Answer:
C. The quadrilateral is a trapezoid.
Step-by-step explanation:
Hope it's right.
A. The equation in slope-intercept form, relating the cost, y, to the number of nights stay, x is y = 755 + 101x.
B. The cost for 10 days is $1765.
<h3>How to calculate the value?</h3>
It should be noted that the information can be illustrated with an arithmetic sequence:
Smile Vacations is offering a 4-night Hawaiian vacation for $1,058. This will be illustrated as:
a + 3d = 1058
a = first term
d = common difference
The 7-night vacation for $1,361. This will be:
a + 6d = 1361
The equation will be represented as:
a + 3d = 1058
a + 6d = 1361
Subtract the equations:
3d = 303
Divide
d = 303/3
d = 101
Recall a + 3d = 1058
a + 3(101) = 1058
a + 303 = 1058
a = 1058 - 303
a = 755
The cost for 10 nights will be:
y = 755 + 101x.
y = 755 + 101(10)
y = 755 + 1010
y = 1765
Learn more about sequence on:
brainly.com/question/6561461
#SPJ1
Step-by-step explanation:
2 gallons are needed for 10 galloms of lemonade
Answer:
- b/a
- 16a²b²
- n¹⁰/(16m⁶)
- y⁸/x¹⁰
- m⁷n³n/m
Step-by-step explanation:
These problems make use of three rules of exponents:
![a^ba^c=a^{b+c}\\\\(a^b)^c=a^{bc}\\\\a^{-b}=\dfrac{1}{a^b} \quad\text{or} \quad a^b=\dfrac{1}{a^{-b}}](https://tex.z-dn.net/?f=a%5Eba%5Ec%3Da%5E%7Bb%2Bc%7D%5C%5C%5C%5C%28a%5Eb%29%5Ec%3Da%5E%7Bbc%7D%5C%5C%5C%5Ca%5E%7B-b%7D%3D%5Cdfrac%7B1%7D%7Ba%5Eb%7D%20%5Cquad%5Ctext%7Bor%7D%20%5Cquad%20a%5Eb%3D%5Cdfrac%7B1%7D%7Ba%5E%7B-b%7D%7D)
In general, you can work the problem by using these rules to compute the exponents of each of the variables (or constants), then arrange the expression so all exponents are positive. (The last problem is slightly different.)
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1. There are no "a" variables in the numerator, and the denominator "a" has a positive exponent (1), so we can leave it alone. The exponent of "b" is the difference of numerator and denominator exponents, according to the above rules.
![\dfrac{b^{-2}}{ab^{-3}}=\dfrac{b^{-2-(-3)}}{a}=\dfrac{b}{a}](https://tex.z-dn.net/?f=%5Cdfrac%7Bb%5E%7B-2%7D%7D%7Bab%5E%7B-3%7D%7D%3D%5Cdfrac%7Bb%5E%7B-2-%28-3%29%7D%7D%7Ba%7D%3D%5Cdfrac%7Bb%7D%7Ba%7D)
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2. 1 to any power is still 1. The outer exponent can be "distributed" to each of the terms inside parentheses, then exponents can be made positive by shifting from denominator to numerator.
![\left(\dfrac{1}{4ab}\right)^{-2}=\dfrac{1}{4^{-2}a^{-2}b^{-2}}=16a^2b^2](https://tex.z-dn.net/?f=%5Cleft%28%5Cdfrac%7B1%7D%7B4ab%7D%5Cright%29%5E%7B-2%7D%3D%5Cdfrac%7B1%7D%7B4%5E%7B-2%7Da%5E%7B-2%7Db%5E%7B-2%7D%7D%3D16a%5E2b%5E2)
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3. One way to work this one is to simplify the inside of the parentheses before applying the outside exponent.
