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Brums [2.3K]
2 years ago
7

A quadrilateral can be inscribed in a circle, if and only if, the opposite angles in that quadrilateral are supplementary.

Mathematics
1 answer:
balandron [24]2 years ago
4 0

The cyclic quadrilateral's opposing angles are 180 degrees, which become supplementary angles.

<h3>What is a cyclic quadrilateral?</h3>

If the quadrilateral is inscribed in a circle then the quadrilateral is known as a cyclic quadrilateral.

A quadrilateral can be inscribed in a circle, if and only if, the opposite angles in that quadrilateral are supplementary.

We know that the sum of the opposite angles of the cyclic quadrilateral is equal to 180 degrees.

Supplementary angle - Two angles are said to be supplementary angles if their sum is 180 degrees.

More about the cyclic quadrilateral link is given below.

brainly.com/question/15061291

#SPJ1

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Solve for w, where w is a real number.
Ber [7]

Answer:

w= 9

Step-by-step explanation:

\sqrt{ - 4w + 61}  = w - 4

Square both sides:

-4w +61= (w -4)²

\boxed{(a - b)^{2}  = a^2 -2ab + b^2 }

Expand:

-4w +61= w² -2(w)(4) +4²

-4w +61= w² -8w +16

Simplify:

w² -8w +16 +4w -61= 0

w² -4w -45= 0

Factorize:

(w -9)(w +5)= 0

w -9= 0 or w +5= 0

w= 9 or w= -5 (reject)

Note:

-5 is rejected since we are only taking the positive value of the square root here. If the negative square root is taken into consideration, then w= -5 would give us -9 on both sides of the equation.

<u>Why </u><u>do </u><u>we </u><u>use </u><u>negative </u><u>square </u><u>root?</u>

When solving an equation such as x²= 4,

we have to consider than squaring any number removes the negative sign i.e., the result of a squared number is always positive.

In the case of x²= 4, x can be 2 or -2. Thus, whenever we introduce a square root, a '±' must be used.

However, back to our question, we did not introduce the square root so we should not consider the negative square root value.

6 0
2 years ago
Read 2 more answers
at 1:30 in the afternoon an old freight train and a new dart express train pull out of the new garland station going in opposite
nydimaria [60]

Solution: The speed of old freight train is 0.5 miles per minute and the speed of new dart express train is 1.5 miles per minute.

Explanation:

Let the speed of old freight train is x miles per minute and the speed of new dart express train is y miles per minute.

It is given that the speed of the dart express train is three times faster than the freight train. So, it can be written as,

3x=y ....(1)

The trains are moving towards the opposite directions, therefore the distance between them is increased at the speed of (x+y) miles per minute.

Distance=Speed\times Time

The distance between both train in 15 minutes is represented by 15(x+y).

According to the given information the distance between trains is 30 miles in 15 minutes.

15(x+y)=30

x+y=2

Use equation (1) and put y=3x

x+3x=2

4x=2

x=0.5

Put this value in equation (1), to find the value of y.

y=3(0.5)

y=1.5

Therefore, the The speed of old freight train is 0.5 miles per minute and the speed of new dart express train is 1.5 miles per minute.

4 0
3 years ago
Write in slope intercept form:<br> (-4,6) slope= -3/4
Hunter-Best [27]

Answer:

Step-by-step explanation:

y= -3/4x+3

8 0
3 years ago
Read 2 more answers
I have 5 digits.My 9 is worth 10000. my 2 is worth 2 thousand one of my 7s is worth 70. the other is worth 10 times as much. my
liberstina [14]

Answer:

92776

Step-by-step explanation:

FIrst multiply:

9*10000= 90000

2*1000=2000

70*10= 700

Then add:

90000+2000+700+70(already given)+6(already given)= 92776

Hope this helps! :)

5 0
3 years ago
A jet flies at a rate of 1.3x10^3 feet per hour . Written in scientific notation which is the best estimate of how many feet the
vichka [17]

Answer:

3 * 10^6 if the answer is 3.64 * 10^6, you really ought to argue the meaning of estimate with your instructor.

Step-by-step explanation:

This is a very valuable question. Put your calculator away when you answer it. Using a calculator is sort of cheating.

1.3 * 10^3 roughly is roughly 1 * 10^3

2.8*10^3 hours is roughly 3 * 10^3

Forget the powers for now and just work with the 1 and 3

1*3 equals 3.

10^3 * 10^3 = 10^6 when the base of two numbers is the same (10 in this case) then the powers are added.

10^(3 + 3) = 10^6

So the answer is roughly 3*10^6

Now you can take out your calculator and get the answer.

1.3*10^3 * 2.8 * 10^3 = 3.64 * 10 ^ 6

Notice that the estimate (done in my head) is close enough to tell you what the answer should be. On a test, that's a very handy skill.

5 0
3 years ago
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