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Nadusha1986 [10]

3 years ago

5

Michael can buy 4 sandwiches and 3 cups of coffee for $23.75. Amy can buy 2 sandwhiches and 5 cups of coffee for $19.75 how much

does one saandwhich cost

1 answer:

Kobotan [32]3 years ago

8 0

Answer: The cost of one sandwich is $4.25 and the cost of one cup of coffee is $2.25.

Step-by-step explanation:

Let x be the cost of one sandwich and y be the cost of one cup of coffee.

By considering the given situation, we have the following equations :-

$4x+3y=23.75.................(1)\\\\2x+5y=19.75................(2)$

Multiply 2 on both sides of equation (2) , we get

$4x+10y=39.5................(3)$

Subtract equation (1) from equation (3), we get

$7y=15.75\\\\\Rightarrow\ y=\dfrac{15.75}{7}=2.25$

Put value of y in (1), we get

$4x+3(2.25)=23.75\\\\\Rightarrow\ 4x+6.75=23.75\\\\\Rightarrow\ 4x =17\\\\\Rightarrow\ x=4.25$

Hence, the cost of one sandwich is $4.25 and the cost of one cup of coffee is $2.25.

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Given the graphs of f(x) =x -7 and g(x) =-5x-1, what is the solution to the equation f() = g(x)?

lions [1.4K]

Answer:

1

Step-by-step explanation:

x-7=-5x-1

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6x-7=-1

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2 years ago

Solve the quadratic equation algebraically 5-x<2(x-3)+5

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x>2

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2 years ago

What set of lengths forms a right triangle?

Leni [432]

The answer is C. 50 in, 48 in, 14 in

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7 0

3 years ago

4. a) A ping pong ball has a 75% rebound ratio. When you drop it from a height of k feet, it bounces and bounces endlessly. If t

Klio2033 [76]

First part of question:

Find the general term that represents the situation in terms of k.

The general term for geometric series is:

$a_{n}=a_{1}r^{n-1}$

$a_{1}$ = the first term of the series

$r$ = the geometric ratio

$a_{1}$ would represent the height at which the ball is first dropped. Therefore:

$a_{1} = k$

We also know that the ball has a rebound ratio of 75%, meaning that the ball only bounces 75% of its original height every time it bounces. This appears to be our geometric ratio. Therefore:

$r=\frac{3}{4}$

Our general term would be:

$a_{n}=a_{1}r^{n-1}$

$a_{n}=k(\frac{3}{4}) ^{n-1}$

Second part of question:

If the ball dropped from a height of 235ft, determine the highest height achieved by the ball after six bounces.

$k$ represents the initial height:

$k = 235\ ft$

$n$ represents the number of times the ball bounces:

$n = 6$

Plugging this back into our general term of the geometric series:

$a_{n}=k(\frac{3}{4}) ^{n-1}$

$a_{n}=235(\frac{3}{4}) ^{6-1}$

$a_{n}=235(\frac{3}{4}) ^{5}$

$a_{n}=55.8\ ft$

$a_{n}$ represents the highest height of the ball after 6 bounces.

Third part of question:

If the ball dropped from a height of 235ft, find the total distance traveled by the ball when it strikes the ground for the 12th time. 

This would be easier to solve if we have a general term for the <em>sum </em>of a geometric series, which is:

$S_{n}=\frac{a_{1}(1-r^{n})}{1-r}$

We already know these variables:

$a_{1}= k = 235\ ft$

$r=\frac{3}{4}$

$n = 12$

Therefore:

$S_{n}=\frac{(235)(1-\frac{3}{4} ^{12})}{1-\frac{3}{4} }$

$S_{n}=\frac{(235)(1-\frac{3}{4} ^{12})}{\frac{1}{4} }$

$S_{n}=(4)(235)(1-\frac{3}{4} ^{12})$

$S_{n}=910.22\ ft$

8 0

3 years ago

I need to know this ASAP

sashaice [31]

Answer:

Problem 1

x=2

y=3

Problem 2

x=-3

y=8

Goodluck :)

3 0

3 years ago