Select the correct answer. Which point lies on the circle represented by the equation x2 + (y − 12)2 = 252? A. (20,-3) B. (-7,24) C. (0,13) D. (-25,-13) Reset Next

By use of determinants, the solution to the system of linear equations is: x = - 17 / 39, y = 71 / 39, z = 22 / 39

In this problem we find a system of three linear equations with three variables. This kind of system can be solved by means of determinants. For this case, we can use Sarrus law and the following definition:

x = D₁ / D, y = D₂ / D, z = D₃ / D

[tex]D = \left|\begin{array}{ccc}1&- 1&3\\4&1&- 2\\2&- 3&1\end{array}\right|[/tex]

D = 1 - 36 + 4 - 6 + 4 - 6

D = 9 - 48

D = - 39

[tex]D_1 = \left|\begin{array}{ccc}- 4&- 1&3\\1&1&- 2\\- 7&- 3&1\end{array}\right|[/tex]

D₁ = - 4 - 9 - 14 + 21 + 1 + 24

D₁ = - 29 + 46

D₁ = 17

[tex]D_{2} = \left|\begin{array}{ccc}1&-4&3\\4&1&- 2\\2&- 7&1\end{array}\right|[/tex]

D₂ = 1 - 84 + 16 - 6 + 16 - 14

D₂ = - 104 + 33

D₂ = - 71

[tex]D_{3} = \left|\begin{array}{ccc}1&- 1&-4\\4&1&1\\2&- 3&-7\end{array}\right|[/tex]

D₃ = - 7 + 48 - 2 + 8 - 28 + 3

D₃ = 22

x = - 17 / 39

y = 71 / 39

z = 22 / 39

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Answer:

it is 17.25 it self

Step-by-step explanation:

because if the number was 17.24 upto 17.21 and less the number is 17.20 and if the number was 27.26 upto 17.29 it will rounded to 17.30.

l hope it would help

may i get branliest

the approximate chance that a single randomly chosen student scores less than 525 on the GRE is 0.4279 or about 42.79%.

What is probability?

Probability is a measure of the likelihood of an event occurring.

To answer this question, we need to standardize the score of 525 using the mean and standard deviation provided:

z = (x - mean) / standard deviation

where x is the score we want to find the probability for, mean is the mean score of the population, and standard deviation is the standard deviation of the population.

In this case:

z = (525 - 544) / 103 = -0.184

We can then use a standard normal distribution table or calculator to find the probability that a randomly chosen student scores less than 525, which is equivalent to finding the probability that a standard normal variable is less than -0.184:

P(z < -0.184) = 0.4279

Therefore, the approximate chance that a single randomly chosen student scores less than 525 on the GRE is 0.4279 or about 42.79%.

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All the quadratic equation solution is done using general formula is true statement.

And the solution of quadratic equation is given by real number is false because it may have complex roots.

Every quadratic equation can be solved with the general formula.

This is true.

The general formula for solving a quadratic equation of the form

ax² + bx + c = 0 is equal to,

x = [-b ± √(b² - 4ac)] / 2a

This formula can be used to find the solutions to any quadratic equation.

Quadratic equations do not always have a solution in real numbers.

There are other types of solutions.

This is known as having complex roots.

For example, the equation x² + 1 = 0 has no real solutions.

Since the square of any real number is positive and cannot equal -1.

However, it does have complex solutions, which involve the imaginary unit i that is  i = √(-1).

The solutions to x² + 1 = 0 are x = i and x = -i, both of which are complex numbers.

Therefore, the quadratic equation solved using general formula is true while quadratic equation have real solution is false as it may have complex roots.

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Because the y-intercept is (0, 1), the correct option must be the second option y = 3^x

Here we can see that we have an exponential function, so it can be written as:

f(x) = A*(b)^x

where A is the initial value and b the base.

When x = 0 we can see that the graph passes through y = 1, then:

f(0) = 1 = A*(b)^0

        1 = A

So our function is of the form:

f(x) = b^x

The only one of that form is the second option, so that is the correct one.

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The base of the exponential functions is 5.

Exponential functions have the form y = a·bˣ,

where a is a constant, x is a variable and b is the base of the function.

For example, if you have the function f(x) = 2·3ˣ, the base will be 3.

In this case we have:

f(x) = (1/2)·5ˣ

Therefore, the base of the function is 5.

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The number of pies in each of the other locations rows are 32 and 18.

Given that, the downtown location has 4 rows in its display. The uptown location has 6 rows in its display.

At the downtown location, there would be 8 pies in each row since the display is a 6×4=32 rectangle.

At the uptown location, there would be 3 pies in each row since the display is a 6×18=18 rectangle.

Therefore, the number of pies in each of the other locations rows are 32 and 18.

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Jasper's z-score for body fat percentage would be 0.26. This means that Jasper's body fat percentage is 0.26 standard deviations above the mean body fat percentage for men in the U.S.

