6. Homer and Bart plan to buy one computer for $499.00 strictly for gam purposes. Games cost $49.99 each. Part A: Define each va
2 answers:
Answer:
The required algebraic expression is where x is the number of games and y is the total cost.
Step-by-step explanation:
Consider the provided information.
It is given that the cost price of computer is $499.00
Let x represents the number of games Homer and Bart bought and y is the total purchasing cost of the computer (before sales tax).
It is given that the cost of each game is 49.99.
If they bought x games, then the total cost will be:
Therefore, the algebraic expression is where x is the number of games they bought and y be the total cost.
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For any quadratic functions, ax² + bx + c, we can easily find the x-coordinate of its vertex through the use of the formula below.
where a and b are the coefficients of the function. For f(x), we have a = -1 and b = -16. Thus, we have
Since we now have the x-coordinate of the vertex, we can just easily substitute 8 into f(x) as shown below.
Thus, the vertex of f(x) is (8, 60). The vertex of the function shows the maximum value that the function can reach. For this particular case, the vertex represents the maximum profit that the shop owner could earn.
The x-intercepts of the function are the values of x when f(x) is zero. By equation f(x) with zero, we can solve the quadratic equation to find the x-intercepts as shown below.
From this, we can see that the x-intercepts are (6, 0) and (10, 0). We just discussed that the x-intercepts are the values of x when y is zero. So, for this case it means that the shop does not earn a profit if they sell 6 or 10 candles. Basically, the x-intercepts represent the number candles sold if the shop wants to break even.
where a and b are the coefficients of the function. For f(x), we have a = -1 and b = -16. Thus, we have
Since we now have the x-coordinate of the vertex, we can just easily substitute 8 into f(x) as shown below.
Thus, the vertex of f(x) is (8, 60). The vertex of the function shows the maximum value that the function can reach. For this particular case, the vertex represents the maximum profit that the shop owner could earn.
The x-intercepts of the function are the values of x when f(x) is zero. By equation f(x) with zero, we can solve the quadratic equation to find the x-intercepts as shown below.
From this, we can see that the x-intercepts are (6, 0) and (10, 0). We just discussed that the x-intercepts are the values of x when y is zero. So, for this case it means that the shop does not earn a profit if they sell 6 or 10 candles. Basically, the x-intercepts represent the number candles sold if the shop wants to break even.
Answer:
x = 14
y = 6
Step-by-step explanation:
<em>*</em><em>Property</em><em>*</em>
In a parallelogram:
Opposite sides are equal.
Since, the given figure is a parallelogram we can apply this property and equate:
- 1) 2y + 1 = 13
- 2) x = y + 8
<u>1) 2y + 1 = 13</u>
<em>subtracting</em><em> </em><em>1</em><em> </em><em>from</em><em> </em><em>both</em><em> </em><em>sides</em><em>:</em>
=> 2y + 1 - 1 = 13 - 1
=> 2y = 12
<em>dividing</em><em> </em><em>both</em><em> </em><em>sides</em><em> </em><em>by</em><em> </em><em>2</em><em>:</em>
=> 2y/ 2 = 12/ 2
<em>On</em><em> </em><em>the</em><em> </em><em>LHS</em><em>,</em><em> </em><em>2</em><em> </em><em>gets</em><em> </em><em>canceled</em><em> </em><em>because</em><em> </em><em>it's</em><em> </em><em>available</em><em> </em><em>in</em><em> </em><em>the</em><em> </em><em>numerator</em><em> </em><em>as</em><em> </em><em>well</em><em> </em><em>as</em><em> </em><em>the</em><em> </em><em>denominator</em><em> </em>
<em>On</em><em> </em><em>the</em><em> </em><em>RHS</em><em>,</em><em> </em><em>2</em><em> </em><em>gets</em><em> </em><em>canceled</em><em> </em><em>when</em><em> </em><em>12</em><em> </em><em>is</em><em> </em><em>factorised</em><em> </em><em>to</em><em> </em><em>6</em><em> </em><em>×</em><em> </em><em>2</em><em>:</em>
<h3>=> y = 6</h3><u>2</u><u>)</u><u> </u><u>x</u><u> </u><u>=</u><u> </u><u>y</u><u> </u><u>+</u><u> </u><u>8</u>
We've got the value of y from equation 1).
<em>Substituting it here:</em>
=> x = 6 + 8
<h3>=> x = 14 </h3>Answer:
Hence, we got the values of x and y as: