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Korvikt [17]
3 years ago
14

you and your friends go to the fair and spend $35 on 10 hot dogs and 5 drinks if the concession stand is advertising seven hot d

ogs and four drinks for $25.25 what is the cost for one hot dog and one drink.
Mathematics
1 answer:
choli [55]3 years ago
8 0

So for this, you will be doing a system of equations. The first equation will be how much you spent and the second equation is how much they advertise.


Let h = cost of hotdog and d = cost of drinks


10h+5d=35\\ 7h+4d=25.25


With this, i'll be using the substitution method. So firstly, subtract 10h on each side of the first equation. It will look like this: 5d=35-10h


Next, divide 5 on each side of the first equation. Your answer will be d=7-2h


Next, replace d in the second equation with (7-2h). Your second equation will look like this: 7h+4(7-2h)=25.25 . From here you can solve for h.



Firstly, foil 4(7-2h). 7h+28-8h=25.25


Next, combine like terms: 28-h=25.25


Next, subtract 28 on each side to get -h=-2.75


Lastly, multiply -1 on each side of the equation to get h=2.75



Now that we got h, we can solve for d by substituting 2.75 in the h variable in either equation. For this, I'll be using the first one.


10(2.75)+5d=35\\ 27.5+5d=35\\ 5d=7.5\\ d=1.5


In short, hotdogs are $2.75 each and drinks are $1.50 each.

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Step-by-step explanation:

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Divide f(x) by d(x), and write a summary statement in the form indicated.
Mandarinka [93]

Answer:

The correct option is B)  f(x) =(x^2+1)(x^2+4x+5)

Step-by-step explanation:

Consider the provided function.

f(x) = x^4 + 4x^3 + 6x^2 + 4x + 5 and d(x) = x^2+1

We need to divide f(x) by d(x)

As we know: Dividend = Divisor × Quotient + Remainder

In the above function f(x) is dividend and divisor is d(x)

Divide the leading term of the dividend by the leading term of the divisor:\frac{x^4}{x^2}=x^2

Write the calculated result in upper part of the table.

Multiply it by the divisor: x^2(x^2+1)=x^4+x^2

Now Subtract the dividend from the obtained result:

(x^4 + 4x^3 + 6x^2 + 4x + 5)-(x^4-x^2)=4x^3+5x^2+4x+5

Again divide the leading term of the obtained remainder by the leading term of the divisor: \frac{4x^3}{x^2}=4x

Write the calculated result in upper part of the table.

Multiply it by the divisor: 4x(x^2+1)=4x^3+4x

Subtract the dividend:

(4x^3+5x^2+4x+5)-(4x^3+4x)=5x^2+5

Divide the leading term of the obtained remainder by the leading term of the divisor: \frac{5x^2}{x^2}=5

Multiply it by the divisor: 5(x^2+1)=5x^2+5

Subtract the dividend:

(5x^2+5)-(5x^2+5)=0

Therefore,

Dividend = x^4 + 4x^3 + 6x^2 + 4x + 5

Divisor = x^2+1

Quotient = x^2+4x+5

Remainder = 0

Dividend = Divisor × Quotient + Remainder

f(x) = (x^2+1)(x^2+4x+5)

Hence, the correct option is B)  f(x) =(x^2+1)(x^2+4x+5)

3 0
3 years ago
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