To calculate the z-score of Jasper's body fat percentage, we use the formula:

z-score = (x - mu) / sigma

where:

x = Jasper's body fat percentage (17.3)

mu = the mean body fat percentage for men in the U.S. (16.75)

sigma = the standard deviation of body fat percentage for men in the U.S. (2.1)

Substituting the values, we get:

z-score = (17.3 - 16.75) / 2.1

z-score = 0.26

Therefore, Jasper's z-score for body fat percentage would be 0.26. This means that Jasper's body fat percentage is 0.26 standard deviations above the mean body fat percentage for men in the U.S.

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Answer:

Probability that the first marble drawn is blue is 10/27, since there are 10 blue marbles and 27 altogether

Probability that the second marble drawn is green is 5/26, since there are 5 green marbles and 26 altogether (a blue one is gone, remember?)

Probability that the third marble drawn is yellow is 12/25, since there are 12 yellow marbles and 25 altogether (both a blue and a green one are now gone)

Probability that all happen is product of all individual odds = 10/27*5/26*12/25 = 3.42%

Sure, I can help you create a tree diagram for this problem.

Start with the first level of choices: Shirt, Skirt, or Blazer.

(see attachment)

Each branch represents a possible choice, and you can count the number of endpoints (outfit combinations) to find the total number of possible outfits.

Using this tree diagram, there are a total of 30 possible outfits that Casey can make.

Answer:x^2 * 5/y^5

Step-by-step explanation:

Answer:

14m^2

Step-by-step explanation:

Area is the space taken up by a two dimensional object.

The formula is (1/2) base times height for only triangles.  Other shapes or objects use different formulas.

7m * 4m = 28m^2

28m^2 * 1/2

28m^2/2

Divide 2 into 28, which is 14.  And two variables multiplied by each other become variable squared or to the second power.

14m^2

So, the area of the triangle is 14m^2.

The height of the hill is approximately 60.62 meters.

Height often refers to the perpendicular distance between the base of a geometric shape (such as a triangle, rectangle, or cylinder) and its highest point.

To solve this problem, we can use the tangent function, which relates the opposite and adjacent sides of a right triangle to the tangent of an angle.

Let h be the height of the hill, and let d be the horizontal distance from the foot of the hill to the point on the ground. Then, we can draw a right triangle with the height of the hill as the opposite side, the distance d as the adjacent side, and the angle of depression (60 degrees) as the angle between the hypotenuse and the adjacent side.

Using the tangent function, we can write:

tan(60) = h / d

We know that d = 35 meters, so we can substitute that into the equation and simplify:

tan(60) = h / 35

We can solve for h by multiplying both sides by 35 and simplifying:

h = 35 * tan(60)

Using a calculator, we find:

h ≈ 60.62 meters

Therefore, the height of the hill is approximately 60.62 meters.

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(A) To use the exponential formula, we need to determine the values of P, r, and n.

P = $8,500, the initial deposit

r = 2.6% = 0.026, the annual interest rate

n = 4, the number of times interest is compounded per year (quarterly)

(B) The formula for the future value of the account is:

A = [tex]P(1 + r/n)^{nt}[/tex]

where t is the time in years. Plugging in the values from part (A) and t = 9, we get:

A = [tex]$8,500(1 + 0.026/4)^{(4×9)}[/tex] = $11,169.62

Therefore, Deshawn will have $11,169.62 in the account after 9 years.

(C) The annual percentage yield (APY) takes into account the effect of compounding on the interest rate. The formula for APY is:

APY = [tex](1 + r/n)^{n}[/tex] - 1

Plugging in the values from part (A), we get:

APY = [tex](1 + 0.026/4)^{4}[/tex] - 1 = 0.02639

Therefore, the APY for the savings account is 2.639%.

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We can use the given equation to solve for the time at which the soccer ball lands. When the soccer ball lands, its height will be zero, so we can set h=0 and solve for t.

h = -4.9t^2 + vt + s

0 = -4.9t^2 + 4.9t + 0 (since the initial height, s, is 0)

0 = t(4.9t - 4.9)

t = 0 or t = 1

We can discard the solution t = 0, since this corresponds to the initial time when the ball is kicked. Therefore, the soccer ball will land after approximately 1 second.

Answer: 9x - 5y + z

Step-by-step explanation:

Answer: E: 71/100

Step-by-step explanation:

The missing reason in the given two column proof is: Reason 3: Converse of corresponding angles theorem

A two-column proof uses a table to present a logical argument and assigns each column to do one job, and then the two columns work in lock-step to take a reader from premise to conclusion.

The complete two column proof in the question is:

Statement 1: ∠WVX ≅ ∠QSR

Reason 1: Given

Statement 2: ∠QSR ≅ ∠TSV

Reason 2: Vertical Angle Theorem

Statement 3: ∠WVX ≅ ∠TSV

Reason 3: Converse of corresponding angles theorem

The Converse of the Corresponding Angles Theorem states that If two lines and a transversal form corresponding angles that are congruent, then it means that the lines are parallel.

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Answer:

An ecosystem is a biological community of interacting organisms (including animals, plants, and microorganisms) and their physical environment (such as air, water, and soil).

Step-by-step explanation:

The function h(x) is increasing on the interval (-2, ∞). The correct answer is an option (C).

