Given the quadratic equation below, determine which situation it could represent.

1 answer:

3 0

Answer: option C. A garage door is 6 feet wider than it is tall. The area of one side of the garage door is 146 square feet.

Justification:

Call x the height of the garage door.

Then, the width is x + 6

And the area of one side is height * width = x (x + 6) = x^2 + 6x

That is equal to 146 feet^2

=> x^2 + 6x = 146

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Floor tile costs $11 per square yard. How much will it cost to tile a bathroom that is 90 square feet?

Usimov [2.4K]

99 Dollars one square foot = 9 square yards

8 0

3 years ago

What is the factorization of 729^15+1000

Nesterboy [21]

$\bf \textit{difference and sum of cubes} \\\\ a^3+b^3 = (a+b)(a^2-ab+b^2) \\\\ a^3-b^3 = (a-b)(a^2+ab+b^2) \\\\[-0.35em] \rule{34em}{0.25pt}\\\\ \begin{cases} 729=27^2\\ \qquad (3^3)^2\\ 1000=10^3 \end{cases}\implies 729^{15}+1000\implies ((3^3)^2)^{15}+10^3 \\\\\\ ((3^2)^{15})^3+10^3\implies (3^{30})^3+10^3\implies (3^{30}+10)~~[(3^{30})^2-(3^{30})(10)+10^2] \\\\\\ (3^{30})^3+10^3\implies (3^{30}+10)~~~~[(3^{60})-(3^{30})(10)+10^2]$

now, we could expand them, but there's no need, since it's just factoring.

3 0

3 years ago

Select the equivalent expression.

Vanyuwa [196]

For this case we must find an expression equivalent to: $(y ^ 3 * 2 ^ 5) ^ 2$

By definition of power properties we have to meet:

$(a ^ n) ^ m = a ^ {n * m}$

So, rewriting the expression we have:

$y^{3 * 2} * 2^ {5 * 2} =\\y^ 6 * 2^{10}$

Answer:

Option B

$y^6*2^{10}$

4 0

4 years ago

The equation (x-3)^2+(y+7)^2=64 models the position and range of the source of a radio signal. Describe the position of the sour

12345 [234]

$\bf \textit{equation of a circle}\\\\ 
(x- h)^2+(y- k)^2= r^2
\qquad 
center~~(\stackrel{}{ h},\stackrel{}{ k})\qquad \qquad 
radius=\stackrel{}{ r}\\\\
-------------------------------\\\\
(x-3)^2+(y+7)^2=64\implies [x-\stackrel{h}{3}]^2+[y-(\stackrel{k}{-7})]^2=\stackrel{r}{8^2}
\\\\\\
center~(3,-7)\qquad radius=8$

so, the broadcast location and range is more or less like the picture below.