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OleMash [197]
3 years ago
9

The sum of three times a number and -4 is at least twice the number plus 8

Mathematics
2 answers:
kicyunya [14]3 years ago
8 0

Answer:

x<=12

Step-by-step explanation:

3x+(-4)<=2x+8

3x-4<=2x+8

3x-2x-4<=8

x-4<=8

x<=8+4

x<=12

kenny6666 [7]3 years ago
7 0

Answer:

12 ≤ x

Step-by-step explanation:

3x-4 ≥ 2x+8

3x-3x-4 ≥ 2x-3x+8

-4-8 ≥ -1x+8-8

-12 ≥ -1x

You divide -1 on both sides and get...

12 ≤ x

Because you have to switch the sign around. I hope this helps!!

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Change each of the following points from rectangular coordinates to spherical coordinates and to cylindrical coordinates.
FromTheMoon [43]

Answer and Step-by-step explanation: Spherical coordinate describes a location of a point in space: one distance (ρ) and two angles (Ф,θ).To transform cartesian coordinates into spherical coordinates:

\rho = \sqrt{x^{2}+y^{2}+z^{2}}

\phi = cos^{-1}\frac{z}{\rho}

For angle θ:

  • If x > 0 and y > 0: \theta = tan^{-1}\frac{y}{x};
  • If x < 0: \theta = \pi + tan^{-1}\frac{y}{x};
  • If x > 0 and y < 0: \theta = 2\pi + tan^{-1}\frac{y}{x};

Calculating:

a) (4,2,-4)

\rho = \sqrt{4^{2}+2^{2}+(-4)^{2}} = 6

\phi = cos^{-1}(\frac{-4}{6})

\phi = cos^{-1}(\frac{-2}{3})

For θ, choose 1st option:

\theta = tan^{-1}(\frac{2}{4})

\theta = tan^{-1}(\frac{1}{2})

b) (0,8,15)

\rho = \sqrt{0^{2}+8^{2}+(15)^{2}} = 17

\phi = cos^{-1}(\frac{15}{17})

\theta = tan^{-1}\frac{y}{x}

The angle θ gives a tangent that doesn't exist. Analysing table of sine, cosine and tangent: θ = \frac{\pi}{2}

c) (√2,1,1)

\rho = \sqrt{(\sqrt{2} )^{2}+1^{2}+1^{2}} = 2

\phi = cos^{-1}(\frac{1}{2})

\phi = \frac{\pi}{3}

\theta = tan^{-1}\frac{1}{\sqrt{2} }

d) (−2√3,−2,3)

\rho = \sqrt{(-2\sqrt{3} )^{2}+(-2)^{2}+3^{2}} = 5

\phi = cos^{-1}(\frac{3}{5})

Since x < 0, use 2nd option:

\theta = \pi + tan^{-1}\frac{1}{\sqrt{3} }

\theta = \pi + \frac{\pi}{6}

\theta = \frac{7\pi}{6}

Cilindrical coordinate describes a 3 dimension space: 2 distances (r and z) and 1 angle (θ). To express cartesian coordinates into cilindrical:

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

Angle θ is the same as spherical coordinate;

z = z

Calculating:

a) (4,2,-4)

r=\sqrt{4^{2}+2^{2}} = \sqrt{20}

\theta = tan^{-1}\frac{1}{2}

z = -4

b) (0, 8, 15)

r=\sqrt{0^{2}+8^{2}} = 8

\theta = \frac{\pi}{2}

z = 15

c) (√2,1,1)

r=\sqrt{(\sqrt{2} )^{2}+1^{2}} = \sqrt{3}

\theta = \frac{\pi}{3}

z = 1

d) (−2√3,−2,3)

r=\sqrt{(-2\sqrt{3} )^{2}+(-2)^{2}} = 4

\theta = \frac{7\pi}{6}

z = 3

5 0
3 years ago
write a simplified polynomial expression in the standard form to represent the area of the rectangle below x-4 5x+2
Ann [662]

The area of the rectangle is 5x^{2} -18x-8

Explanation:

One side of the rectangle is x-4

The another side of the rectangle is 5x+2

The formula to find the area of the rectangle is length × width

Area = length × width

Substituting the values, we have,

\begin{aligned}\text { Area } &=(x-4)(5 x+2) \\&=5 x^{2}+2 x-20 x-8 \\&=5 x^{2}-18 x-8\end{aligned}

Thus, the area of the rectangle is 5x^{2} -18x-8

3 0
3 years ago
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The answer is 4x^3 + 4x + C

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The answer is 4. 2x plus 7 is equal to 15. First you subtract 7 from both sides then divide by 2 to get the answer 4. Hope this helps!
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Copy and write the missing factor<br> https://ibb.co/gAKUJA
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I think that the answer would be 5/5
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