Can someone please help me this is stressing me out :(

The standard form of the equation of the circle with a center at (3, -1) and a point on the circle at (5, 2) is (x - 3)² + (y + 1)² = 13.

To obtain the standard form of the equation of a circle provided its center and a point on the circle, we can use the distance formula.

The distance between the center of the circle (h, k) and a point on the circle (x, y) is equal to the radius of the circle.

Provided that the center of the circle is (3, -1) and a point on the circle is (5, 2), we can obtain the distance between these two points to determine the radius.

Using the distance formula:

\(\[ r = \sqrt{(x - h)^2 + (y - k)^2} \]\)

Substituting the values:

\(\\$r = \sqrt{(5 - 3)^2 + (2 - (-1))^2}$\\$= \sqrt{2^2 + 3^2}$\\$= \sqrt{4 + 9}$\\$= \sqrt{13}$\)

Now that we have the radius, we can write the equation of the circle in standard form:

(x - h)² + (y - k)² = r²

Substituting the values:

(x - 3)² + (y - (-1))² = (sqrt(13))²

(x - 3)² + (y + 1)² = 13

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Answer:

bottom option

inverse is opposite

Answer:

x = 2

Step-by-step explanation:

multiply (16/48) by 6 to get rid of the fraction and then you get x = 2

Answer:

see explanation

Step-by-step explanation:

note that \(3^{p+1}\) = \(3^{p}\) × 3 ( when multiplying exponents are added )

Given

\(\frac{3^{p+1}-3^{p} }{2.3^{p} }\) ← factor out \(3^{p}\) on numerator

= \(\frac{3^{p}(3-1) }{2.3^{p} }\)

= \(\frac{2.3^{p} }{2.3^{p} }\)

= 1

Answer:

The first one

Step-by-step explanation:

4 x 4 = 16  16 x 4= 64.

Step-by-step explanation:

Hey there!

Given;

-1b - 8 > -7

Take '-8' to right side.

-1b > -7+8

-1b > 1

b > -1

Hope it helps...

Answer:

36, 38, 40, 42, 44

Step-by-step explanation:

We can denote an even number as 2n (where n is a natural number).

Each consecutive even number will be 2 more than the previous number.

Let 1st number = 2n

⇒ 2nd number = 2n + 2

⇒ 3rd number = 2n + 4

⇒ 4th number = 2n + 6

⇒ 5th number = 2n + 8

Sum of all 5 numbers is 200.  

⇒ 2n + 2n + 2 + 2n + 4 + 2n + 6 + 2n + 8 = 200

⇒ 10n + 20 = 200

⇒ 10n = 180

⇒ n = 18

If n = 18, then 2n = 36

Therefore, the numbers are 36, 38, 40, 42, 44

Answer: 1. (p^2 - 6)(1 - q(p^2 - 6)) 2. (a - b)(z + a - b)

Step-by-step explanation:

In the first question think of p^2 - 6 as the letter A. You would get A - q A^2, factorizing it to get A(1-qA). Then substituting the A with the p^2 - 6, you would get (p^2 - 6)(1 - q(p^2 - 6))

Now in the next question, you need to understand the priniciple

(a - b) ^ 2 = (b - a) ^ 2

As a^2 - 2ab + b^2 = b^2 - 2ab + a^2

So we get z(a - b) + (a - b) ^ 2 and using the same technique from the last question, you get (a - b)(z + a - b)

Hope this helps!!!

Answer:

Step-by-step explanation:

\((x-h) ^2+(y-k) ^2 =r^2\)

The above equation is the general standard equation for the circle centered at (h,k) with radius r

Given that the equation of the circle is

\((x-2) ^2+(y+3) ^2 =25\)

Comparing this with the general equation we can get the center and the radius as

\((x-h) ^2+(y-k) ^2 =r^2\\(x-(2)) ^2+(y-(-3)) ^2 =5^2\)

We can now see that

h= 2

k= -3 and

r= 5

Answer:

1/3

Step-by-step explanation:

1 rise

3 run

The c.d.f of a random variable can be given as

Fx(x) = {-x/2, for x ≥ 0if x < 0,

where Fx(x) is the CDF of the random variable. We need to compute P(X ≥2).

We are given that the c.d.f. of a random variable is Fx(x) = {-x/2, for x ≥ 0if x < 0, for any real number x.

Now, let us see what happens when x = 2.

