Using the ratio of perfect squares method, what is square root of 112 rounded to the nearest hundredth?

1 answer:

4 0

First, you have to think of any perfect squares that multiply to 112. The only ones I can think of are 16 and 7. So now you have the square root of 16 * 7. Now you can reduce the 16 because the square root of 16 is 4. So the answer is 4 times the square root of 7.

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NEED TO KNOW ASAP<br> Which of the following is a quadratic inequality?<br> Oy<2x+7<br> Oy Oy

Burka [1]

Answer:

Step-by-step explanation:

A quadratic inequality is one that involves a quadratic polynomial.

<h3>Identification</h3>

The degree of a polynomial is the value of the largest exponent of the variable. When the degree of a polynomial is 2, we call it a <em>quadratic</em>.

For the following inequalities, the degree of the polynomial in x is shown:

y < 2x +7 . . . degree 1
y < x^3 +x^2 . . . degree 3
y < x^2 -5x . . . degree 2 (quadratic)

<h3>Application</h3>

We see that the degree of the polynomial in x is 2 in ...

y < x^2 -5x

so that is the quadratic inequality you're looking for.

<em>Additional comment</em>

When a term involves only one variable, its degree is the exponent of that variable: 5x^3 has degree 3. When a term involves more than one variable, the degree of the term is the sum of the exponents of the variables: 8x^4y3 has degree 4+3=7.

8 0

2 years ago

Find the volume of the garden shed

Leno4ka [110]

Answer:

47.3 m³

Step-by-step explanation:

The garden shed is made up of a rectangular prism and a pyramid.

<h3><u>Volume of a rectangular prism</u></h3>

$\begin{aligned}\textsf{Volume of a rectangular prism}&=\sf width \times length \times height\\&=4 \times 4 \times 2\\&=16 \times 2\\&=32\;\; \sf m^3\end{aligned}$

<h3><u>Volume of a pyramid</u></h3>

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From inspection of the given diagram, the slant height of the pyramid is 3.5 m.

Calculate the perpendicular height of the pyramid using Pythagoras Theorem:

$\begin{aligned}\implies a^2+b^2&=c^2\\2^2+h^2&=3.5^2\\h^2&=8.25\\h&=\sqrt{8.25}\;\; \sf m\end{aligned}$

Therefore:

$\begin{aligned}\textsf{Volume of a pyramid}&=\dfrac{\sf length \times width \times height}{3}\\\\&=\dfrac{\sf 4 \times 4 \times \sqrt{8.25}}{3}\\\\& = 15.31883372\;\; \sf m^3\end{aligned}$

<h3><u>Volume of the garden shed</u></h3>

$\begin{aligned}\implies \textsf{Volume of shed}&=\textsf{Volume of rectangular prism}+\textsf{Volume of pyramid}\\&=32+15.31883372\\& = 47.3\;\; \sf m^3\;(nearest\;tenth)\end{aligned}$