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2 years ago

Write the following as an inequality. w is less than 8 and greater than or equal to -3

Mathematics

1 answer:

ser-zykov [4K]2 years ago

5 0

8>w
w>/= -3
Meaning the inequality is 8>w>/= -3

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Is anyone able to figure this out, I can't do this

katrin [286]

Answer:

C. √2 - 1

Step-by-step explanation:

If we draw a square from the center of the large circle to the center of one of the small circles, we can see that the sides of the square are equal to the radius of the small circle (see attached diagram)

Let r = the radius of the small circle

Using Pythagoras' Theorem $a^2+b^2=c^2$

(where a and b are the legs, and c is the hypotenuse, of a right triangle)

to find the diagonal of the square:

$\implies r^2 + r^2 = c^2$

$\implies 2r^2 = c^2$

$\implies c=\sqrt{2r^2}$

So the diagonal of the square = $\sqrt{2r^2}$

We are told that the radius of the large circle is 1:

⇒ Diagonal of square + r = 1

$\implies \sqrt{2r^2}+r=1$

$\implies \sqrt{2r^2}=1-r$

$\implies 2r^2=(1-r)^2$

$\implies 2r^2=1-2r+r^2$

$\implies r^2+2r-1=0$

Using the quadratic formula to calculate r:

$\implies r=\dfrac{-b\pm\sqrt{b^2-4ac}}{2a}$

$\implies r=\dfrac{-2\pm\sqrt{2^2-4(1)(-1)}}{2(1)}$

$\implies r=\dfrac{-2\pm\sqrt{8}}{2}$

$\implies r=-1\pm\sqrt{2}$

As distance is positive, $r=-1+\sqrt{2}=\sqrt{2}-1$ only

5 0

2 years ago

Read 2 more answers

Find the measure of each angle indicated 12,13,14

sp2606 [1]

Answer:

Step-by-step explanation:

12. 15 (3x5x1)

13. 8 (4x2x1)

14. 18 (6x3x1)

3 0

2 years ago

One number is 12 more than another number. If one half of the smaller number equals one third of the larger number, what is the

NikAS [45]

Answer:

x=24

y=36

Step-by-step explanation:

x=smaller number

y=larger number

x+12=y x/2=y/3

x/2=(x+12)/3

cross multiply and distribute

3x=2x+24

x=24

24+12=y

y=36

5 0

3 years ago

Quiz Instructions

bazaltina [42]

I believe it would be dilated by 3/4

If you think of a rectangle, let’s say it is 8 by 4, the perimeter of this rectangle would be 24.

Now if you dilate the side values, you get 6 by 3 and the perimeter equals 18

So you then get 18/24 which is equal to 3/4

Hope this is right and makes sense! Have a good day!

7 0

3 years ago

There are nine balls. One is slightly lighter than the rest; the difference is small enough that you can't tell just by picking

icang [17]

<span>You will need to weight those balls only twice. You weight 6 balls, 3 on one side of weight and 3 on another, and other 3 balls you have are in your hand.

Check picture bellow</span>

8 0

3 years ago

Read 2 more answers

Write the following as an inequality. w is less than 8 and greater than or equal to -3​

Write the following as an inequality. w is less than 8 and greater than or equal to -3