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MAVERICK [17]
3 years ago
9

Prove that the lengths of the diagonals of an isosceles trapezoid are equal

Mathematics
1 answer:
SOVA2 [1]3 years ago
6 0
AD || BC 
<span>• AB = CD </span>
<span>• ∠BAD = ∠CDA (a given condition ∵ ABCD is an isosceles trapezium) </span>

<span>The diagonals AC and BD create two ∆'s: ∆ABD, and ∆ACD </span>

<span>The two ∆'s are congruent (SAS).  </span>
 
<span>(S): AB = CD </span>
<span>(A): ∠BAD = ∠CDA 
</span><span>(S): AD = DA (common side) </span>
<span>
The corresponding sides of the two ∆'s, BD and AC, are also congruent. </span>
<span>(the two diagonals of the trapezium/trapezoid) 
</span>
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2. Find the center and radius of the circle with equation (x-6)2+ (y + 5)2 = 9.
Romashka-Z-Leto [24]

Answer:

Center (6 , -5)   and radius = 3

Step-by-step explanation:

The Standard equation of circle can  be written as

(x - a)² + (y - b)² = r²

with center (a , b)   and radius  = r

Now from given circle equation

(x - 6)² + (y +5)² = 9

so, from here center of circle (6 , -5) and radius = 3

4 0
3 years ago
The six-digit number 63X904 is an even multiple of 27. What does the digit X represent?
olga2289 [7]
Let's solve this problem step-by-step.

STEP-BY-STEP SOLUTION:

To begin with, let's establish that ( x ) can equal to any number from 0 to 9.

Meaning, that ( x ) is equal to one of the following: 0, 1, 2, 3, 4, 5, 6, 7, 8 or 9.

Now that we know which values ( x ) can equal to, we will simply substitute each of the numbers as potential values of ( x ) into the six-digit number and divide it by 27 to see if it is a multiple of 27.

If X = 0

= 63X904 / 27

= 630904 / 27

= Not a whole number

Therefore, X is not equal to 0.

If X = 1

= 63X904 / 27

= 631904 / 27

= Not a whole number

Therefore, X is not equal to 1.

If X = 2

= 63X904 / 27

= 632904 / 27

= Not a whole number

Therefore, X is not equal to 2.

If X = 3

= 63X904 / 27

= 633904 / 27

= Not a whole number

Therefore, X is not equal to 3.

If X = 4

= 63X904 / 27

= 634904 / 27

= Not a whole number

Therefore, X is not equal to 4.

If X = 5

= 63X904 / 27

= 635904 / 27

= 23552

ANSWER:

Therefore, the answer is:

X = 23, 552

Please mark as brainliest if you found this helpful! :)
Thank you <3
8 0
3 years ago
I am a square. My perimeter is 48 inches what is my area?
Fynjy0 [20]

Answer:

area=144

Step-by-step explanation:

so we need to find the length of each side

since its a square there is 4 sides

perimeter is all the sides added up

48/4=12

the formula for a squares are is b*h

12*12= 144

3 0
3 years ago
Read 2 more answers
Find lim<br> 12+1)-(2)<br> if f(x) = x² + x + 1
kotegsom [21]

Answer:

The answer is 11 Hope this helps ;)

Step-by-step explanation:

7 0
3 years ago
An ice cream truck was parked near a beach, and some kids ran to it and formed a line. Then, more kids joined the line by fillin
Irina-Kira [14]

Answer:

7

Step-by-step explanation:

So, we know that this process happened 3 times in total. The original amount of kids we can call x, so the next wave filled in the gaps inbetween, so we call that amount x-1, the next wave would be (x+x-1)-1 or 2x-2, and the last would be 4x-4

adding this all up we get 8x-7=49, so 8x = 56 or x = 7

3 0
2 years ago
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