Then P(X ≥2) = 1 - P(X < 2)P(X < 2) = P(X ≤ 1)

We have Fx(x) = {-x/2, for x ≥ 0if x < 0

Let us compute

Fx(x) for x ≥ 0For x ≥ 0,Fx(x) = -x/2P(X ≤ x) = Fx(x) for x ≥ 0.For x < 0, P(X ≤ x) = 0.So, for 0 ≤ x < 2, P(X ≤ x) = Fx(x) = -x/2Now, P(X ≤ 1) = -1/2P(X ≤ 2) = -2/2 = -1.

Now, P(X < 2) = P(X ≤ 1) = -1/2. So, P(X ≥2) = 1 - P(X < 2) = 1 - (-1/2) = 3/2 = 1.5 (which is more than 1)

Hence, the probability P(X ≥2) cannot be calculated.

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Answer:

\(60\:\mathrm{cm^2}\)

Step-by-step explanation:

The total surface area of a figure can be found by adding the areas of the 2D shapes that make up the surface of it.

In this case, we can add up the areas of the square, two rectangles, and two triangles that make the figure up.

\(A=4\cdot 4 +4\cdot 3+4\cdot 5+\frac{1}{2}\cdot 2\cdot 3\cdot 4,\\A=16+12+20+12,\\A=\boxed{60\:\mathrm{cm^2}}\)

Answer:

  B.  An irrational number

Step-by-step explanation:

A rational number is one that can be written as a ratio (of integers).

An irrational number cannot be written as a ratio of integers.

Answer:

B

Step-by-step explanation:

An irrational number is something that doesn't have an end like pi it goes on forever so therefore it can't be written as a fraction.

Answer:

The answer is -4000.

Step-by-step explanation:

The answer is -4000 because you took money from your bank account, withdraw.

Answer

The slope of the function is 5.

Step-by-step explanation:

There is a 35% chance that fund A rises and fund B does not rise in price.

Probability is simply how likely something is to happen. Whenever we're unsure about the outcome of an event, we can talk about the probabilities of certain outcomes—how likely they are.

To calculate the probability that fund A rises and fund B does not rise in price, we need to multiply the probability of fund A rising (let's assume it is 50% for the sake of this example) by the probability of fund B not rising (which is 70%). So the probability would be:

0.5 (probability of fund A rising) x 0.7 (probability of fund B not rising) = 0.35 or 35%.

Therefore, there is a 35% chance that fund A rises and fund B does not rise in price.

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There are no solutions to the given logarithmic equation that satisfy the conditions.

Let's solve the logarithmic equation step by step:

log₃(x) + 7 = 11 - log₃(x - 80)

Combine logarithms

Using the property logₐ(M) + logₐ(N) = logₐ(MN), we can combine the logarithms on the left side of the equation:

log₃(x(x - 80)) + 7 = 11

Simplify the equation

Using the property logₐ(a) = 1, we simplify the equation further:

log₃(x(x - 80)) = 11 - 7

log₃(x(x - 80)) = 4

Rewrite in exponential form

The equation logₐ(M) = N is equivalent to aᴺ = M. Applying this to our equation, we get:

3⁴ = x(x - 80)

Convert to a quadratic equation

Expanding the equation on the right side, we have:

81 = x² - 80x

Set the equation equal to 0

Rearranging the terms, we get:

x² - 80x - 81 = 0

Solve for x

To solve the quadratic equation, we can factor or use the quadratic formula. However, upon closer examination, it appears that the equation does not have any integer solutions.

Check for extraneous solutions

Since we don't have any solutions from the quadratic equation, we don't need to check for extraneous solutions in this case.

Therefore, there are no solutions to the given logarithmic equation that satisfy the conditions.

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If the post office is 13 blocks away from the library and each block is 275 meters, approximately, the distance from the post office to the library, in miles, is 2.2 miles.

To determine the distance or the number of miles from the post office to the library, we use unit conversions and mathematical operations (multiplication and division).

Using multiplication, the number of blocks is converted to meters.

The distance is converted from meters to miles by division.

The distance of a block in the city = 275 meters

The number of blocks from the library to the post office = 13 blocks

The distance from the post office to the library = 3,575 meters (13 x 275)

1,609.34 Meters = 1 Miles

The distance in miles from the post office to the library = 2.2 miles (3,575/1,609.34)

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The measures of x are obtained with the Pythagorean Theorem, as follows:

1. x = 10.2.

2. x = 7.2.

3. x = 13.7.

4. x = 36.2.

5. x = 10.7.

The Pythagorean Theorem is a geometry axiom which states that for a right triangle, the length of the hypotenuse squared is equals to the sum  of the lengths of the sides squared.

