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Elis [28]
2 years ago
14

Jayden has $2.95 worth of dimes and quarters. He has 2 more quarters than dimes. Determine the number of dimes and the number of

quarters that Jayden has.
Mathematics
1 answer:
saveliy_v [14]2 years ago
6 0

There are 7 dimes and 9 quarters Jayden has.

Step-by-step explanation:

Given,

Worth of dimes and quarters = $2.95 = 2.95*100 = 295 cents

One dime = 10 cents

One quarter = 25 cents

Let,

x be the number of dimes

y be the number of quarters

According to given statement;

10x+25y=295       Eqn 1

y = x+2                  Eqn 2

Putting value of y from Eqn 2 in Eqn 1

10x+25(x+2)=295\\10x+25x+50=295\\35x=295-50\\35x=245

Dividing both sides by 35

\frac{35x}{35}=\frac{245}{35}\\x=7

Putting x=7 in Eqn 2

y=7+2\\y=9

There are 7 dimes and 9 quarters Jayden has.

Keywords: linear equation, substitution method

Learn more about substitution method at:

  • brainly.com/question/1369568
  • brainly.com/question/1386181

#LearnwithBrainly

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We have the following function:

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The graph corresponding to the function is the following:

We determine in each case what the statement asks for, like this:

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\begin{gathered} \text{ in this case y = 0, therefore:} \\  \\ \frac{x-1}{x^2-x-6}=0 \\  \\ x-1=0\cdot(x^2-x-6) \\  \\ x=1 \\  \\ \text{The x-intercept is \lparen1, 0\rparen} \end{gathered}

b. the y-intercept:

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c. the equation(s) of any vertical asymptote(s). The horizontal asymptotes are the values that x cannot take since the function would be discontinuous for those values.

In this case, since it is a rational function, it would be when the denominator is 0, therefore, we solve the following:

\begin{gathered} x^2-x-6=0 \\  \\ (x-3)(x+2)=0 \\  \\ x-3=0\rightarrow x=3 \\  \\ x+2=0\operatorname{\rightarrow}x=-2 \\  \\ \text{ The equation\lparen s\rparen of any vertical asymptote are:} \\  \\ x=3,x=-2 \end{gathered}

d. the equation of the horizontal asymptote. If the degree of the denominator is greater than that of the numerator, the horizontal asymptote is the x-axis, that is:

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e. information about the behavior at the asymptote(s).

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