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4 years ago

A square has an area of 16j^2 + 24j + 9. How can you find the length of the side of the square?

1 answer:

7 0

first off let's recall that a square has all equal sides, so its area is just one side squared, namely A = s², or A = (s)(s).

we know the area is 16j² + 24j + 9, that simply means that two twin factors are in it, and it also means that the area polynomial is a perfect square trinomial.

$\bf \qquad \textit{perfect square trinomial} \\\\ (a\pm b)^2\implies a^2\pm \stackrel{\stackrel{\text{\small 2}\cdot \sqrt{\textit{\small a}^2}\cdot \sqrt{\textit{\small b}^2}}{\downarrow }}{2ab} + b^2 \\\\[-0.35em] ~\dotfill\\\\ 16j^2+24j+9\implies 4^2j^2+2(4j)(3)+3^2\implies (4j)^2+2(4j)(3)+3^2 \\\\\\ (4j+3)^2\implies \stackrel{\textit{area}}{(4j+3)(4j+3)}~\hspace{7em} \stackrel{\textit{one side}}{4j+3}$

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How many square tiles of side 10cm each will be needed to tile a floor which is 300cm long and 150cm wide?

S_A_V [24]

Step 1

Find the area of one tile

we know that

the area of a square is

$A=b^{2}$

where b is the length side of the square

In this problem

$b=10\ cm$

Substitute

$A=10^{2}=100\ cm^{2}$

Step 2

Find the area of the floor

The area of a rectangle is equal to

$A=LW$

where

L is the length of the rectangle

h is the width of the rectangle

In this problem

$L=300\ cm$

$W=150\ cm$

Substitute

$A=300*150=45,000\ cm^{2}$

Step 3

Find the number of tiles needed

by proportion

$\frac{1}{100} \frac{tile}{\ cm^{2}} =\frac{x}{45,000} \frac{tile}{\ cm^{2}} \\ \\x=45,000/100 \\ \\x=450 \ tiles$

therefore

<u>the answer is</u>

$450 \ tiles$

5 0

3 years ago

Polygon ABCD is defined by the points A(-5, 1), B(-4, 3), C(-2, 7) and D(-1, 2) if the polygon rotates 90 counterclockwise to cr

Akimi4 [234]

If the polygon ABCD rotates 90° counterclockwise then every point rotates the same. The coordinates of C´ are: B) (-7,-2)

6 0

3 years ago

Read 2 more answers

Match the expression on the left with the correct simplified expression on the right.

andriy [413]

Given: The expression below

$\begin{gathered} (\frac{(3x^3y^4)^3}{(3x^2y^2)^2})^2 \\ (\frac{(3x^4y^2)^4}{(3x^5y^2)^3})^2 \end{gathered}$

To Determine: The matching expression to the given expressions

Solution

Let us simplify each of the expressions using exponents rule

$\begin{gathered} Exponent-Rule1=(a^m)^n=a^{m\times n} \\ Exponent-Rule2=(\frac{a^m}{a^n})=a^{m-n} \end{gathered}$

Applying the exponent rule 1 above to the given expressions

$\begin{gathered} (3x^3y^4)^3=3^3x^{3\times3}y^{4\times3}=27x^9y^{12} \\ (3x^2y^2)^2=3^2x^{2\times2}y^{2\times2}=9x^4y^4 \end{gathered}$ $\begin{gathered} (3x^4y^2)^4=3^4x^{4\times4}y^{2\times4}=81x^{16}y^8 \\ (3x^5y^2)^3=3^3x^{5\times3}y^{2\times3}=27x^{15}y^6 \end{gathered}$

Applying the exponent rule 2

$\frac{(3x^{3}y^{4})^{3}}{(3x^{2}y^{2})^{2}}=\frac{27x^9y^{12}}{9x^4y^4}=\frac{27}{9}x^{9-4}y^{12-4}=3x^5y^8$ $\frac{(3x^{4}y^{2})^{4}}{(3x^{5}y^{2})^{3}}=\frac{81x^{16}y^8}{27x^{15}y^6}=\frac{81}{27}x^{16-15}y^{8-6}=3xy^2$

Let us not apply exponent rule 1 above

$(\frac{(3x^{3}y^{4})^{3}}{(3x^{2}y^{2})^{2}})^2=(3x^5y^8)^2=3^2x^{5\times2}y^{8\times2}=9x^{10}y^{16}$ $(\frac{(3x^{4}y^{2})^{4}}{(3x^{5}y^{2})^{3}})^2=(3xy^2)^2=3^2x^2y^{2\times2}=9x^2y^4$

Hence, the matching is as shown below