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3 years ago

Please answer this question step by step with formula.

Mathematics

1 answer:

Agata [3.3K]3 years ago

5 0

Answer:

Net price = $191.25

Discount Price = $33.75

Step-by-step explanation:

Cost of one pen = $0.50

Cost of 200 pen = 200 × 0.50 = $100

Cost of one pad =$0.70

Cost of 150 pads = 150 × 0.70 = $105

Cost of one pencil = $0.20

Cost of 100 pencils = $20

Total cost of the order = 100 + 105 + 20 = $225

Discount % = 15% of 225

Discount price = ( 15% × 225) = $33.75

Total amount after discount = 225 - 33.75 = $191.25

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If T: (x, y) → (x + 6, y + 4), then T-1: (x,y) → _____.

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T is a linear transformation from R²→R² with basis {(1,0),(0,1)}
T: (x,y)→(x+6,y+4)

A function from one vector space to another that preserves the underlying (linear) structure of each vector space is called a linear transformation.

Then the vector (1,0) goes to (1+6,4)=(7,4)=7(1,0)+4(0,1)

and the vector (0,1) goes to (6,1+4)=(6,5)=6(1,0)+5(0,1)

So, the matrix of the transformation is

$\left[\begin{array}{ccc}7&6\\4&5\end{array}\right]$

The inverse of the matrix is

$\left[\begin{array}{ccc}\frac{5}{11}&\frac{-6}{11}\\ \\\frac{-4}{11}&\frac{7}{11}\end{array}\right]$

So, the Inverse Transformation is given by

$T^{-1}(x,y)=\left[\begin{array}{ccc}\frac{5}{11}&\frac{-6}{11}\\ \\\frac{-4}{11}&\frac{7}{11}\end{array}\right]\left[\begin{array}{ccc}x\\y\end{array}\right] =(\frac{5x-6y}{11}, \frac{-4x+7y}{11})$