Hence, for item 1, we have that:

x² + 16² = 19²

x = square root(19² - 16²)

x = 10.2.

For item 2, we have that:

x² + 12² = 14²

x = square root(14² - 12²)

x = 7.2.

For item 3, we have that:

x² + 9.2² = 16.5²

x = square root(16.5² - 9.2²)

x = 13.7.

For item 4, we have that:

x² = 15² + 33²

x = square root(15² + 33²)

x = 36.2.

For item 5, first we find the side of the top right triangle, hence:

h² + 16² = 25²

h = square root(25² - 16²)

h = 19.2.

Then the value of x is obtained as follows:

x² + 19.2² = 22²

x = square root(22² - 19.2²)

x = 10.7.

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In general, observational studies are more problematic than randomized controlled trials because they can produce spurious relationships.

Observational studies rely on the natural variation in exposures and outcomes that occur in the population, without any intervention or manipulation by the researcher.

This can lead to confounding variables, which are factors that are associated with both the exposure and the outcome and can produce a false association between them.

Randomized controlled trials, on the other hand, assign participants to different exposure groups at random, which reduces the risk of confounding and allows for a more accurate assessment of causality.

Therefore, researchers must be cautious when interpreting observational studies and consider the potential for spurious relationships.

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In a 2 x 2 between-subjects factorial experiment, there are a total of four treatment conditions in the experiment, and each participant serves in one condition(s).

In a 2 x 2 between-subjects factorial experiment, there are a total of four treatment conditions in the experiment, and each participant serves in one condition. The four conditions in a 2 x 2 between-subjects factorial experiment are created by manipulating two independent variables, each with two levels.

The levels of these independent variables are crossed together to create four unique conditions.The factorial experiment design is used to analyze the effect of multiple independent variables on a dependent variable. When the levels of each independent variable are combined in a factorial design, this results in treatment conditions.

Each participant serves in one condition in a between-subjects design. Because each condition represents a distinct treatment in a factorial design, each participant serves in one treatment condition only. Therefore, in a 2 x 2 between-subjects factorial experiment, each participant serves in one of the four treatment conditions.

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Answer: 18

Step-by-step explanation:

150/100 = 1.5

12(1.5) = 18

By answering the given question, we may state that Therefore, equation

8/15 ÷ 2/5 = 4/3.

Using the equals symbol (=) to indicate equivalence, a math equation links two statements. Algebraic equations prove the equality of two mathematical expressions by a mathematical assertion. The equal sign, for example, provides a gap between the numbers 3x + 5 and 14 in the equation 3x + 5 = 14. You can use a mathematical formula to understand the connection between the two phrases that are written on opposite sides of a letter. Most of the time, the logo and the particular software match. e.g., 2x - 4 = 2 is an example.

divide two fractions, we multiply the first fraction by the reciprocal of the second fraction.

8/15 ÷ 2/5

is the same as

8/15 x 5/2

Now we can simplify by canceling common factors:

= 2*(2/3)

= 4/3

Therefore,

8/15 ÷ 2/5 = 4/3.

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Answer:

y = 1/4x + 1/2 and x = -2 +4y

Step-by-step explanation:

Solving it in a way that x/4 is a fraction and not division so you would make that 1/4x. y = x/4 +1/2 x/4 is 1/4x so then you subtract 1/2 from both sides to get y - 1/2 = 1/4x. You can then divide 1/4 on both sides. -1/2 divided by 1/4 is -2 and 1/4y. This will get your answer of x = 1/4y -2 for x. Y is just 1/4x + 1/2

Answer:

12/6 simplified to lowest terms is 2/1.

Step-by-step explanation:

Divide both the numerator and denominator by the HCF

12 ÷ 6

6 ÷ 6

Reduced fraction:

12/6 simplified to lowest terms is 2/1.

Answer: 2:1

Step-by-step explanation:

12:6

Both left and right can be divided by 6, like a fraction, reduce.

= 2:1

Answer:

\(50.27\) \(cm\)

Step-by-step explanation:

\(\pi r^2h \times 1/3\)

\(\pi \times 2^2 \times 12 \times 1/3\)

\(\pi \times 4 \times 12 \times 1/3\)

\(16\pi\)

\(\approx 50.265482\)

Answer:

16π cm^3  or 50.27 cm^3 to the nearest hundredth.

Step-by-step explanation:

V = 1/3 π r^2 h

= 1/3 π 2^2 12

= 16π cm^3.

Answer:

i want some kitty Kat