function.

2. Factor out the function with its repeated roots and re-write the equation.

Now, let us solve.

1. Add and subtract the square of the half of the coefficient of x to the function.

$\begin{gathered} g(x)=2x^2+20x+49=2(x^2+10x+\frac{49}{2}) \\ \text{half of coefficient of x:} \\ \frac{10}{2}=5 \\ \text{square of the half of the coefficient of x:} \\ 5^2=25 \\ \\ \therefore g(x)=2(x^2+10x+25-25+\frac{49}{2}) \end{gathered}$

2. Factor out the function with its repeated roots and re-write the equation.

$\begin{gathered} g(x)=2(x^2+10x+25)-2(25+\frac{49}{2}) \\ re-\text{write the above function} \\ g(x)=2(x^2+10x+25)-1 \\ \text{Let us factorize this:} \\ g(x)=2(x+5)^2-1 \end{gathered}$

Therefore, we can conclude that the Equation and vertex of the equation is:

$\begin{gathered} Equation\colon g(x)=2(x+5)^2-1 \\ \\ Vertex\colon(-5,-1) \end{gathered}$

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2 years ago