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ahrayia [7]
3 years ago
6

On Monday your bank account balance was -$12.58. Because you didn't realize this you wrote a $30.72 check. A. What is the new ba

lance in your checking account? B. The bank charges a $25 fee for paying a check on a negative balance. What is the balance in your checking account after this fee? C. How much money do you need to deposit to bring your account balance back up to $0 after the fee?
Mathematics
1 answer:
zlopas [31]3 years ago
8 0

<u><em>Explanation</em></u>

On Monday, the bank account balance was -$12.58

A.  As you wrote a $30.72 check, so the new balance in your checking account will be: (-12.58+30.72)dollar =18.14 dollar

B.  The bank charges a $25 fee for paying a check on a negative balance. So, the balance in your checking account after this fee =(18.14-25)dollar= -6.86 dollar

C.   For bringing your account balance back up to $0 after the fee, the money need to deposit =[0-(-6.86)]dollar =6.86 dollar.

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<h2>SEE BELOW</h2>

Step-by-step explanation:

<h3>to understand this</h3><h3>you need to know about:</h3>
  • quadratic function
  • PEMDAS
<h3>let's solve:</h3>

vertex:(h,k)

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vertex:(-1,4)

axis of symmetry:x=h

therefore

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  • to find the quadratic equation we need to figure out the vertex form of quadratic equation and then simply it to standard form i.e ax²+bx+c=0

vertex form of quadratic equation:

  • y=a(x-h)²+k

therefore

  • y=a(x-(-1))²+4
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it's to notice that we don't know what a is

therefore we have to figure it out

the graph crosses y-asix at (0,3) coordinates

so,

3=a(0+1)²+4

simplify parentheses:

3 = a(1 {)}^{2}  + 4

simplify exponent:

3 =  a + 4

therefore

a =  - 1

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let's simplify it to standard form

simplify square:

y =  - ( {x}^{2}  + 2x + 1)  + 4

simplify parentheses:

y =  -  {x}^{2}  - 2x - 1 + 4

simplify addition:

y =  -  {x}^{2}  - 2x + 3

therefore our answer is D)y=-x²-2x+3

the domain of the function

x\in \mathbb{R}

and the range of the function is

y\leqslant 4

zeroes of the function:

-  {x}^{2}  - 2x + 3 = 0

\sf divide \: both \: sides \: by \:  - 1

{x}^{2}  + 2x - 3 = 0

\implies \:  {x}^{2} +   3x  - x  +  3 = 0

factor out x and -1 respectively:

\sf \implies \: x(x + 3)   - 1(x  + 3 )= 0

group:

\implies \: (x - 1)(x + 3) = 0

therefore

\begin{cases} x_{1} = 1 \\  x_{2}  =  - 3\end{cases}

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