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Debora [2.8K]
2 years ago
9

. Points A (-1,y) and B(5,7) lie on a circle with centre O(2, -3y). Find the values of y. Hence find the radius of the circle

Mathematics
1 answer:
kakasveta [241]2 years ago
4 0

Answer: y = 7, y = -1

<u>Step-by-step explanation:</u>

Since both A and B lie on the circle, their distances to the origin is the radius which will be equal.

d_{AO}=\sqrt{(-1-2)^2+(y + 3y)^2}\\d_{BO}=\sqrt{(5 - 2)^2+(7 + 3y)^2} \\\qquad \qquad \qquad \qquad d_{AO} = d_{BO}\\\sqrt{(-1-2)^2+(y + 3y)^2}=\sqrt{(5 - 2)^2+(7 + 3y)^2}\\\sqrt{(-3)^2+(4y)^2}=\sqrt{(3)^2+(7 + 3y)^2}\\\sqrt{9+16y^2}=\sqrt{9+(49+42y+9y^2)}\\\sqrt{9+16y^2}=\sqrt{58+42y+9y^2}\\(\sqrt{9+16y^2})^2=(\sqrt{58+42y+9y^2})^2\\\\9+16y^2=58+42y+9y^2\\7(y^2-6y-7)=0\\7(y - 7)(y + 1)=0\\y - 7 = 0 \qquad\text{and}\qquad y + 1 = 0\\\quad y = 7 \qquad \text{and}\qquad y = -1

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Dwight and Walt are building model cars. Dwight builds 7 fewer models than 4 times the number Walt builds.Dwight builds at most
romanna [79]

 4x-7\leq 9  inequality could be used to find the number of models Walt builds. Correct option B).

<u>Step-by-step explanation:</u>

Here we have , Dwight and Walt are building model cars. Dwight builds 7 fewer models than 4 times the number Walt builds.Dwight builds at most 9 models. We need to find Which inequality could be used to find the number of models Walt builds . Let's find out:

Let the  the number Walt builds is x , So Dwight builds 7 fewer models than 4 times the number Walt builds i.e.

⇒ 4x-7

But , according to question Dwight builds at most 9 models i.e.

⇒ 4x-7\leq 9

⇒ 4x\leq 16

⇒ \frac{4x}{4}\leq \frac{16}{4}

⇒ x\leq 4

Therefore ,  4x-7\leq 9  inequality could be used to find the number of models Walt builds which is Dwight builds at most 9 and Walt builds at most 4 .

4 0
2 years ago
(x2 − 8x + 5) − (−3x2 + 5x − 9)
julia-pushkina [17]
(X²-8X+5)-(-3X²+5X-9)
=X²-8X+5+3X²-5X+9
=4X²-13X+14
That's your answer lovely~
7 0
2 years ago
A swimming class has 20 students. Only 8 students know how to dive off
Allisa [31]

Answer: 40%  

Step-by-step explanation:

To write 8/20 as a percent have to remember that 1 equal 100% and that what you need to do is just to multiply the number by 100 and add at the end symbol % . 8/20 * 100 = 0.4 * 100 = 40% And finally we have: 8/20 as a percent equals 40%

6 0
3 years ago
Which answer shows 2.13786 times 10 Superscript 4 written in standard form?
ivolga24 [154]

Answer:

Answer:

21378.6

Step-by-step explanation:

You move the decimal point four places towards the right.

3 0
2 years ago
Read 2 more answers
This last one I need help on too
ExtremeBDS [4]

Answer:

x=\frac{3}{4}+i\frac{\sqrt{7}}{4},\:x=\frac{3}{4}-i\frac{\sqrt{7}}{4}

Step-by-step explanation:

simplify \frac{-3}{x-2} by putting the negative sign on the outside. \frac{2x}{x-1}-\frac{2x-5}{x^2-3x+2}=-\frac{3}{x-2}

find the LCM of the denominators. It is (x-1)(x-2). Multiply by the LCM:

\frac{2x}{x-1}\left(x-1\right)\left(x-2\right)-\frac{2x-5}{x^2-3x+2}\left(x-1\right)\left(x-2\right)=-\frac{3}{x-2}\left(x-1\right)\left(x-2\right)

Simplify:

2x\left(x-2\right)-\left(2x-5\right)=-3\left(x-1\right)

solve: x=\frac{3}{4}+i\frac{\sqrt{7}}{4},\:x=\frac{3}{4}-i\frac{\sqrt{7}}{4}

3 0
3 years ago
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