![\left(\dfrac{4mn}{m^{-2}n^6}\right)^{-2}=\left(4m^{1-(-2)}n^{1-6}}\right)^{-2}=\left(4m^3n^{-5}}\right)^{-2}\\\\=4^{-2}m^{-6}n^{10}=\dfrac{n^{10}}{16m^6}](https://tex.z-dn.net/?f=%5Cleft%28%5Cdfrac%7B4mn%7D%7Bm%5E%7B-2%7Dn%5E6%7D%5Cright%29%5E%7B-2%7D%3D%5Cleft%284m%5E%7B1-%28-2%29%7Dn%5E%7B1-6%7D%7D%5Cright%29%5E%7B-2%7D%3D%5Cleft%284m%5E3n%5E%7B-5%7D%7D%5Cright%29%5E%7B-2%7D%5C%5C%5C%5C%3D4%5E%7B-2%7Dm%5E%7B-6%7Dn%5E%7B10%7D%3D%5Cdfrac%7Bn%5E%7B10%7D%7D%7B16m%5E6%7D)
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4. This works the same way the previous problem does.
![\left(\dfrac{x^{-4}y}{x^{-9}y^5}\right)^{-2}=\left(x^{-4-(-9)}y^{1-5}\right)^{-2}=\left(x^{5}y^{-4}\right)^{-2}\\\\=x^{-10}y^{8}=\dfrac{y^8}{x^{10}}](https://tex.z-dn.net/?f=%5Cleft%28%5Cdfrac%7Bx%5E%7B-4%7Dy%7D%7Bx%5E%7B-9%7Dy%5E5%7D%5Cright%29%5E%7B-2%7D%3D%5Cleft%28x%5E%7B-4-%28-9%29%7Dy%5E%7B1-5%7D%5Cright%29%5E%7B-2%7D%3D%5Cleft%28x%5E%7B5%7Dy%5E%7B-4%7D%5Cright%29%5E%7B-2%7D%5C%5C%5C%5C%3Dx%5E%7B-10%7Dy%5E%7B8%7D%3D%5Cdfrac%7By%5E8%7D%7Bx%5E%7B10%7D%7D)
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5. In this problem, you're only asked to eliminate the one negative exponent. That is done by moving the factor to the numerator, changing the sign of the exponent.
![\dfrac{m^7n^3}{mn^{-1}}=\dfrac{m^7n^3n}{m}](https://tex.z-dn.net/?f=%5Cdfrac%7Bm%5E7n%5E3%7D%7Bmn%5E%7B-1%7D%7D%3D%5Cdfrac%7Bm%5E7n%5E3n%7D%7Bm%7D)
![\left[\begin{array}{cc|c}-1&-1&-12\\-3&2&32\end{array}\right]](https://tex.z-dn.net/?f=%5Cleft%5B%5Cbegin%7Barray%7D%7Bcc%7Cc%7D-1%26-1%26-12%5C%5C-3%262%2632%5Cend%7Barray%7D%5Cright%5D)
Multiply through row 1 by -1:
![\left[\begin{array}{cc|c}1&1&12\\-3&2&32\end{array}\right]](https://tex.z-dn.net/?f=%5Cleft%5B%5Cbegin%7Barray%7D%7Bcc%7Cc%7D1%261%2612%5C%5C-3%262%2632%5Cend%7Barray%7D%5Cright%5D)
Add 3(row 1) to row 3:
![\left[\begin{array}{cc|c}1&1&12\\0&5&68\end{array}\right]](https://tex.z-dn.net/?f=%5Cleft%5B%5Cbegin%7Barray%7D%7Bcc%7Cc%7D1%261%2612%5C%5C0%265%2668%5Cend%7Barray%7D%5Cright%5D)
Multiply through row 2 by 1/5:
![\left[\begin{array}{cc|c}1&1&12\\0&1&\frac{68}5\end{array}\right]](https://tex.z-dn.net/?f=%5Cleft%5B%5Cbegin%7Barray%7D%7Bcc%7Cc%7D1%261%2612%5C%5C0%261%26%5Cfrac%7B68%7D5%5Cend%7Barray%7D%5Cright%5D)
Add -1(row 2) to row 1:
![\left[\begin{array}{cc|c}1&0&-\frac85\\&&\\0&1&\frac{68}5\end{array}\right]](https://tex.z-dn.net/?f=%5Cleft%5B%5Cbegin%7Barray%7D%7Bcc%7Cc%7D1%260%26-%5Cfrac85%5C%5C%26%26%5C%5C0%261%26%5Cfrac%7B68%7D5%5Cend%7Barray%7D%5Cright%5D)