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g100num [7]
2 years ago
6

You and your friend each purchase an equal number n of magazines. Your magazines cost $1.50 each and your friend’s magazines cos

t $2 each. The total cost for you and your friend is $10.50.
Write and solve an equation to find the number of magazines you purchased.
Mathematics
2 answers:
Brilliant_brown [7]2 years ago
8 0
The answer would be 7
yanalaym [24]2 years ago
3 0

Answer:

7

Step-by-step explanation:

Hope this helped!

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Which statement describes the inverse of m(x) = x2 – 17x?
stealth61 [152]

Answer:

The correct option is;

The \ domain \ restriction \ x \geq \dfrac{17}{2} \ results \ in \ m^{-1}(x) = \dfrac{17}{2} \pm \sqrt{x + \dfrac{289}{4} }}

Step-by-step explanation:

The given information is that m(x) = x² - 17·x

The above equation can be written in the form;

y = x² - 17·x

Therefore;

0 = x² - 17·x - y

From the general solution of a quadratic equation, 0 = a·x² + b·x + c we have;

x = \dfrac{-b\pm \sqrt{b^{2}-4\cdot a\cdot c}}{2\cdot a}

By comparison to the equation,0 = x² - 17·x - y, we have;

a = 1, b = -17, and c = -y

Substituting the values of a, b and c into the formula for the general solution of a quadratic equation, we have;

x = \dfrac{-(-17)\pm \sqrt{(-17)^{2}-4\times (1) \times (-y)}}{2\times (1)} = \dfrac{17\pm \sqrt{289+4\cdot y}}{2}

Which can be simplified as follows;

x =  \dfrac{17\pm \sqrt{289+4\cdot y}}{2}= \dfrac{17}{2} \pm \dfrac{1}{2}  \times \sqrt{289+4\cdot y}} = \dfrac{17}{2} \pm \sqrt{\dfrac{289}{4} +\dfrac{4\cdot y}{4} }}

And further simplified as follows;

x = \dfrac{17}{2} \pm \sqrt{\dfrac{289}{4} +y }} = \dfrac{17}{2} \pm \sqrt{y + \dfrac{289}{4} }}

Interchanging x and y in the function of the inverse, m⁻¹(x), we have;

m^{-1}(x) = \dfrac{17}{2} \pm \sqrt{x + \dfrac{289}{4} }}

We note that the maximum or minimum point of the function, m(x) = x² - 17·x found by differentiating the function and equating the result to zero, gives;

m'(x) = 2·x - 17 = 0

x = 17/2

Similarly, the second derivative is taken to determine if the given point is a maximum or minimum point as follows;

m''(x) = 2 > 0, therefore, the point is a minimum point on the graph

Therefore, as x increases past the minimum point of 17/2, m⁻¹(x) increases to give;

The \ domain \ restriction \ x \geq \dfrac{17}{2} \ results \ in \ m^{-1}(x) = \dfrac{17}{2} \pm \sqrt{x + \dfrac{289}{4} }} to increase m⁻¹(x) above the minimum.

8 0
2 years ago
What is 783 divided by 18
alukav5142 [94]
43.5 is 783 divided by 18      783 ÷ 18 = 43.5
4 0
2 years ago
Read 2 more answers
Solve 10/y = 5/2 The solution is y=_
kolezko [41]

Answer:

y is equal to 4.

Step-by-step explanation:

To find this, cross multiply and then divide.

10*2 = y*5

20 = 5y

4 = y

5 0
3 years ago
11z/16+7z/8=5/16 as a decimal
babunello [35]
11z/16+7z/8=5/16
(11z+14z)/16=5/16
25z=5
z=5/25=1/5
4 0
2 years ago
What were the three parts to Hamilton's financial plan ?
earnstyle [38]
The paramount problem facing Hamilton was a huge national debt. He proposed that the government assume the entire debt of the federal government and the states. His plan was to retire the old depreciated obligations by borrowing new money at a lower interest rate.
7 0
3 years ago
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