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4 years ago

If the points (x,y) be equidistant from the points A(a+b,b-a) and B(a-b,a+b), prove that bx-ay=0

Mathematics

2 answers:

LenKa [72]4 years ago

8 0

Solution:-

It is given that the points (x,y) be equidistant from the points A(a+b,b-a) and B(a-b,a+b).

PA=PB

Take square both side,

PA^2=PB^2

Now use distance

formula ,

{x-(a+b)}^2+{y-(b-a)}^2={x-(a-b)}^2+{y-(a+b)}^2

=>x^2+(a+b)^2-2x(a+b)+y^2+(b-a)^2-2y(b-a)y=x^2+(a-b)^2-2x(a-b)+y^2+(a+b)^2-2y(a+b)

=>2x(a-b)-2x(a+b)=2y(b-a)-2y(a+b)

=>2x{a-b-a-b}=2y{b-a-a-b}

=>2x(-2b)=2y(-2a)

=>bx=ay

Hence, it is proved.

BaLLatris [955]4 years ago

7 0

Answer:Christopher took out a 4 year loan for $1150 at a sports-equipment store to be paid back with monthly payments at a 42% APR, compounded monthly. If...

Step-by-step explanation:

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Write the equation of the line that passes through the points (-7,9) and (-7,1). Put your answer in fully reduced point-slope fo

gulaghasi [49]

Answer:

It is a vertical line

Step-by-step explanation:

Find the slope using rise over run (y2 - y1) / (x2 - x1)

Plug in the points:

(y2 - y1) / (x2 - x1)

(1 - 9) / (-7 + 7)

-8/0

= undefined

Dividing by 0 gives you an undefined number. This means that the slope is undefined, and the line is a vertical line.

8 0

3 years ago

PLEASE HELP MEEEEEEEE.<br> Also can you explain how you got your answer

goldenfox [79]

Answer:

the last option, 10,12,15

Step-by-step explanation:

for every 3 of something you have 5 of something else, so the ratio is 3:5. That means when you have 6, double the amount of 3, you have the double amount of 5, 10.

5 0

3 years ago

Read 2 more answers

PLEASE HELP thanks!!

mrs_skeptik [129]

Answer:

b = 70

b = a = 70

b = c = 70

Step-by-step explanation:

snice b and 70 are opposite the top; they are equal.

b and a are alternate internal they are again equal so a is 70.

and finally a is equal with c because they are opposite at the top.

I hope I helped you! :)))

6 0

2 years ago

Based on the information from Harper's Index, 37 out of 100 adult Americans who did not attend college believe in extraterrestri

vazorg [7]

Answer: Yes, this indicate the proportion of adult americans that attended college and believe in extraterrestrials is higher than the proportion that did not attend college.

Step-by-step explanation:

Since we have given that

Hypothesis:

$H_0:p_1=p_2\\\\H_a:p_1>p_2$

n₁ = 100

x₁ = 37

So, $p_1=\dfrac{x_1}{n_1}=\dfrac{37}{100}=0.37$

n₂ = 100

x₂ =47

So, $p_2=\dfrac{47}{100}=0.47$

At 0.01 level of significance, z = 2.33

So, test statistic value would be

$z=\dfrac{p_1-p_2}{\sqrt{\dfrac{p_1(1-p_1)}{n_1}+\dfrac{p_2(1-p_2)}{n_2}}}\\\\z=\dfrac{0.37-0.47}{\sqrt{\dfrac{0.37\times 0.63}{100}+\dfrac{0.47\times 0.53}{100}}}\\\\z=-1.44$

Since, 2.33>-1.44

Hence, we will reject the null hypothesis.

Therefore, Yes, this indicate the proportion of adult americans that attended college and believe in extraterrestrials is higher than the proportion that did not attend college

4 0

3 years ago

Solve the inequality 5(2h+8)<60

zimovet [89]

Answer:

Step-by-step explanation:

5(2h+8) < 60

Expand the terms in the bracket

We have

10h + 40 < 60

Group like terms

10h < 60 - 40

10h < 20

Divide both sides by 10

h < 2

Hope this helps you

7 0

3 years ago