MATHEMATICS HIGH SCHOOL

A circle is centered at the point (5, -4) and passes through the point (-3, 2).The equation of this circle is (x + ___)2 + (y + ___)2 = ___

Answers

Answer 1
Answer:

Answer: (x-5)^2+(y+4)^2=100

Step-by-step explanation:

We know that the general equation of a circle can be written as :

(x-h)^2+(y-k)^2=r^2   (1), where (center )= (h,k) and r= radius

As per given , we have

(h,k) = (5,-4)

(x,y) =(-3,2)

Substitute these value in equation (1), we get

(-3-5)^2+(2-(-4))^2=r^2\n\n\Rightarrow\ (-8)^2+(2+4)^2=r^2\n\n\Rightarrow\ 64+6^2=r^2\n\n\Rightarrow\ 64+36=r^2\n\n\Rightarrow\ 100=r^2\n\n\Rightarrow\ r=√(100)=\pm10

Since radius cannot be negative , thus r= 10 units

Put value of r^2  and (h,k) in equation (1), we get

(x-5)^2+(y+4)^2=100

Thus , the equation of given circle is (x-5)^2+(y+4)^2=100.
Answer 2
Answer: you have to use the distance formula in order to find the radius. By doing that you get the answer 10. so the equation is:

(x-4)^2 + (y+5)^2 = 10

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A group of Physicians must build an addition to their existing private clinic. They are considering three different sized additions; a small addition, a medium addition and a large addition. If the medical demand is high (there is a favorable market for the addition) they would realize a net profit of $100,000 with a large addition, a net profit of $40,000 with a medium addition and a net profit of $10,000 with a small addition. If the medical demand is low (there is an unfavorable market for the addition) they would realize a net loss of $40,000 with the large addition, a net loss of $10,000 with the medium addition and a net profit of $5,000 with the small addition. The Physicians were also able to assign the following utility preference values to each of the potential payoffs they could encounter. Utility of $100,000 is 1.0, U ($40,000) is 0.9, U ($10,000) is 0.6, U ($5,000) is 0.5, U ($-10,000) is 0.4, and U ($-40,000) is 0.0. The physicians also have a reliable forecast indicating a 40% probability of the high medical demand. Using expected monetary value theory, what should they do and what is the expected value of that decision? Using expected utility theory, what should they do and what is the expected utility of that decision?

Answers

Therefore , the solution of the given problem of probability comes out to be the medium addition because it has the greatest expected utility (0.72).

What is probability, exactly?

The primary goal of the structures within a methodology expression known as criteria is to provide an indication of the probability that the assertion is true or that a specific event will occur. Any number between zero and one, at which 0 is frequently indicated as a possibility and 1 has frequently used to denote a level of confidence, can be used to represent chance. The chance that a specific event will occur is displayed in a probability diagram.

Here,

The following formula can be used to determine each option's anticipated financial value:

=> EMV of big addition =  (0.4 * $100,000) plus (0.6 * -$40,000) for a total of $16,000.

=>  EMV of the middle addition is

= (0.4 * $40,000) plus (0.6 * -$10,000) for a total of $14,000.

=>  EMV of a minor addition =  (0.4 * 10,000) plus (0.6 * 5,000), which equals $6,000

The large addition should be chosen by the physicians as it has the greatest expected financial value of $16,000.

dividing each outcome's usefulness value by its likelihood, then adding the results:

=> (0.4 * 1.0) + (0.6 * 0.0) = 0.4 is the EU of the big addition.

=> (0.4 * 0.9) + (0.6 * 0.6) = 0.72 is the EU of medium addition.

Smaller EU =  (0.4 * 0.5) +  (0.6 * 0.6) = 0.58

The doctors should choose the medium addition because it has the greatest expected utility (0.72), according to expected utility theory.

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WHAT IS 1/3 TO THE TENTH POWER IN FRACTION FORM?AND WHAT IS (1/3)^10 x 9^4(( (1)/(3)) ^(10)) 9^4

1/3 to the tenth power times 9 to the 4th power

Answers

Well, 1/3 to the 10th power. Since the numerator is 1, just ignore that.

Find the tenth power of 3.
3 x 3 x 3 x 3 x 3 x 3 x 3 x 3 x 3 x 3 = 59049
So, 1/3 to the 10th power is equal to 1/59049.
(1)/(3) ^(10) = (1)/(59049)

Okay, for the second equation we know that 1/3 to the tenth power is already 1/59049.

Now find the 4th power for 9.

9 x 9 x 9 x 9 = 6561
9*9*9*9=6561

Convert 6561 into a fraction, which is 6561/1.


Now multiply.

1/59049 x 6561/1 = 6561/59049

That fraction reduces into 1/9.

Answer #1: 1/59049
Answer #2: 1/9
1/3 ^ 10 = 1/3 * itself ten times.
1/59049 x 9 ^ 4
1/59049 x 6561 = 6561/59049
1/9

Find the first five terms of the sequence defined by each of these recurrencerelations and initial conditions.
a) an = 6an-1, a0 = 2
b) an = −2an-1, a0 = −1
c) an = an-1 – an-2, a0 = 2, a1 = −1

Answers

a) The first five terms of the sequence are 2, 12, 72, 432, 2592.
b) The first five terms of the sequence are -1, 2, -4, 8, -16.

c) The first five terms of the sequence are 2, -1, -3, -2, 1.

To find the first five terms of the sequence defined by each of these recurrence relations and initial conditions, we will use the given recurrence relation and initial conditions to find the next terms in the sequence.

a) an = 6an-1, a0 = 2

The first term is given as a0 = 2. We will use the recurrence relation to find the next terms.
a1 = 6a0 = 6(2) = 12
a2 = 6a1 = 6(12) = 72
a3 = 6a2 = 6(72) = 432
a4 = 6a3 = 6(432) = 2592

So, the first five terms of the sequence are 2, 12, 72, 432, 2592.

b) an = −2an-1, a0 = −1

The first term is given as a0 = -1. We will use the recurrence relation to find the next terms.
a1 = -2a0 = -2(-1) = 2
a2 = -2a1 = -2(2) = -4
a3 = -2a2 = -2(-4) = 8
a4 = -2a3 = -2(8) = -16

So, the first five terms of the sequence are -1, 2, -4, 8, -16.

c) an = an-1 – an-2, a0 = 2, a1 = −1

The first two terms are given as a0 = 2 and a1 = -1. We will use the recurrence relation to find the next terms.
a2 = a1 - a0 = -1 - 2 = -3
a3 = a2 - a1 = -3 - (-1) = -2
a4 = a3 - a2 = -2 - (-3) = 1

So, the first five terms of the sequence are 2, -1, -3, -2, 1.

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Its says use rounding or compatible numbers to estimate the sum and example 198 + 727 ans is 200+725=925 I still don't understand how to do it. Heres a problem 87+34 and here is one 222+203

Answers

Answer:

a) 121

b) 425  

Step-by-step explanation:

We are given the following information in the question:

198 + 727 + 200 + 725 = 925

This can be explained with the help of associative of addition and subtraction and commutative property of the addition.

Associative property:

a+(b+c) = (a +b )+c

Commutative property:

a+b = b+a

198 + 727 \n= 198 + ( 727 + 2)\n=198 + ( 2 + 727)\n=(198 + 2) + 725\n= 200+ 725 \n= 925

a)

87 + 34\n= 87 + ( 31 + 3)\n=87 + ( 3 + 31)\n=(87 + 3) + 31\n=90 + 31\n=121

b)

222 + 203\n=(220 + 2) + 203\n=220 + ( 2 + 203)\n=220 + 205\n=425
Okay, rounding is when you take a number such as 198 and imagine that it is something easier to do math with, like 200. 
200 is easier to add with because there are zeroes in the tens place and the ones place. 
725 is easier to add with than 727 because the ones place digit, (5), is an easier base to use, just like zero. 
Using the easier numbers, 200 + 725 = 925
Using the original numbers, 198 + 727 + 925
*Because you took two pieces from the 727 and added them to 198, the four numbers in this problem are compatible. 
Compatible numbers are when you use numbers that are close to the original ones and make it easier to do the problem in your head. 
____
In the case of 87+ 34, the simplest numbers to use would be 90 instead of 87 and 35 instead of 34. Not as easy as the first equation, but still doable. 
90+35+125
    or
87+34=121
____
In the case of 222+203, the simplest substitutions are 220 and 200. 
220+200=420
or
222+203=425
Hope this helps, 
Ahawk

Solve for mFind the measure of angle MHL





Please help me!!!!!!

Answers

Answer:

  • m = 10°
  • ∠MHL = 30°

Explanation:

∠MHL and ∠MHJ are supplementary angles that is some of the measure of both angle is 180°, because these angle are on a line.

∠MHL + ∠MHJ = 180°

substituting values.

⟹ (2m + 10)° + (5m + 100)° = 180°

⟹ 5m + 2m + 10 + 100 = 180°

⟹ 7m + 110 = 180°

⟹ 7m = 180° - 110°

⟹ 7m = 70°

⟹ m = 70/7

⟹ m = 10

m=10°

measure of ∠MHL is

⟹ (2m + 10 )°

⟹ 2(10°) + 10°

⟹ 20° + 10°

⟹ 30°

∠MHL=30°

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Hello. What are the vertices, foci, endpoints of the conjugate axis, and the equation of the asymptote of 7x^2-9y^2-14x+72y-200=0?

Answers

Answer: is ( 1,4 )

Step-by-step explanation:
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