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2 years ago

Write as a polynomial. a(a+9b)^2

1 answer:

4 0

Answer: a^3+81ab^2
First, you square (a+9b) which will become (a^2+81b^2)
Then, you multiply it by a and you will get a^3+81ab^2

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2 3/4+3 5/8 simplified

otez555 [7]

$2\frac{3}{4}+3 \frac{5}{8}=6\frac{3}{8}$

Solution:

Given expression is $2\frac{3}{4}+3 \frac{5}{8}$ .

To simplify the expression $2\frac{3}{4}+3 \frac{5}{8}.$

Let us first convert the mixed fraction into improper fraction.

$2\frac{3}{4}+3 \frac{5}{8}=\frac{(2\times 4) + 3}{4}+ \frac{(3 \times 8)+5}{8}$

$=\frac{8+ 3}{4}+ \frac{24+5}{8}$

$=\frac{11}{4}+ \frac{29}{8}$

Take LCM for the denominators (LCM of 4, 8 = 8) and make the same.

$=\frac{11\times2}{4\times 2}+ \frac{29\times1}{8\times1}$

$=\frac{22}{8}+ \frac{29}{8}$

$=\frac{51}{8}$

Now, divide 51 by 8 and again write it in the mixed fraction.

$=6\frac{3}{8}$

$2\frac{3}{4}+3 \frac{5}{8}=6\frac{3}{8}$

Hence, the simplified answer is $6\frac{3}{8}$ .

7 0

3 years ago

Select the correct expressions. 1 Identify each expression that represents the slope of a tangent to the curve y= * +1 at any po

Olegator [25]

The expressions which represents the slope of a tangent to the curve $y=\frac{1}{x+1}$ at any point (x, y) are:

$f'(x) =limh \rightarrow 0\frac{-h}{h(x+1)(x+h+1)}\\\\f'(x) =limh \rightarrow 0\frac{-h}{x^2h+2xh+xh^2+h^2 +1}$

<h3>The slope of a tangent to the curve.</h3>

Mathematically, the slope of a tangent line to the curve is given by this equation:

$f'(x) =limh \rightarrow 0\frac{f(x+h)-f(x)}{h}$

Given the function:

$f(x)=y=\frac{1}{x+1}$

When (x + h), we have:

$f(x+h)=y=\frac{1}{x+h+1}$

Next, we would find the derivative of f(x):

$f'(x) =limh \rightarrow 0\frac{\frac{1}{x+h+1} -\frac{1}{x+1}}{h}\\\\f'(x) =limh \rightarrow 0\frac{x+1 -(x+h+1)}{h(x+1)(x+h+1)}\\\\f'(x) =limh \rightarrow 0\frac{x+1 -x-h-1}{h(x+1)(x+h+1)}\\\\f'(x) =limh \rightarrow 0\frac{-h}{h(x+1)(x+h+1)}\\\\f'(x) =limh \rightarrow 0\frac{-h}{x^2h+2xh+xh^2+h^2 +1}\\\\f'(x) = \frac{-1}{(x+1)(x+1)} \\\\f'(x) = \frac{-1}{(x+1)^2}$

Read more on slope of a tangent here: brainly.com/question/26015157

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5 0

2 years ago

smith put some money in a saving certificate which earns 8% a year. the yearly interest in $600. how much did smith invest?

pshichka [43]

$~~~~~~ \textit{Simple Interest Earned} \\\\ I = Prt\qquad \begin{cases} I=\textit{interest earned}\dotfill&\$600\\ P=\textit{original amount deposited}\\ r=rate\to 8\%\to \frac{8}{100}\dotfill &0.08\\ t=years\dotfill &1 \end{cases} \\\\\\ 600=P(0.08)1\implies \cfrac{600}{0.08}=P\implies 7500=P$