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irina1246 [14]
3 years ago
8

Find the simple interest rate needed in order for an investment of $2000 to grow to an account of $5000 in 3 years

Mathematics
1 answer:
Nutka1998 [239]3 years ago
5 0

\bf ~~~~~~ \textit{Simple Interest Earned Amount} \\\\ A=P(1+rt)\qquad \begin{cases} A=\textit{accumulated amount}\dotfill & \$5000\\ P=\textit{original amount deposited}\dotfill&\$2000\\ r=rate\to r\%\to \frac{r}{100}\\ t=years\dotfill &3 \end{cases} \\\\\\ 5000=2000(1+r3)\implies \cfrac{5000}{2000}=1+3r\implies \cfrac{5}{2}=1+3r \\\\\\ 5=2+6r\implies 3=6r\implies \cfrac{3}{6}=r\implies 0.5=r\implies \stackrel{\textit{converting to percent}}{0.5\cdot 100\implies 50\%}

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Find the distance between the two points (0,0), (4,3)
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Answer:

Distance between the points=5

Step-by-step explanation:

The distance between two points in coordinate geometry is measured by using the distance formula:

If we have given two points

                   (x_1,y_1)\\\\(x_2,y_2)

Distance formula=  \sqrt{(x_2-x_1)^2+(y_2-y_1)^2}

For (0,0) and (4,3)

      Distance:                          

                        \sqrt{(4-0)^2+(3-0)^2} \\\\\sqrt{4^2+3^2}\\\\\sqrt{16+9}\\\\\sqrt{25}

Or

      Distance between the points=5

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What are the coordinates of the vertex of the parabola represent by the equation y=-5x^2+30x-25
Jobisdone [24]

Answer:

The coordinate of the  vertex of the parabola is (h,k) =  (3,20)

Step-by-step explanation:

The given equation of the parabola is y=-5x^2+30x-25

Now, the General Parabolic Equation is of the form:

y = a (x-h)^2 + k, then the vertex is the point (h, k).

Now, to covert the given equation in the standard form:

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Using the COMPLETE THE SQUARE METHOD,

-5(x^2  -6x   + 5)  = -5(x^2  -6x  +  (3)^2 +  5  - (3)^2)\\\implies -5(((x^2  -6x +(3)^2)  + 5 - 9)\\= -5((x-3)^3 -4)\\= -5(x-3)^2 + 20

ory = -5(x-3)^2 + 20

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