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2 years ago

Write a system of equations to describe the situation below, solve using elimination, and fill in

Mathematics

1 answer:

Andrej [43]2 years ago

6 0

Answer: Child is $1 and Adult is $3, per person.

Step-by-step explanation:

We have two unknowns, so we need at least two equations. Let C and A stand for the price of a ticket for a child and an adult, respectively.

The income for Monday and Tuesday can be calculated:

Monday: 16C + 42A = $142

Tuesday: 24C + 26A = $102

Rearrange the second equation to isolate one of the variables. I'll pick C:

24C + 26A = $102

C = ($102 - 26A)/24

Now use this expression for C in the first equation

16C + 42A = $142

16(($102 - 26A)/24) + 42A = $142

(1632 - 416A)/24 + 42A = $142

(68 - 17.3333A + 42A = $142

24.6667A = 74

A = 3 [The price of an adult pool admission is $3]

Use this value in either equation to find the price of a child's admission:

24C + 26A = $102

24C + 26*($3) = $102

24C = 102 - 78

C = $1 [The price of a child's admission to the pool is $1]

Check to see if these prices satisfy both equations:

Monday: 16C + 42A = $142

Tuesday: 24C + 26A = $102

---

Monday: 16*(1) + 42*(3) = $142 ? YES

Tuesday: 24*(1) + 26*(3) = $102 ? YES

<u>Child is $1 and Adult is $3, per person.</u>

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Answer:

5 2/6 + 2 4/6 = 8

Step-by-step explanation:

So Gina has 8 feet of ribbon in total.

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3 years ago

A number to the 10th power divided by the same number to the 7th power equals 125. What is the number?

Viefleur [7K]

Answer:

the number is 5

Step-by-step explanation:

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3 years ago

Which expression is equivalent to (r Superscript negative 7 Baseline) Superscript 6? r Superscript 42 StartFraction 1 Over r Sup

vodomira [7]

Power rule of exponents says that the power of the power of a exponent is equal to the multiplying both the powers. The expression which is equal to the given expression is,

$\dfrac{1}{(r)^{42}}$

The option B is the correct option.

Given information-

The given expression in the problem is,

$[(r)^{-7}]^5$

<h3>Power rule of exponents</h3>

Power rule of exponents says that the power of the power of a exponent is equal to the multiplying both the powers.

Suppose<em> </em><em>x</em> is a number with power <em>a. </em>The power is power of the power of number <em>x. </em>Then by the power rule of the exponents,

$(x^a)^b=x^{ab}$

Using the power rule of the exponents given expression can be written as,

$[(r)^{-7}]^6=(r)^{-7\times 6} 
$

$[(r)^{-7}]^6=(r)^{-42}$

<h3>Negative exponents rule</h3>

Negative exponents rule says that when a power of a number is negative, then write the number in the denominator with the same power with positive sign.Thus,

$[(r)^{-7}]^6=\dfrac{1}{(r)^{42}}$