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Ainat [17]
3 years ago
5

Question below

Mathematics
1 answer:
jekas [21]3 years ago
7 0

(r+s)(x)=r(x)+s(x)\\\\(r\cdot s)(x)=r(x)\cdot s(x)\\\\(r-s)(x)=r(x)-s(x)\\\\r(x)=x-4,\ s(x)=2x+2.\ \text{Substitute:}\\\\(r+s)(x)=x-4+2x+2=(x+2x)+(-4+2)=\boxed{3x-2}\\\\(r\cdot s)(x)=(x-4)(2x+2)=(x)(2x)+(x)(2)+(-4)(2x)+(-4)(2)\\\\=2x^2+2x-8x-8=\boxed{2x^2-6x-8}\\\\(r-s)(x)=x-4-(2x+2)=x-4-2x-2=(x-2x)+(-4-2)\\\\=\boxed{-x-6}

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James has 14{,}500\text { g}14,500 g14, comma, 500, start a text, space, g, end text of sand in his sandbox. He brings home anot
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Question:

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Answer:

The quantity of sandbox James has is 21.9kg

Step-by-step explanation:

Given

Initial quantity of sandbox = 14,500 g

Additional quantity = 7,400 g

Required

Total quantity of sandbox in kg

Tp get the total quantity of sandbox, we simply add in the initial and additional quantity of sandbox together;

This is represented mathematically as follows;

Total = Initial Quantity + Additional Quantity

Total = 14,500 g + 7,400 g

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Two points in the Cartesian plane are A(2.00 m, −4.00 m) and B(−3.00 m, 3.00 m). Find the distance between them and their polar
Brrunno [24]

The distance between the two points is d=8.6m

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The polar coordinate of B is \left(4.24,135\right)

Explanation:

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The distance between two points is given by,

d=\sqrt{(2+3)^{2}+(-4-3)^{2}}\\d=\sqrt{(5)^{2}+(-7)^{2}}\\d=\sqrt{25+49}\\d=8.6

Thus, the distance between the two points is d=8.6m

The polar coordinates of A can be written as (Distance, tan^{-1} \frac{y}{x} )

Distance = \sqrt{x^{2} +y^{2} }

Substituting A(2,-4), we get,

Distance = \sqrt{2^{2} +(-4)^{2} }=\sqrt{4+16 }=4.47

tan^{-1} \frac{y}{x} =tan^{-1} \frac{-4}{2}=-63.43

To make the angle positive, let us add 360,

\theta=360-63.43=296.57

The polar coordinate of A is \left(4.47,296.57\right)

Similarly, The polar coordinate of B can be written as (Distance, tan^{-1} \frac{y}{x} )

Distance = \sqrt{x^{2} +y^{2} }

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To make the angle positive, let us add 360,

\theta=180-45=135^{\circ}

The polar coordinate of B is \left(4.24,135\right)

5 0
3 years ago
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