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Evgesh-ka [11]
3 years ago
10

Alan deposited $300 into a savinga account. At the end of the first year, the amount of money in the account has increased to $3

36. At the end of the second year, he had $420. Find the percentg increase in the amount of money in his savings account at the end of the first year. HOW DO I SOLVE THIS????
Mathematics
1 answer:
Step2247 [10]3 years ago
4 0
He had put in $300 and got out $336 at the end of the year.
This means an increase of $36 over a year.

10% of $300 = $30 dollars
This shows that he definitely got more than a 10% increase.

Alan got $6 more than $30 so to find 6 from 30, you divide by 5

so ( 10% = $30 ) divided by 5 = ( 2% = $6 )

Adding the amount of money and percentages gives you 12% = $36

So the amount of mpercentage increase is 12%

Overall the amount of money in his bank now compared to when he deposited it, he has 112% in the bank.
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Step-by-step explanation:

8 0
3 years ago
What is the axis of symmetry for f(x) = -3x2 + 18 - 7
solong [7]

The vertex form:

y=a(x-h)^2+k\\\\(h,\ k)-vertex

The axis of symetry is x = h.

y=ax^2+bx+c\to h=\dfrac{-b}{2a}

We have

f(x)=-3x^2+18x-7\to a=-3,\ b=18,\ c=-7

Substitute:

h=\dfrac{-18}{(2)(-3)}=\dfrac{-18}{-6}=3

<h3>Answer: x = 3</h3>
6 0
3 years ago
Find the distance between (8,8) and (3,1)
Vesnalui [34]

Answer:

About 8.6

Step-by-step explanation:

d=(x2-x1)^2+(y2-y1)^2

8=x1 8=y1   3=x2 1=y2

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3 0
4 years ago
Find the minimum value of the function f(x)=x^2+5x-6
mash [69]
<h3><u>Explanation</u></h3>
  • Method 1 (Formula)

\begin{cases}h =  -  \frac{b}{2a}  \\ k =  \frac{4ac -  {b}^{2} }{2a}  \end{cases}

The vertex of Parabola is the maximum/minimum point depending on the value of a.

  • Find Vertex

<u>h-value</u>

h =  -  \frac{5}{2(1)}  \\ h =  -  \frac{5}{2}

<u>k-value</u>

k =  \frac{4(1)( - 6) -  {(5)}^{2} }{4(1)}  \\ k =  \frac{ - 24 - 25}{4}  \\ k =  \frac{ - 49}{4}  \\ k =  -  \frac{49}{4}

The minimum value is the value of k. Therefore the minimum value is - 49/4 at x = -5/2.

  • Method 2 (Derivative)

This is Calculus method. We simply differentiate the function then substitute y' = 0.

  • Differentiate Function

f'(x) = 2 {x}^{2 - 1}  +  {5x}^{1 - 1}  - 0 \\ f'(x) = 2x + 5

Substitute f'(x) = 0

0 = 2x + 5 \\  - 5 = 2x \\   -  \frac{5}{2}  = x

Substitute x = -5/2 in the original equation.

f(x) =  {( -  \frac{5}{2} )}^{2}  + 5( -   \frac{5}{2} ) - 6 \\ f(x) =  \frac{25}{4}  -  \frac{25}{2}  - 6 \\ f(x) =  \frac{25}{4}  -  \frac{50}{4}  -  \frac{24}{4}  \\ f(x) =  \frac{25}{4}  -  \frac{74}{4}  \\ f(x) = -   \frac{49}{4}

<h3><u>Answer</u><u /></h3>

<u>\sf{the  \:  \: minimum  \:  \: value \:  \:  is   \:  \: -  \frac{49}{4}  \:  \: at \:  \:  x =  -  \frac{5}{2} }</u>

4 0
3 years ago
280ft of their living room wall with 4/5 gallons of paint. How many square feet can they paint with 3 gallons of paint?
Vilka [71]
3 gallons of paint would cover 1050 square feet
6 0
3 years ago
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