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Elena-2011 [213]
3 years ago
9

The solution set for the inequality x + 4 ≤ 1/2 (x - 3) includes -11 as an element.

Mathematics
1 answer:
Sindrei [870]3 years ago
6 0

Answer:

<h2>x ≤ -11, Yes. The solution set include -11.</h2>

Step-by-step explanation:

x+4\leq\dfrac{1}{2}(x-3)\qquad\text{multiply both sides by 2}\\\\2x+8\leq1(x-3)\\\\2x+8\leq x-3\qquad\text{subtract 8 from both sides}\\\\2x\leq x-11\qquad\text{subtract x from both sides}\\\\\boxed{x\leq-11}

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Write the equation of the circle centered at ( 4 , − 5 ) with radius 18.
Free_Kalibri [48]

Answer:

(x-4)^2 + (y+5)^2 = 324

Step-by-step explanation:

The equation of a circle is given by the equation (x-h)^2 + (y-k)^2 = r^2, where (h,k) is the center point of the circle.

Therefore, since the center point of the circle and the radius is given, we can just plug the numbers into the formula:

(x-4)^2 + (y+5)^2 = 18^2

<u>(x-4)^2 + (y+5)^2 = 324</u>

3 0
3 years ago
120 is the same as 394 fewer than Z
SpyIntel [72]

Answer:

z=514

Step-by-step explanation:

120=z-394

+394. +394

514=z

Hope this helps

8 0
3 years ago
Jenny rides her bike one mile to school every day. She always stops at Claire’s house on her way. Claire lives ¼ of a mile from
Snezhnost [94]

Answer:

to get our answer, we multiply the two fractions together. 6/8× 3/5= 3/5 or 0.6

hope this helps! mark me brailyest please :D

5 0
3 years ago
Read 2 more answers
Erica can paint her room 5 hours .If she had her friend Rachel help her , they can paint the room together in 3 hours .How long
LUCKY_DIMON [66]

Answer:

7 hours 30min

Step-by-step explanation:

Step one :

Given data

We are told that Erica can paint 1 room in 5hours

Her work rate is 1/5 room per hour

And also with the assistance of her friend they can paint 1 room in 3 hours

Hence their combined work rate is 1/3 room per hour

Step two

The combined work expression is

1/A+1/B=1/T

Where A=Erica's work rate

B=Rachael's work rate

T=combined work

1/5+1/B=1/3

1/B=1/3-1/5

1/B=5-3/15

1/B=2/15

B=15/2

B=7.5 hours

It will take Rachel 7 hours 30min to paint the room

4 0
3 years ago
The height, h, in feet of a ball above the ground is given by h = −16t2 + 64t + 80, where t is the time in seconds. How long doe
Gwar [14]

Answer:

t = 5 seconds

Step-by-step explanation:

It is given that, the height h, in feet of a ball above the ground is given by :

h=-16t^2+64t+80

Where t is in seconds

We need to find how long does it take the ball to hit the ground? When it hits the ground, its height will be equal to 0. So,

-16t^2+64t+80=0\\\\t=\dfrac{-64\pm \sqrt{(64)^2-4\times (-16)(80)} }{2\times -16}\\\\t=\dfrac{-64+ \sqrt{(64)^2-4\times (-16)(80)} }{2\times -16},\dfrac{-64-\sqrt{(64)^2-4\times (-16)(80)} }{2\times -16}\\\\t=-1\ s\ \text{and}\ t=5\ s

Neglecting negative time.

It means ball will take 5 seconds to hit the ground.

3 0
3 years ago
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