Rewrite the following quadratic functions in intercept or factored form. Show your work.

Mathematics

2 answers:

Mariulka [41]4 years ago

4 0

Answer:

y = 5x (x+2)

Step-by-step explanation:

We are given the following the quadratic function and we are to rewrite it in intercept or factored form:

$y = 5x^2 + 10x$

We can factorize the given expression so taking the common factors out of it to get:

$y=5x^2 + 10x$

$y = 5x (x + 2)$

Therefore, the factored form of the given quadratic function is y = 5x (x+2).

Inga [223]4 years ago

3 0

Answer:

y = 5x(x+2)

Step-by-step explanation:

Given quadratic equation is:

y = 5x²+10x

We have to transform given function into factored form.

Taking x common from given function,we get

y = x(5x+10)

5 and 10 are multiple of 5.

Hence,

taking 5 as common,we get

y = x(5)(x+2)

y = 5x(x+2) is factored form of given quadratic function.

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Two certificates of deposit pay interest that differ by 3%. Money invested for one year in the first CD earns $240 interest. The

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a = interest rate of first CD

b = interest rate of second CD

and again, let's say the principal invested in each is $X.

$\bf a-b=3\qquad \implies \qquad \boxed{b}=3+a~\hfill \begin{cases} \left( \frac{a}{100} \right)X=240\\\\ \left( \frac{b}{100} \right)X=360 \end{cases} \\\\[-0.35em] ~\dotfill\\\\ \left( \cfrac{a}{100} \right)X=240\implies X=\cfrac{240}{~~\frac{a}{100}~~}\implies X=\cfrac{24000}{a} \\\\\\ \left( \cfrac{b}{100} \right)X=360\implies X=\cfrac{360}{~~\frac{b}{100}~~}\implies X=\cfrac{36000}{b} \\\\[-0.35em] ~\dotfill\\\\$

$\bf X=X\qquad thus\qquad \implies \cfrac{24000}{a}=\cfrac{36000}{b}\implies \cfrac{24000}{a}=\cfrac{36000}{\boxed{3+a}} \\\\\\ (3+a)24000=36000a\implies \cfrac{3+a}{a}=\cfrac{36000}{24000}\implies \cfrac{3-a}{a}=\cfrac{3}{2} \\\\\\ 6-2a=3a\implies 6=5a\implies \cfrac{6}{5}=a\implies 1\frac{1}{5}=a\implies \blacktriangleright 1.2 = x\blacktriangleleft$

$\bf \stackrel{\textit{since we know that}}{b=3+a}\implies b=3+\cfrac{6}{5}\implies b=\cfrac{21}{5}\implies b=4\frac{1}{5}\implies \blacktriangleright b=4.2 \blacktriangleleft$