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iren [92.7K]
3 years ago
10

Solve the compound inequality,

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

Answer:

\large\boxed{y\in(-6,\ \infty)}

Step-by-step explanation:

(1)\\2y-2>-14\qquad\text{add 2 to both sides}\\\\2y-2+2>-14+2\\\\2y>-12\qquad\text{divide both sides by 2}\\\\\dfrac{2y}{2}>\dfrac{-12}{2}\\\\y>-6

(2)\\\\4y-4\geq12\qquad\text{add 4 to both sides}\\\\4y-4+4\geq12+4\\\\4y\geq16\qquad\text{divide both sides by 4}\\\\\dfrac{4y}{4}\geq\dfrac{16}{4}\\\\y\geq4

\text{From (1) and (2) we have:}\\\\y>-6\ or\ y\geq4\to y\in(-6,\ \infty)\ \cup\ [4,\ \infty)\Rightarrow y\in(-6,\ \infty)

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M(6,5) is the mid-point of the straight line joining A(2 , 3) to the
charle [14.2K]

Given :

M(6,5) is the mid-point of the straight line joining A(2 , 3) to the

point B.

To Find :

The coordinates of B.

Solution :

Let, coordinates of point B is ( h , k ) .

It is given that M is the mid - point of the straight line joining points A and B.

Coordinates of M is given by :

M = (\dfrac{2+h}{2},\dfrac{3+k}{2})\\\\(6,5 ) = (\dfrac{2+h}{2},\dfrac{3+k}{2})\\\\\dfrac{2+h}{2} = 6 \ , \  \dfrac{3+k}{2} = 5\\\\h = 10 \ ,\ k = 7

Therefore, coordinates of point B is ( 10 , 7 ).

7 0
2 years ago
Select the solutions to the following inequality: |x| < 7
Rasek [7]
|x| < 7
means x < 7 and x > -7

answer is -7 < x < 7
4 0
3 years ago
HELP PLEASE I honestly need help please help
eduard

9514 1404 393

Answer:

  5.  x = 160; y = 20

  6.  h = 125°; g = i = 55°

Step-by-step explanation:

Vertical angles are found on opposite sides of a point where lines cross. Each angle is formed from rays opposite those of the other angle. Vertical angles are congruent.

5. x° and 160° are vertical angles: x° = 160°

  y° and 20° are vertical angles: y° = 20°

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6. h° and 125° are vertical angles: h° = 125°

The angles g° and 125° form a "linear pair" so total 180°.

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3 years ago
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olga2289 [7]
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5 0
2 years ago
Blocks numbered 0-9 are placed in a box and a black is randomly picked the probability of picking an odd prime number is
Andrews [41]

Answer:

Step-by-step explanation:

B_n = 0, 1, 2, 3, 4, 5, 6, 7, 8, 9\\B_p = 2, 3, 5, 7\\B_{o_p} = 3, 5, 7\\

There are 3 odd primes, namely : 3, 5, 7

The total amount of blocks is 9

The odds of picking and odd prime is \frac{3}{9} \cdot 100\% = 33,(3)\%

6 0
3 years ago
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