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3 years ago

Determine the approximate length of AC

Mathematics

1 answer:

castortr0y [4]3 years ago

4 0

Answer:

B: 7.07 units

Step-by-step explanation:

We see a radius of circle A labeled 3, so we know that the other radius of circle A that contains the side of the rectangle also measures 3 units. The side of the rectangle measures 2, so the part of the radius of circle A that is not part of the rectangle measures 1 unit. That is one leg of the right triangle.

Opposite sides of a rectangle are congruent, so the side of the rectangle opposite the side that measures 7 also measures 7. That is the other leg of the right triangle. Now we use the Pythagorean theorem to find AC which is the hypotenuse of the right triangle.

a² + b² = c²

1² + 7² = c²

1 + 49 = c²

c² = 50

c = √50

c = 7.07

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the sum of three times one number, x, and five times a second number,y, is 77. if the sum of the two numbers is 19, find the two

HACTEHA [7]

Answer:

x=9, y=10. (9, 10). The two numbers are 9 and 10.

Step-by-step explanation:

3x+5y=77

x+y=19

------------------

3x+5y=77

-3(x+y)=-3(19)

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3x+5y=77

-3x-3y=-57

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2y=20

y=20/2

y=10

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x=19-10

x=9

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3 years ago

Given: circle k(O), m∠P=95°, m∠J=110°, m∠LK=125°<br> Find: m∠PJ

IRINA_888 [86]

Answer:

The measure of the arc PJ is $75\°$

Step-by-step explanation:

step 1

Find the measure of angle L

we know that

In a inscribed quadrilateral opposite angles are supplementary

$m$

we have

$m$

substitute

$m$

step 2

Find the measure of arc KJ

we know that

The inscribed angle measures half that of the arc comprising

$m$

substitute the values

$95\°=\frac{1}{2}(125\°+arc\ KJ)$

$190\°=(125\°+arc\ KJ)$

$arc\ KJ=190\°-125\°=65\°$

step 3

Find the measure of arc PJ

we know that

The inscribed angle measures half that of the arc comprising

$m$

substitute the values

$70\°=\frac{1}{2}(65\°+arc\ PJ)$

$140\°=(65\°+arc\ PJ)$

$arc\ PJ=140\°-65\°=75\°$

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Answer:

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Step-by-step explanation:

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