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Margarita [4]
4 years ago
9

In the diagram below O is circumscribed about quadrilateral DEFG. What is the value of x

Mathematics
2 answers:
yKpoI14uk [10]4 years ago
8 0

Answer:

Option D

68 degrees is the answer.

Step-by-step explanation:

In the picture there is a quadrilateral DEFG and a circle circumscribing the quadrilateral.

In other words, DEFG is a cyclic quadrilateral.

We know that in cyclic quadrilateral, opposite angles are supplementary.

Hence in the given quadrilateral, Angles D and F are supplementary and also the pair E and G are supplementary.

Angle G is x and we have to find x.

Sum of angles G and E = 180  degrees (since they are supplementary)

Angle E = 112 degrees (given)

Hence angle G = x = 180-112 = 68 degrees.


Ivan4 years ago
4 0

Answer C. 68

Step-by-step explanation:

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Please help!!! I will mark someone brainliest!
valina [46]

Answer:

a = 8, b = \frac{3}{2}

Step-by-step explanation:

Given the exponential function

f(x) = ab^{x}

To find a and b use the given coordinate points on the graph

Using (0, 8 ), then

8 = ab^{0} [ b^{0} = 1 ] , then

a = 8

f(x) = 8b^{x}

Using (2, 18 ) , then

18 = 8b² ( divide both sides by 8 )

\frac{18}{8} = b² , that is

b² = \frac{9}{4} ( take the square root of both sides )

b = \sqrt{\frac{9}{4} } = \frac{3}{2}

Thus

f(x) = 8(\frac{3}{2}) ^{x}

3 0
3 years ago
The width of a rectangle is (x+1) and the length is (x-6). What is the length and width of the rectangle if the area is 30 squar
jolli1 [7]

Answer:

The length of the rectangle (l) = 3 feet

The width of the rectangle (W) =  10 feet

Step-by-step explanation:

<u><em>Step(i):-</em></u>

<em>Given that the width of the rectangle  = (x+1) feet</em>

<em>Given that the length of the rectangle = ( x-6) feet</em>

<em>The area of the rectangle = 30 square feet</em>

<u><em>Step(ii):-</em></u>

We know that the area of the rectangle

                = length ×width

    30   = ( x+1)(x-6)

    30   = x² - 6x + x -6

⇒ x² - 5 x - 6 = 30

⇒ x² - 5 x - 6 - 30 =0

⇒ x² - 5 x - 36 =0

 x² - 9 x +4x - 36 =0

   x (x-9) +4 ( x-9) =0

   ( x+4 ) ( x-9) =0

     ( x+4 ) =0 and  ( x-9) =0

     x =-4 and x =9

<u><em>Step(iii):-</em></u>

we have to choose x =9

     The length of the rectangle (l) =  x-6 = 9-6 =3

      The width of the rectangle (W) =  x+1 =  9 +1 = 10

<u><em>Final answer:-</em></u>

The length of the rectangle (l) = 3 feet

The width of the rectangle (W) =  10 feet

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