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2 years ago

A B 21 48° 6x-24 D [?] << <[ ] 11 C

Mathematics

1 answer:

r-ruslan [8.4K]2 years ago

3 0

The shape in the figure is a composite shape with two triangles, and the inequality is 4 < x < 12

<h3>How to determine the range of value of x?</h3>

In the given figure, the side lengths AB and AD are equivalent.

This means that, we have the following angle relationship:

CAD < CAB

Substitute known values

6x - 24 < 48

Add 24 to both sides

6x < 72

Divide both sides by 6

x < 12

Also, we have the following angle relationship:

CAD > 0

Substitute known values

6x - 24 > 0

Add 24 to both sides

6x < 24

Divide both sides by 6

x < 4

This means that:

x < 4 and x < 12

Combine both inequalities

4 < x < 12

Hence, the inequality is 4 < x < 12

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3 years ago

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The center of the circle is (h,k) = (-2,-3)

The radius of the circle is r = 2

The standard form of equation of the circle is

${(x + 2)}^{2} + {(y + 3)}^{2} = 4$

<h3>How to find the center, radius and standrad form of the circle?</h3>

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${(x - h)}^{2} + {(y - k)}^{2} = {r}^{2}$

Here, (h,k) means centre of the circle.

r means radius of the circle.

given that coordinate points of centre of circle is (-2,-3).

Hence the (h,k) = (-2,-3)

<h3>How to find the radius of the circle?</h3>

Now to find the radius of the circle

The distance from a circle's centre to its circumference is its radius.

The distance from a circle's centre (-2,-3) to its circumference (0,-3) is its radius.

using the formula, distance between the two points to obtain radius.

$d = \sqrt{(x1 - x2) {}^{2} + {(y1 - y2)}^{2} } \\ r = \sqrt{ {( - 2 - 0)}^{2} + {( - 3 - ( - 3))}^{2} } \\ r = \sqrt{ {( - 2)}^{2} + {( - 3 + 3)}^{2} } \\ r = \sqrt{ {4}^{2} + 0 } \\ r = \sqrt{4} \\ r = 2$