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2 years ago

Circle O has a center at (-2, -2) and a diameter of 10 units. What point lies on circle O?

Mathematics

1 answer:

Sophie [7]2 years ago

8 0

The point r(-6,-5) lies on the circle.

Explanation

Given that the center of the circle=(-2,-2)

diameter=10 units

we have to determine which point among the given points lies on the circle.

radius=diameter/2=10/2=5 units

let (x,y) be a point on the circle

The distance between the center and (x,y) is equal to the radius of the circle

The distance between them= $\sqrt{(x-(-2))^2+y-(-2))^2}=5\\\\ \sqrt{(x+2)^2+(y+2)^2} =5\\\\$

squaring both sides $(x+2)^2+(y+2)^2=25\\$

The option (-6,-5) satisfies the equation

therefore the point that lies on the circle is (-6,-5)

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Charlie is watching hot air balloons. Balloon A has risen at a 60° angle. Balloon B has risen at an 82° angle. If the distance f

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Answer:

(B)1005 feet

Step-by-step explanation:

In the attached diagram

$\angle y =82^\circ\\\angle x =60^\circ$

|AG|=1400 feet

Distance from point C to point G=|CG|

Using Trigonometry in Triangle ACG

$\tan 60^\circ=\dfrac{1400}{CG}\\ CG=\dfrac{1400}{\tan 60^\circ}\\\approx 808$ feet$

Using Trigonometry in Triangle BCG'

$\tan 82^\circ=\dfrac{1400}{CG'}\\ CG'=\dfrac{1400}{\tan 82^\circ}\\\approx 197$ feet$

Therefore, the distance from balloon B from balloon A

=CG+CG'

=808+197

=1005 feet

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We assume all employees are either full-time or part-time.

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If the number of full-time employees is 24 or less, the number of part-time employees must be 12 or more. (Thinking, based on knowledge of sums.)

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You can write the inequality in two stages.

First, write and solve an equation for the number of full-time employees in terms of the number of part-time employees.
Then apply the given constraint on full-time employees. This gives an inequality you can solve for the number of part-time employees.

Let f and p represent the numbers of full-time and part-time employees, respectively.

... f + p = 36 . . . . . . given

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... f ≤ 24 . . . . . . . . . given

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2 years ago

To go bowling, it costs $2 to rent shoes and then $3.25 for each game bowled. Which of the following functions gives the total c

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2+3.25g=y
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2+3.25g=y

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2 years ago

Read 2 more answers

A cubic box is completely filled with 2,179 g of water. What is the length of one side of the box, in meters? m Explain your rea

lisov135 [29]

Answer:

$l\approx 1.296\,cm$

Step-by-step explanation:

The water density is approximately 1 gram per cubic centimeter, which means that 1 gram of water occupies a volume of a cubic centimeter. Hence, 2.179 grams occupies a volume of 2.179 cubic centimeters.

Let assume volume occupied by the water has a cube-like shape, whose side has the following measure:

$l = \sqrt[3]{2.179\,m^{3}}$