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kotegsom [21]
2 years ago
10

19. Given that angle BFC = 58°. Angle BXG = 48° and angle CBF 22 Find () 2BGX (iv) BCG (i) 2BGF (iv) ZBFG (ii) BCF H EE 58 48° D

C 220 A- Figure 5.74​
Mathematics
1 answer:
RoseWind [281]2 years ago
6 0

The unknown angles in the cyclic quadrilateral is as follows:

∠BGX = 74° (sum of angles in a triangle)

∠BGF = 180° (opposite angles of cyclic quadrilateral are supplementary)

∠BCF = 100°(sum of angles in a triangle)

∠BCG  = 26°

∠BFG = 22°

<h3>Cyclic Quadrilateral</h3>

A cyclic quadrilateral has all its angles equal to 360 degrees. The sum of angles in a cyclic quadrilateral is equals to 360 degrees.

Let's find the missing angles as follows:

∠BGX = 180 - 48 - 58 = 74° (sum of angles in a triangle)

∠BGF = 180 - 100 = 80° (opposite angles of cyclic quadrilateral are supplementary)

∠BCF = 180 - 22 - 58 = 100°(sum of angles in a triangle)

∠BCG = 100 - 74 = 26°

∠BFG ≅ CBF = 22°(alternate angles)

learn more on angles here: brainly.com/question/19430381

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​Arif's backyard is 24 by 37 meters. He wants to put a flower garden in the middle of the​ backyard, leaving a strip of grass of
Tpy6a [65]

Answer:

Length of the flower garden = 29 meters

Width of the flower garden = 16 meters

Step-by-step explanation:

I have also attached a diagram for your convenience

Now First let us see the data we are given with:

Arif's backyard length = 37 meters

Arif's backyard Width = 24 meters

Area that should be left with grass = 424 m^2

Now lets suppose the width of the stirp of grass be "a"

According the image the area of backyard will be:

Area ABCD = 24 x 37

Area ABCD = 888 m^2

The length LM will be = (37 -2a)

The Width LO will be = (24 -2a)

Area LMNO = (37 -2a) x  (24 -2a)

Area LMNO = 888 -74a -48a +4a^2

Area LMNO = 4a^2 -122a + 888

Now in order the to calculate the area of the grass strip we must subtract the area LMNO from the total area ABCD and we already know that the areas the area of grass strip should be 424 m^2

hence, A = Area ABCD - Area LMNO

424 = 888 - (4a^2 -122a + 888)

424 = 888 - 4a^2 +122a - 888

424 = -4a^2 +122a

4a^2 -122a +424=0

(We can solve this quadratic equation by breaking the middle term method)

2(2x-53)(x-4) = 0

2(2x-53) = 0

2x -53 = 0

x = 53/2

x = 26.5 (Not Possible)

x-4 = 0

x = 4

Length of the flower garden = 37 -2(4)

Length of the flower garden = 29 meters

Width of the flower garden = 24 -2(4)

Width of the flower garden = 16 meters

4 0
3 years ago
1 question need help thank you!!
inn [45]
The correct answer is:  [D]:  "  x² – 5x – 24 " .
____________________________________________________
Explanation:
_____________________________________
Given:  " (x + 3)(x – 8) " ; expand :
______________________________________
Note:  (a + b) (c + d) = ac + ad + bc + bd .
_____________________________________
a = x ; 

b = 3 ; 

c = x  

d = 8
_______________________________________

   " (x + 3)(x – 8) " ; 

        =  (x * x)  + ( -8 * x)  + ( 3 * x ) + (3 * -8) ; 

        =  x² + (-8x) + 3x + (-24) ;

         = x² – 8x + 3x – 24 ;

→ Combine the "like terms" :

          – 8x  +  3x  =  – 5x ;

And simplify the expression; 

to get: 

→  " x² – 5x – 24 " ; which is:  Answer choice:  [D]:  " x² – 5x – 24 " .
________________________________________________________
7 0
3 years ago
Steven's school is selling chocolate bars to earn money for new band instruments. The school will receive 33% of the total sales
shtirl [24]
The x-intercept of the linear equation is the value of x when y is equal to zero. From the given equation above, 
                                 y = 0.33x
When y is zero, 
                                0 = 0.33x   ; x = 0
When y is zero, x is also zero. This means that the school will not receive any amount when they are unable to sell anything. 
8 0
3 years ago
Read 2 more answers
I rlly hate math, pweaseeee help me asap!!!
jekas [21]

Answer:

See explanation.

Step-by-step explanation:

Part C)

5+(-10)

When adding a positive to a negative, the result will be the sign of the larger absolute value. In this case, 10 is greater than 5, so the result will be negative.

Adding a negative is also the same thing as subtracting a positive.

5+(-10)\\5-10\\-5

For your second problem, 5 is larger than 3, so the result will be positive.

5+(-3)\\5-3\\2

-----

When adding a positive to another positive, the result will be positive.

5+3\\8

When adding a number to zero, the answer will always be the number.

5+0\\5

Part D)

When multiplying a positive times a negative, the result will always be negative.

5*(-10)\\-50

5*(-3)\\-15

-----

When multiplying a positive times a positive, the result will always be positive.

5*10\\50

When multiplying a positive or a negative times zero, the result will always be zero.

5*0\\0

6 0
3 years ago
What is the decomposition of 43.586
Fiesta28 [93]
43.586- anything 5 and more rounds up, so the 6 rounds the 8 up to 9, the 9 rounds the 5 up to a 6, so your answer wound be 43.6 because 43.5(tenths)8(hundredths)6(thousandths), i hope this helps 

Leave a thanks :D
3 0
3 years ago
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