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2 years ago

How can distributive property be used to solve 7 x 391

Mathematics

1 answer:

Advocard [28]2 years ago

7 0

Answer:

7x ³⁹¹

Step-by-step explanation:

1: "x3" was replaced by "x^3".

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Let T:ℝ2→ℝ2 be the linear transformation that first rotates points clockwise through 45∘ (????/4 radians) and then reflects poin

Alisiya [41]

Answer:

$T = \left[\begin{array}{ccc}-\frac{1}{\sqrt{2} } &\frac{1}{\sqrt{2} }\\\frac{1}{\sqrt{2} }&\frac{1}{\sqrt{2} }\end{array}\right]$

Step-by-step explanation:

Let General Transformation matrix be denoted as T

Step 1: Clockwise rotation of 45 degrees

General counterclockwise rotation matrix in 2-dimension is given as

$R(\theta)=\left[\begin{array}{ccc}cos\theta & - sin\theta\\sin\theta&cos\theta\\\end{array}\right]$

For clockwise rotation we need to insert θ as negative in the above matrix. Therefore, the resulting matrix is

$R(-\theta)=\left[\begin{array}{ccc}cos\theta & sin\theta\\-sin\theta&cos\theta\\\end{array}\right]$

as sin(-θ) = -sin (θ) and cos(-θ) = cos (θ)

For 45 degrees

$sin(45) = \frac{1}{\sqrt{2} }$ and $cos(45) = \frac{1}{\sqrt{2} }$

$R(-45)=\left[\begin{array}{ccc}\frac{1}{\sqrt{2} } & \frac{1}{\sqrt{2} }\\-\frac{1}{\sqrt{2} }&\frac{1}{\sqrt{2} }\\\end{array}\right]$

Step 2: Reflection through line y = x

This type of reflection maps (x,y)→(y,x)

Therefore the general matrix is

$R(x,y)=\left[\begin{array}{ccc}0&1\\1&0\end{array}\right]$

Step 3: General Transformation Matrix

T = R(x,y) R(-θ)

$T=\left[\begin{array}{ccc}0&1\\1&0\end{array}\right] \left[\begin{array}{ccc}\frac{1}{\sqrt{2} } & \frac{1}{\sqrt{2} }\\-\frac{1}{\sqrt{2} }&\frac{1}{\sqrt{2} }\\\end{array}\right]$

$T = \left[\begin{array}{ccc}-\frac{1}{\sqrt{2} } &\frac{1}{\sqrt{2} }\\\frac{1}{\sqrt{2} }&\frac{1}{\sqrt{2} }\end{array}\right]$

3 0

2 years ago

I need help simplifying this

faust18 [17]

Answer:

n^2

Step-by-step explanation:

cancel the common factor between n^7 and n^2

3 0

2 years ago

그 기 . 1 1 키 Which normal distribution has the greatest standard deviation? O O 80 88 104 112

Scorpion4ik [409]

Answer:

그 기 = That Flag

키 = Key

I think it is 112.

Step-by-step explanation:

4 0

3 years ago

carmen works at a pet store. To feed 8 cats, she empties four 6-ounce cans of cat food into a large bowl.Carmen divides the food

Y_Kistochka [10]

6 x 4 = 24
each cat will get 3 ounces each :)

4 0

2 years ago

Read 2 more answers

The terminal side of an angle in standard position passes through P(-3,-4). What is the value of tan e?

exis [7]

Answer:

$Tan \theta= \dfrac{4}{3}$

Step-by-step explanation:

Given:

The terminal side of an angle in standard position passes through P(-3,-4).

Point P is in Quadrant III
In Quadrant |||, $Tan \theta$ is positive.

$Tan \theta= \dfrac{Opposite}{Adjacent}\\Tan \theta= \dfrac{y}{x}\\Tan \theta= \dfrac{-4}{-3}\\Tan \theta= \dfrac{4}{3}$

8 0

3 years ago