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Dafna11 [192]
3 years ago
8

Match the solution set of each of the following inequalities with its graph.

Mathematics
1 answer:
8090 [49]3 years ago
7 0

Answer:

Step-by-step explanation:

From the picture attached,

            Number line                                                             Inequality

1). Arrow starting with a solid point from x = -2                   x ≤ -2

directing towards negative numbers of x                                                         2).Arrow starting with a hollow circle from x = 2                 x >2  

directing towards positive numbers of x

3). Arrow starting with a hollow circle from x = 2                x < 2 ⇒ x - 2 < 0  

directing towards negative numbers of x

4). Arrow starting with a solid circle from x = 2                   x ≥ 2 Or 2 ≤ x

directing towards positive numbers of x

5). Arrow starting with a hollow circle from x = -2                   x > -2

directing towards positive numbers of x

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What is the image of (1,0) after a counterclockwise rotation of 60 degrees?
Anestetic [448]

Answer:

\vec s = \left(\frac{1}{2},\frac{\sqrt{3}}{2}  \right)

Step-by-step explanation:

The coordinate has the following polar form:

\vec r = (1, 0^{\circ})

The image of the coordinate rotated counterclockwise 60° is:

\vec s = (1, 60^{\circ})

Its equivalent form in rectangular coordinates is:

\vec s = (1\cdot \cos 60^{\circ}, 1 \cdot \sin 60^{\circ})

\vec s = \left(\frac{1}{2},\frac{\sqrt{3}}{2}  \right)

3 0
3 years ago
Simplify the expression .
katovenus [111]

10xy^2(3x^3-5x)-2x^2y(6y^3+3y)=\\\\=30x^4y^2-50x^2y^2-12x^3y^4-6x^2y^2=\\\\=\boxed{30x^4y^2-12x^3y^4-56x^2y^2}

3 0
3 years ago
A designer builds a model of a sports car. The finished model is exactly the same shape as the original, but smaller. The scale
lesantik [10]

Answer:

Ratio = 2 : 15

Step-by-step explanation:

Given

k = 2 : 15 --- scale factor

Required [missing from the question]:

The ratio of width of the model to the original

From the question, we understand that the scale factor is: 2 : 15

The ratio of the width of the model to the original equals the given scale factor i.e.

Ratio = 2 : 15

8 0
3 years ago
Which of the following best shows two elements combining to form a compound!? Explain...
ioda

Answer:

C because elements are form by atoms and when we study about atom we draw atom like circle

so, that's why I think C is correct

 

Step-by-step explanation:

5 0
3 years ago
Using properties of sets show that : a) A ∩ (A’ U B) = A ∩ B b) A ∩ (A U B )’ = Ф
asambeis [7]

Answer:

a) From A ∩ A' = ∅, we have;

A ∩ (A' ∪ B) = A ∩ B

b) From A ∩ (A' ∩ B') = (A ∩ A') ∩ B' and A ∩ A' = ∅, we have;

A ∩ (A ∪ B)' = ∅

Step-by-step explanation:

a) By distributive law of sets, we have;

A ∩ (B ∪ C) = (A ∩ B) ∪ (A ∩ C)

From the complementary law of sets, we have;

A ∩ A' = ∅

Therefore, for A ∩ (A' ∪ B) = A ∩ B, we have

A ∩ (A' ∪ B) = (A ∩ A') ∪ (A ∩ B) (distributive law of sets)

A ∩ A' = ∅ (complementary law of sets)

Therefore;

(A ∩ A') ∪ (A ∩ B) = ∅ ∪ (A ∩ B)  = (A ∩ B) (Addition to zero identity property)

∴  A ∩ (A' ∪ B) = A ∩ B

b) By De Morgan's law

(A ∪ B)' = A' ∩ B'

Therefore, A ∩ (A ∪ B)' = A ∩ (A' ∩ B')

By associative law of sets, we have;

A ∩ (A' ∩ B') = (A ∩ A') ∩ B'

A ∩ A' = ∅ (complementary law of sets)

Therefore, (A ∩ A') ∩ B' = ∅  ∩ B' = ∅

Which gives;

A ∩ (A ∪ B)' = ∅.

4 0
3 years ago
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