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Tems11 [23]
3 years ago
6

Can someone help me with #18 & #20?​

Mathematics
1 answer:
Nuetrik [128]3 years ago
4 0

Answer:

\large\boxed{18)\ x=13\ and\ y=9}\\\boxed{20)\ AO=8}

Step-by-step explanation:

18)

If a quadrilateral is inscribed in a circle, the opposite angles add up to 180°.

Therefore we have the system of equations:

\left\{\begin{array}{ccc}(6x+23)+(8y+7)=180\\(6x-4)+(12y-2)=180\end{array}\right\\\\\left\{\begin{array}{ccc}6x+8y+(23+7)=180\\6x+12y+(-4-2)=180\end{array}\right\\\left\{\begin{array}{ccc}6x+8y+30=180&|\text{subtract 30 from both sides}\\6x+12y-6=180&|\text{add 6 to both sides}\end{array}\right\\\left\{\begin{array}{ccc}6x+8y=150\\6x+12y=186&|\text{multiply both sides by (-1)}\end{array}\right

\underline{+\\\left\{\begin{array}{ccc}6x+8y=150\\-6x-12y=-186\end{array}\right}\qquad\text{add both sides of the equations}\\.\qquad\qquad-4y=-36\qquad|\text{divide both sides by (-4)}\\.\qquad\qquad\boxed{y=9}\\\\\text{Put the value of y to the first equation and solve them for x:}\\\\6x+8(9)=150\\6x+72=150\qquad\text{subtract 72 from both sides}\\6x=78\qquad\text{divide both sides by 6}\\\boxed{x=13}

20)

If line AB is tangent to the circle, then the angle A is a right angle

m\angle A=90^o

Therefore the triangle is a right triangle. We can use the Pythagorean theorem:

Let O - center of the circle. Therefoe OA is the radius of a circle.

From a Pythagorean theorem:

AO^2+15^2=(9+8)^2\\\\AO^2+225=17^2\\\\AO^2+225=289\qquad\text{subtract 225 from both sides}\\\\AO^2=64\to AO=\sqrt{64}\\\\AO=8

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The true conditional statement, "If 5x + 7 = 2x - 1, then 3x + 7 = -1," illustrates which property of equality?
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<span>The given condition is:
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</span>



3 0
3 years ago
PLEASE HELP I GIVE THANKS
ohaa [14]

Take one of the points in the table,

like  x=1  y=5
or    x=2  y=7

Write them into one of the choices on the list,
and see if the result is true.

For example,

-- Take the line in table that says   x=1   y=5.

-- And take the first choice on the list     y = x + 3 .

-- Write '1' in place of 'x', and write '5' in place of 'y'.

-- Then you have    <u>5 = 1 + 3</u> .

Is this true ?  I don't think so.
So the first choice on the list can't be correct.

Try thesame point    x=1   y=5   with  the other choices.
You'll find one that IS correct, and that's the answer.



4 0
3 years ago
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