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4 years ago

The product of two consecutive square numbers is 900. What is the sum of these two numbers? What is an easy way to solve this

1 answer:

4 0

900=22 x 32 x 52900=22 x 32 x 52. There is only a limited number of options to build squares out of these factors. You can try them all, but in fact it is easy to see that the solution to your problem is p=22 x 32=36p=22 x 32=36 and Q=52=25Q=52=25. Their sum is 61.

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The father earns $2194 a month and the mother works 40 hours per week assuming a month has four weeks what minimum hourly wage d

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3 years ago

Rewrite the function in standard form, intercept form, find the vertex, find the y-intercept, and find the x-intercepts.

jasenka [17]

Answer:

We have the function, $f(x)=(x+3)^{2}-4$

On simplifying, we get,

$f(x)=x^2+6x+9-4$

i.e. $f(x)=x^2+6x+5$

Thus, the standard form of the function is $f(x)=x^2+6x+5$ .

Now, the factors of the given functions are (x+1) and (x+5).

Since, the intercept form of the function is the factored form of the function.

So, we have, intercept form of the function is $f(x)=(x+1)(x+5)$ .

Now, we know that,

Value of x-coordinate of the vertex is $\frac{-b}{2a}$ i.e. $\frac{-6}{2\times 1}$ i.e. $\frac{-6}{2}$ i.e. x= -3

Then, $f(-3)=(-3)^2+6\times (-3)+5$ i.e. $f(-3)=9-18+5$ i.e. f(-3)=-4

So, the vertex of the function is (-3,-4).

Further, we know that, 'the y-intercept of a function is the point where the function crosses y-axis'.

So, when x=0, we have, $f(0)=0^2+6\times 0+5$ i.e. f(0) = 5

Thus, the y-intercept is (0,5)

Also, 'the x-intercept of a function is the point where the function crossese x-axis'.

Then, for f(x)=0, we have $0=x^2+6x+5$ i.e. $0=(x+1)(x+5)$ i.e. x= -1 and x= -5

Thus, the x-intercept are (-1,0) and (-5,0).

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3 years ago

What is the simplest radical form of the expression? (x^3y^5)^(4/3)

satela [25.4K]

$\bf ~\hspace{7em}\textit{rational exponents} \\\\ a^{\frac{ n}{ m}} \implies \sqrt[ m]{a^ n} ~\hspace{10em} a^{-\frac{ n}{ m}} \implies \cfrac{1}{a^{\frac{ n}{ m}}} \implies \cfrac{1}{\sqrt[ m]{a^ n}} \\\\[-0.35em] \rule{34em}{0.25pt}\\\\ (x^3y^5)^{\frac{4}{3}}\implies \left( x^{3\cdot \frac{4}{3}}y^{5\cdot \frac{4}{3}} \right)\implies x^4y^{\frac{20}{3}}\implies x^4 y^{\frac{18}{3}+\frac{2}{3}}\implies x^4 y^{\frac{18}{3}} y^{\frac{2}{3}} \\\\\\ x^4y^6 y^{\frac{2}{3}}\implies x^4y^6\sqrt[3]{y^2}$

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4 years ago