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3 years ago

Quadrilateral STRW is inscribed inside a circle as shown below. Write a proof showing that angles T and R are supplementary.

Mathematics

1 answer:

hodyreva [135]3 years ago

5 0

Minor point: the quadrilateral is STWR, <em>not STRW</em>. Vertices are named in order.

The measure of angle T is half the measure of arc WRS. The measure of angle R is half the measure of arc STW. The sum of the measures of the two arcs is the measure of a circle, 360°, so you have

... T + R = (WRS)/2 + (STW)/2

... ... = (WRS + STW)/2

... ... = 360°/2 = 180°

Since the sum of T and R is 180°, they are supplementary.

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When deriving the quadratic formula by completing the square, what expression can be added to both sides of the equation to crea

nignag [31]

The expression that would be added to both sides is (b/2a)^2

<h3>How to determine the expression?</h3>

The equation is given as:

x^2 + b/ax + __ = c/a + __

Take the coefficient of x

b/a

Divide by 2

b/2a

Square the expression

(b/2a)^2

Hence, the expression that would be added to both sides is (b/2a)^2

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2 years ago

Pls solve the simultaneous equation in the attachment.

siniylev [52]

Answer:

Part a) The solution is the ordered pair (6,10)

Part b) The solutions are the ordered pairs (7,3) and (15,1.4)

Step-by-step explanation:

Part a) we have

$\frac{x}{2}-\frac{y}{5}=1$ ----> equation A

$y-\frac{x}{3}=8$ ----> equation B

Multiply equation A by 10 both sides to remove the fractions

$5x-2y=10$ ----> equation C

isolate the variable y in equation B

$y=\frac{x}{3}+8$ ----> equation D

we have the system of equations

$5x-2y=10$ ----> equation C

$y=\frac{x}{3}+8$ ----> equation D

Solve the system by substitution

substitute equation D in equation C

$5x-2(\frac{x}{3}+8)=10$

solve for x

$5x-\frac{2x}{3}-16=10$

Multiply by 3 both sides

$15x-2x-48=30$

$15x-2x=48+30$

Combine like terms

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<em>Find the value of y</em>

$y=\frac{x}{3}+8$

$y=\frac{6}{3}+8$

$y=10$

The solution is the ordered pair (6,10)

Part b) we have

$xy=21$ ---> equation A

$x+5y=22$ ----> equation B

isolate the variable x in the equation B

$x=22-5y$ ----> equation C

substitute equation C in equation A

$(22-5y)y=21$

solve for y

$22y-5y^2=21$

$5y^2-22y+21=0$

Solve the quadratic equation by graphing

The solutions are y=1.4, y=3

see the attached figure

<em>Find the values of x</em>

For y=1.4

$x=22-5(1.4)=15$

For y=3

$x=22-5(3)=7$

therefore

The solutions are the ordered pairs (7,3) and (15,1.4)

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Answer:

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Step-by-step explanation:

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mestny [16]

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Then
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