A curve is traced by a point P(x, y) which moves such that its distance from the point A(1, -2) is twice its distance from the point B(4, -3). Determine the equation of the curve.

Answers

Answer 1

Answer: $|PA|=√((1-x)^2+(-2-y)^2)\n\n|PB|=√((4-x)^2+(-3-y)^2)\n\n|PA|=2|PB|\n\n√((1-x)^2+(-2-y)^2)=2√((4-x)^2+(-3-y)^2)\n\n(1-x)^2+(-2-y)^2=4[(4-x)^2+(-3-y)^2]\n\n1-2x+x^2+4+4y+y^2=4(16-8x+x^2+9+6y+y^2)$

$x^2+y^2-2x+4y+5=4(x^2+y^2-8x+6y+25)\n\nx^2+y^2-2x+4y+5=4x^2+4y^2-32x+24y+100\n\nx^2-4x^2-2x+32x+y^2-4y^2+4y-24y+5-100=0\n\n-3x^2+30x-3y^2-20y-95=0\ \ \ \ /:(-3)\n\nx^2-10x+y^2+(20)/(3)y+(95)/(3)=0\n\nx^2-2x\cdot5+5^2-5^2+y^2+2y\cdot(10)/(3)+\left((10)/(3)\right)^2-\left((10)/(3)\right)^2=-(95)/(3)$

$(x-5)^2+(y+(10)/(3))^2=-(95)/(3)+(100)/(9)+25\n\n(x-5)^2+(y+(10)/(3))^2=-(285)/(9)+(100)/(9)+(225)/(9)\n\n(x-5)^2+(y+(10)/(3))^2=(40)/(9)\n\nit's\ the\ circle\n\ncenter:(5;-(10)/(3))\n\nradius:r=\sqrt(40)/(9)=(√(4\cdot10))/(\sqrt9)=(2√(10))/(3)$

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Tom Slick buys a set of tires for his car. The price, including tax, is $950.00. Tom finances the tires over 12 months after making a $50 down payment. The true annual interest rate is 18%. What are his monthly payments (principal plus interest)?

Kirby places frog and Beth's snail on point 0 in on the number line. As Beth's snail slowly slimed forward in the positive direction, Kirby's frog hopped in the opposite direction. By the time Beth's snail reached the number 2, Kirby's frog me four jumps, each 3 units long. How far apart are the snail and the frog at this point?

Answers

That picture doesn't have anything to do with the problem.

Snail went right, into positive numbers, frog went left, negative numbers. Their distance is the absolute difference.

d = | 2 - 4(-3) | = | 14 | = 14

Answer: 14

Which statement implies that A and B are independent events?A. P(B|A) = P(B A)

B. P(B|A) = P(B)
P(A)
C. P(B|A) = P(A)

D. P(B|A) = P(B)

Answers

The events $A,B$ are independent if and only if $P(A\cap B)=P(A)\cdot P(B)$ . Under this condition, we have conditional probabilities

$P(A\mid B)=(P(A\cap B))/(P(B))=(P(A)\cdot P(B))/(P(B))=P(A)$

$P(B\mid A)=P(B)$

so the answer is D.

Answer:

The answer is D.

Step-by-step explanation:

Solve the equation s + 2.8 = 6.59

Answers

s + 2.8 = 6.59
s = ?

To solve for s use the inverse operation of addition, which is subtraction.

s + 2.8 = 6.59
6.59 - 2.8 = s
6.59 - 2.8 = 3.79
s = 3.79

Check:

s + 2.8 = 6.59
s = 3.79
3.79 + 2.8 = ?
3.79 + 2.8 = 6.59
Correct!

This proves: s = 3.79 ;)

In order to solve for the variable, isolate the variable.

s + 2.8 = 6.59
- 2.8 -2.80 ( 2.8 is the same as 2.80 )

s = 3.79

Double check by plugging in the variable.

s + 2.8 = 6.59
3.79 + 2.8 = 6.59
6.59 = 6.59

Yes, it's correct!

Hope I helped!

Of all the species in the world 4, out of every 5 are insects. What percentage of species are insects

Answers

If 4/5 are insects, 8/10, or .8, of the species are insects. To find a percentage, multiply by 100 to find that 80% of the species are insects.

Answer:

80%

Step-by-step explanation:

khan academy lol

If E is on the interior of ∠ABD, m∠ABE = (2x - 5)°, m∠EBD = (x + 1)°, and m∠ABD = 50°, find the value of x.

Answers

$\displaystyle \n m\ \textless \ ABE + m\ \textless \ EBD = m\ \textless \ ABD \n \n (2x - 5)^o + (x + 1)^o = 50^o \n \n 2x-5+x+1=50 \n \n 3x - 4 = 50 \n \n 3x = 50+4 \n \n 3x = 54 \n \n x = (54)/(3) = \boxed{18^o}$

Simplify the following expression. 7- 5/8 x 7 -7/8 A. 1/14
B. 14
C. 1/49
D. 49

Answers

Answer:

Step-by-step explanation:

$7 - (5)/(8) * 7 - (7)/(8)$

$7 - (35)/(8) - (7)/(8)$

multiple through by 8

56 - 35 - 7 =14

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