Answer:
1. 181.59 is her net pay and she worked 25.25 hours.
Step-by-step explanation:
Answer:
The set of polynomial is Linearly Independent.
Step-by-step explanation:
Given - {f(x) =7 + x, g(x) = 7 +x^2, h(x)=7 - x + x^2} in P^2
To find - Test the set of polynomials for linear independence.
Definition used -
A set of n vectors of length n is linearly independent if the matrix with these vectors as columns has a non-zero determinant.
The set is dependent if the determinant is zero.
Solution -
Given that,
f(x) =7 + x,
g(x) = 7 +x^2,
h(x)=7 - x + x^2
Now,
We can also write them as
f(x) = 7 + 1.x + 0.x²
g(x) = 7 + 0.x + 1.x²
h(x) = 7 - 1.x + 1.x²
Now,
The coefficient matrix becomes
A = ![\left[\begin{array}{ccc}7&1&0\\7&0&1\\7&-1&1\end{array}\right]](https://tex.z-dn.net/?f=%5Cleft%5B%5Cbegin%7Barray%7D%7Bccc%7D7%261%260%5C%5C7%260%261%5C%5C7%26-1%261%5Cend%7Barray%7D%5Cright%5D)
Now,
Det(A) = 7(0 + 1) - 1(7 - 7) + 0
= 7(1) - 1(0)
= 7 - 0 = 7
⇒Det(A) = 7 ≠ 0
As the determinant is non- zero ,
So, The set of polynomial is Linearly Independent.
Answer:
![15 \sqrt[3]{2}](https://tex.z-dn.net/?f=15%20%5Csqrt%5B3%5D%7B2%7D%20)
Step-by-step explanation:
![{(27 \times 250)}^{ \frac{1}{3} } = {(27 \times 125 \times 2)}^{ \frac{1}{3} } \\ = {27}^{ \frac{1}{3} } \times {125}^{ \frac{1}{3} } \times {2}^{ \frac{1}{3} } \\ = \sqrt[ 3]{27} \times \sqrt[3]{125} \times \sqrt[3]{2} \\ = \sqrt[3]{ {3}^{3} } \times \sqrt[3]{ {5}^{3} } \times \sqrt[3]{2} \\ = 3 \times 5 \times \sqrt[3]{2} \\ = 15 \sqrt[3]{2}](https://tex.z-dn.net/?f=%20%7B%2827%20%5Ctimes%20250%29%7D%5E%7B%20%5Cfrac%7B1%7D%7B3%7D%20%7D%20%20%3D%20%20%7B%2827%20%5Ctimes%20125%20%5Ctimes%202%29%7D%5E%7B%20%5Cfrac%7B1%7D%7B3%7D%20%7D%20%20%5C%5C%20%20%3D%20%20%7B27%7D%5E%7B%20%5Cfrac%7B1%7D%7B3%7D%20%7D%20%20%5Ctimes%20%20%7B125%7D%5E%7B%20%5Cfrac%7B1%7D%7B3%7D%20%7D%20%20%5Ctimes%20%20%7B2%7D%5E%7B%20%5Cfrac%7B1%7D%7B3%7D%20%7D%20%20%5C%5C%20%20%3D%20%20%5Csqrt%5B%203%5D%7B27%7D%20%20%5Ctimes%20%20%5Csqrt%5B3%5D%7B125%7D%20%20%5Ctimes%20%20%5Csqrt%5B3%5D%7B2%7D%20%20%5C%5C%20%20%3D%20%20%5Csqrt%5B3%5D%7B%20%7B3%7D%5E%7B3%7D%20%7D%20%20%5Ctimes%20%20%5Csqrt%5B3%5D%7B%20%7B5%7D%5E%7B3%7D%20%7D%20%20%5Ctimes%20%20%5Csqrt%5B3%5D%7B2%7D%20%20%5C%5C%20%20%3D%203%20%5Ctimes%205%20%5Ctimes%20%20%5Csqrt%5B3%5D%7B2%7D%20%20%5C%5C%20%20%3D%2015%20%5Csqrt%5B3%5D%7B2%7D%20)
Answer:
The actual dimensions of the kitchen are
by 
Step-by-step explanation:
step 1
Find the scale of the drawing
To find the scale , remember that is equal to the ratio of the corresponding dimension in the drawing divided by the corresponding actual dimension
so

step 2
To find the actual dimensions of the kitchen, divide the dimension in the drawing by the scale
so

