Megan:
x to the one third power =

<span>x to the one twelfth power = </span>

<span>The quantity of x to the one third power, over x to the one twelfth power is:
</span>

<span>
Since </span>

then

Now, just subtract exponents:
1/3 - 1/12 = 4/12 - 1/12 = 3/12 = 1/4

Julie:
x times x to the second times x to the fifth = x * x² * x⁵
<span>The thirty second root of the quantity of x times x to the second times x to the fifth is
</span>
![\sqrt[32]{x* x^{2} * x^{5} }](https://tex.z-dn.net/?f=%20%5Csqrt%5B32%5D%7Bx%2A%20x%5E%7B2%7D%20%2A%20x%5E%7B5%7D%20%7D%20)
<span>
Since </span>

Then
![\sqrt[32]{x* x^{2} * x^{5} }= \sqrt[32]{ x^{1+2+5} } =\sqrt[32]{ x^{8} }](https://tex.z-dn.net/?f=%5Csqrt%5B32%5D%7Bx%2A%20x%5E%7B2%7D%20%2A%20x%5E%7B5%7D%20%7D%3D%20%5Csqrt%5B32%5D%7B%20x%5E%7B1%2B2%2B5%7D%20%7D%20%3D%5Csqrt%5B32%5D%7B%20x%5E%7B8%7D%20%7D)
Since
![\sqrt[n]{x^{m}} = x^{m/n} }](https://tex.z-dn.net/?f=%20%5Csqrt%5Bn%5D%7Bx%5E%7Bm%7D%7D%20%3D%20x%5E%7Bm%2Fn%7D%20%7D%20)
Then
![\sqrt[32]{ x^{8} }= x^{8/32} = x^{1/4}](https://tex.z-dn.net/?f=%5Csqrt%5B32%5D%7B%20x%5E%7B8%7D%20%7D%3D%20x%5E%7B8%2F32%7D%20%3D%20x%5E%7B1%2F4%7D%20)
Since both Megan and Julie got the same result, it can be concluded that their expressions are equivalent.
To find the residual I would subtract the predicted value from the measured value so for x-value 1 the residual would be 2-2.6 = -0.6
(y^2 + 7y +12) / (y^2+8y +15)
factor both equations:
(y+3)(y+4) / (y+3) (y+5)
cancel out common factors to get:
y+4 / y+5
Answer:
Question #1
m∠4 + m∠7 = 180° - Given.
∠4 and ∠7 are supplementary angles - Definition of supplementary angles.
∠7 and ∠2 form a linear pair - Definition of linear pair.
∠7 and ∠2 are supplementary angles - Definition of linear pair.
m∠7 + m∠2 = 180° - Definition of supplementary angles.
m∠2 = m∠4 - Substitution property.
c ║ d - Converse of corresponding angles postulate.
Question #2
m∠3 = m∠8 - Given.
∠8 and ∠6 form a linear pair - Definition of linear pair.
∠8 and ∠6 are supplementary angles - Definition of linear pair.
m∠8 + m∠6 = 180° - Definition of supplementary angles.
∠3 and ∠6 are supplementary angles - Substitution property.
m∠3 + m∠6 = 180° - Definition of supplementary angles.
Question #3
p ║ q - Given.
∠1 ≅ ∠5 - Given.
∠1 ≅ ∠2 - Alternate interior angle theorem.
∠2 ≅ ∠5 - Substitution property.
~Hope this helps!~
Answer:
3. the mode is 5 and 7
4. she tested 5
5. clare has tested 3 friends
6. 12
5 is the median for both on number 7
Step-by-step explanation: