Circle A has center of (2,8), and a radius of 2 and circle B has a center of (5,

insens350 [35]

Answer:

Step-by-step explanation:

$2x > 30+\frac{5}{4x} \\2x-\frac{5}{4x} > 30\\\frac{8x^2-5}{4x} > 30\\case~1\\if~x > 0\\8x^2-5 > 120x\\8x^2-120x > 5\\x^2-15x > \frac{5}{8} \\adding~(-\frac{15}{2} )^2~to~both~sides\\(x-\frac{15}{2} )^2 > \frac{5}{8}+\frac{225}{4} \\(x-\frac{15}{2} )^2 > \frac{455}{8} \\x-\frac{15}{2} < -\sqrt{\frac{455}{8} } \\x < \frac{15}{2}-\sqrt{\frac{455}{8} } \\or~x < 0\\rejected~as~x > 0$

$x-\frac{15}{2} > \sqrt{\frac{455}{8} } \\x > \frac{15}{2} +\sqrt{\frac{455}{8} }$

case~2

$if~x < 0\\8x^2-5 < 120x\\8x^2-120x < 5\\x^2-15x < \frac{5}{8} \\adding~(-\frac{15}{2} )^2\\(x-\frac{15}{2} )^2 < \frac{5}{8} +(-\frac{15}{2} )^2\\|x-\frac{15}{2} | < \frac{5+450}{8} \\-\sqrt{\frac{455}{8} } < x-\frac{15}{2} < \sqrt{\frac{455}{8} } \\\frac{15}{2} -\sqrt{\frac{455}{8} } < x < \frac{15}{2} +\sqrt{\frac{455}{8} } \\but~x < 0\\7.5-\sqrt{\frac{455}{8} } < x < 0$

8 0

2 years ago

Charles drew a plan for a rectangular piece of

dalvyx [7]

The fourth coordinate of rectangular piece of material is (2.8 , -2.7)

According to the question,

Charles drew a plan for a rectangular piece of material that he will use for a blanket. Three of the vertices are (-1.4, -2.7), (-1.4,3.7), and (2.8,3.7).

As we know , the opposite sides of rectangle are equal

If we locate these coordinates in our graph and join them

Length of rectangle will be = 2.8+1.4 = 4.2cm

Breadth of rectangle will be = 3.7 + 2.7 = 6.4cm

So, the fourth coordinate should lie 6.4cm far from (2.8,3.7)

Subtracting 6.4 from y-axis,

Fourth coordinate = 3.7 - 6.4

= -2.7

Therefore , The fourth side of rectangle = (2.8 , -2.7)

To know more about Rectangle here

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4 0

1 year ago

Determine the constant of variation for the direct variation given. Type a numerical answer in the space provided.

Andreyy89

Answer:

B. 4

Step-by-step explanation:

Determine the constant of variation for the direct variation given.

(0, 0), (3, 12), (9, 36)

A. 3

B. 4

C.12

Direct variation is given by:

y = kx

Where,

k = constant of variation

(3, 12)

x = 3; y = 12

y = kx

12 = k*3

12 = 3k

k = 12 / 3

k = 4

(9, 36)

x = 9; y = 36

y = kx

36 = k * 9

36 = 9k

k = 36 / 9

= 4

k = 4

Constant of the variation = 4

5 0

3 years ago

Is 7 a factor of 56 or is 8 a factor of 56?

adelina 88 [10]

8 and 7 are both a factor of 56.

8 0

3 years ago

Read 2 more answers

Four times a difference of 17 and a number is 84.

hichkok12 [17]

4×17-x=84
68-x=84
-x=16
x=-16

5 0

3 years ago