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1 year ago

Are both 7 and -½ integers? why or why not?

Mathematics

2 answers:

Setler [38]1 year ago

8 0

No because integers are whole number and fraction that equal a decimal aren’t

Tems11 [23]1 year ago

4 0

Answer:

No. (-1/2) is not an integer

Integers involve all the no. +ve and -ve. which can be written without fraction. ie whole no. are counted as integers.

(-1/2) is a fraction

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2 years ago

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the actual distance between two cities is 70 miles. A map uses a scale in which 1 inch represents 14 miles. What is the distance

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2 years ago

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

Solve <br><br> (X^2+2xy+y^2)(x+1)

erik [133]

Answer:

x = -1 or x = -y

Step-by-step explanation:

Solve for x:

(x + 1) (x^2 + 2 x y + y^2) = 0

Split into two equations:

x + 1 = 0 or x^2 + 2 x y + y^2 = 0

Subtract 1 from both sides:

x = -1 or x^2 + 2 x y + y^2 = 0

Write the left hand side as a square:

x = -1 or (x + y)^2 = 0

Take the square root of both sides:

x = -1 or x + y = 0

Subtract y from both sides:

Answer: x = -1 or x = -y

7 0

3 years ago

Are both 7 and -½ integers? why or why not?​

Are both 7 and -½ integers? why or why not?