True or False? A circle could be circumscribed about the quadrilateral below.

Mathematics

2 answers:

Aleks04 [339]3 years ago

4 0

Answer:

The answer is False.

Step-by-step explanation:

Given a quadrilateral ABCD with angles ∠A=90°, ∠B=90°, ∠C=115° and ∠D=65°

We have to tell about the statement true or false

'A circle could be circumscribed about the quadrilateral'

As, we say a circle can be circumscribed about the quadrilateral if and only if the quadrilateral is cyclic and also if the opposite angles of a quadrilateral are supplementary, then only the quadrilateral is cyclic.

Hence, we have to check for the opposite angles of quadrilateral if they are supplementary then we say the above statement is true i.e A circle could be circumscribed about the quadrilateral.

∠A+∠C=90+115=205° ≠ 180°

⇒ opposite angles are not supplementary.

∴ A circle could not be circumscribed about the quadrilateral.

The above statement is false.

BlackZzzverrR [31]3 years ago

3 0

Answer: false

Step-by-step explanation: the answer is false because suplimentary angled dont add up to 180

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Solve the system of equations: X+y+z=5 -3x-4y+4z=15 2x-y-4z=-8

atroni [7]

Answer:

(x, y, z) = (3, -2, 4)

Step-by-step explanation:

The attachment shows a solution using a graphing calculator where the first equation is solved for z, and that expression is substituted into each of the other two equations. The solution to that system is (x, y) = (3, -2). Using these values in the expression for z, we find ...

z = 5 -(3 +(-2)) = 4

The solution is (x, y, z) = (3, -2, 4).

Your graphing calculator and/or online tools can give you the reduced row echelon form of the augmented matrix representing the system:

$\left[\begin{array}{ccc|c}1&1&1&5\\-3&-4&4&15\\2&-1&-4&-8\end{array}\right]$

If you're solving by hand, you can do the substitution described above to eliminate z from one equation. You can eliminate z from another equation by adding the last two:

-3x -4y +4(5 -x -y) = 15 ⇒ -7x -8y = -5

(-3x -4y +4z) +(2x -y -4z) = (15) +(-8) ⇒ -x -5y = 7

This pair of equations can be solved for x and y in any of the usual ways. Using the second equation to substitute for x, for example, gives you ...

-7(-5y -7) -8y = -5 ⇒ 27y = -54 ⇒ y = -2

x = -5(-2) -7 = 3

z = 5 -(3) -(-2) = 4

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Additional comment

If all that is needed is a solution, we prefer a graphical or matrix approach. These take about the same amount of time. Both require a little additional effort to determine exact values when the solutions are not integers.