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Over [174]
3 years ago
15

#4 Kerry created a pattern with rectangles. Her first step contained 1

Mathematics
1 answer:
Iteru [2.4K]3 years ago
8 0

Answer:

The constant rate of change is <em>2 rectangles</em>

Step-by-step explanation:

Looking at this question, we can see that what we have is in the form of an arithmetic progression otherwise known as A.P

An arithmetic progression refers to a series of numbers that differ by a constant addition or subtraction of a certain constant number. What this means is that subsequent terms are formed by the addition of a certain constant number to preceding terms.

Now, let's look at the situation in the question;

1, 3 , 5, ?, ?

Looking at the first three terms, we can see that the difference between the first two terms is 2, the difference between the third term and the second term is 2 also. This gives us an ideas of an arithmetic progression, with the first term being 1 and the common difference being 2.

The common difference is what is referred to as the constant term in this questions which is equal to 2

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Solve for x.
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ANSWER

x=\frac{2-\sqrt{10}} {3}

or

x=\frac{\sqrt{10}+2} {3}

We have

3x^2-4x-2=0

Since we cannot factor easily, we complete the square.

Adding 2 to both sides give,

3x^2-4x=2

Dividing through by 3 gives

x^2-\frac{4}{3}x= \frac{2}{3}

Adding (-\frac{2}{3})^2 to both sides gives

x^2-\frac{4}{3}x+(-\frac{2}{3})^2= \frac{2}{3}+(-\frac{2}{3})^2

The expression on the Left Hand side is a perfect square.

(x-\frac{2}{3})^2= \frac{2}{3}+\frac{4}{9}

\Rightarrow (x-\frac{2}{3})^2= \frac{10}{9}

\Rightarrow (x-\frac{2}{3})=\pm \sqrt{\frac{10}{9}}

\Rightarrow (x)=\frac{2}{3} \pm {\frac{\sqrt{10}}{3}

Splitting the plus or minus sign gives

x=\frac{2- \sqrt{10}} {3}

or

x=\frac{\sqrt{10}+2} {3}
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Step-by-step explanation:

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