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4 years ago

Solve the inequality 2x - 3 < x 2 ≤ 3x 5. show your work

2 answers:

8 0

2x − 3 < x + 2 
∴ x − 3 < 2 
∴ x < 5 

x + 2 ≤ 3x + 5 
∴ 2 ≤ 2x + 5 
∴ -3 ≤ 2x 
∴ -3/2 ≤ x 

-3/2 ≤ x < 5

Alexxx [7]4 years ago

3 0

Answer:

-3/2 ≤ x < 5

Step-by-step explanation:

2x - 3 < x + 2 ≤ 3x+5

Solve the inequality separately

2x-3 <x+2 and x+2≤ 3x+5

LEts solve one by one

2x-3 <x+2

Subtract x from both sides

x -3 < 2

add 3 on both sides

x< 5

x+2≤ 3x+5

Subtract 3x from both sides

-2x + 2 ≤ 5

Subtract 2 from both sides

-2x ≤ 3

Divide both sides by -2

x ≥ -3/2

we got x>= -3/2 and x<5

so x lies between -3/2 and 5

-3/2 ≤ x < 5

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Two semicircles are attached to the sides of a rectangle as shown.

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Answer:

$157\ in^{2}$

Step-by-step explanation:

we know that

The area of the figure is equal to the area of rectangle plus the area of two semicircles

The area of rectangle is equal to

$A=14*5=70\ in^{2}$

The area of the small semicircle is equal to

$A=\pi r^{2} /2$

$r=5/2=2.5\ in$ -----> radius is half the diameter

substitute

$A=(3.14)(2.5^{2})/2=9.8125 in^{2}$

The area of the larger semicircle is equal to

$A=\pi r^{2} /2$

$r=14/2=7\ in$ -----> radius is half the diameter

substitute

$A=(3.14)(7^{2})/2=76.93\ in^{2}$

The area of the figure is equal to

$70+9.8125+76.93=156.7425=157\ in^{2}$

8 0

3 years ago

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Flura [38]

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3 years ago

If the fraction 414/x-10 is equivalent to -23 , find the value of x. Show your work. Use reasoning to find x.

NemiM [27]

Answer:

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Step-by-step explanation:

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svlad2 [7]

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I hope this will help you

(-:

Step-by-step explanation:

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3 years ago