Given the function h of x equals 2 times the square root x plus 2 end root minus 3.

It can be written as: h(x) = 2√(x +2) - 3

Now, take the derivative of h(x):

h'(x) = (2/2√x+2) = 1/√x+2

Since the denominator is always positive, the sign of the derivative is determined by the numerator.

The numerator is positive for all x > -2, meaning that the function is increasing on that interval.

Therefore, the function is increasing on the interval (–2, ∞).

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Answer:

160 degrees

Step-by-step explanation:

If the number of the terms will be 14. Then the sum of the series will be 595.

We know that,

A series is a sum of sequence terms. That is, it is a list of numbers with adding operations between them.

First term (a₁) = 10

Common difference (d) = 5

If the nth term is 75, then the number of the terms will be

75 = 10 + (n - 1)5

65 = (n - 1)5

13 = n - 1

n = 14

Then the sum of the series will be

S = a₁ x n + [n (n - 1)d] / 2

S = 10 x 14 + 14 x 13 x 5 / 2

S = 140 + 455

S = 595

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The complete question is given below.

Find the sum of each arithmetic series described or shown below. The sum of multiples of five from 10 to 75, inclusive.

Answer:

The system has a solution at (-20,-2).

Step-by-step explanation:

To find the solution of the system, you need to find where the two equations intersect, or are equal to each other. You may do this with a calculator, but I find it much easier using a graphing software online, like Desmos.

Once I graphed these two equations, I found that they intersected each other at the point (-20,-2), so the system has ONE solution.

At x=-20, both equations have y=-2.

**I would also like to note that the second equation, y will ALWAYS equal -2, so you're really just finding where the first equation equals that as well.**

Answer:

28

Step-by-step explanation:

Answer:

28

Step-by-step explanation:

Simplifying the logarithm expression 7 log 3 k + 6 log 3 m - 9 log 3 n, we have log3(k^7m^6/n^9)

From the question, we have the following parameters that can be used in our computation:

7 log 3 k + 6 log 3 m - 9 log 3 n.

Apply the power rule of logarithm

So, we have

log3k^7 + log3m^6 - log3n^9

Apply the product rule of logarithm

So, we have

log3(k^7m^6/n^9)

Hence, the solution is log3(k^7m^6/n^9)

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Answer:3655.29

Step-by-step explanation:

First step is null hypothesis and alternative test and next steps includes testing these hypothesis.

To conduct hypothesis testing on these data, we need to follow the following steps:

Step 1, State the null hypothesis and alternative hypothesis

Null Hypothesis (H0), There is no significant difference in life expectancy between people who eat fruits and vegetables and people who do not eat fruits and vegetables.

Alternative Hypothesis (Ha), People who eat fruits and vegetables have a higher life expectancy than people who do not eat fruits and vegetables.

Step 2, Decide the level of significance (alpha)

Let's assume the level of significance to be 0.05 (5%).

Step 3, Determine the test statistic and the critical value

We will use a two-sample t-test since we are comparing two independent samples. We can use Excel or any statistical software to calculate the test statistic and the critical value.

Using Excel, the test statistic (t) is -1.98, and the critical value (t_critical) is ±2.306.

Step 4, Determine the p-value

The p-value is the probability of obtaining a test statistic as extreme or more extreme than the observed one, assuming the null hypothesis is true.

Using Excel, the p-value is 0.077.

Step 5, Make a decision and interpret the results

Since the p-value (0.077) is greater than the level of significance (0.05), we fail to reject the null hypothesis. There is insufficient evidence to conclude that people who eat fruits and vegetables have a higher life expectancy than people who do not eat fruits and vegetables.

Therefore, we can conclude that there is no significant difference in life expectancy between people who eat fruits and vegetables and people who do not eat fruits and vegetables, based on the given data. However, we should keep in mind that this conclusion is based on a small sample size and may not be generalizable to the entire population.

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Thus, the pre-split market cap for Rockville corporation is found to be -  $145,912,000,000.

Stock splits have no impact on the market capitalization as a whole. Just the share price and total number of outstanding shares are impacted. Overall, we have doubled the number of shares outstanding while halving the share price, having no impact on the market capitalization.

The number of shares of a firm grow when it announces a stock split, but the market capitalization stays the same. Although existing shares were split, the underlying value was not altered. Price per share decreases as the number of shares rises.

Given data:

Number of shares = 2.3 billion = 2,300,000,000

Market price = $63.44

Pre-split market cap = Number of shares x Market price

Pre-split market cap = 2,300,000,000 x $63.44

Pre-split market cap = $145,912,000,000

Thus, the pre-split market cap for Rockville corporation is found to be -  $145,912,000,000.

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Complete Question:

Yesterday the Rockville corporation instituted a 2-for-1 split. Before the split, the market share price was $63.44 per share and the corporation had 2.3 billion shares outstanding. ?

What was the pre-split market cap for Rockville?

Answer: x = 50

Step-by-step explanation:

In the given image, the alternate interior angles are equal. Therefore, 80 + x = 180 - 50 (since straight angles measure 180 degrees). Simplifying this equation, we get 130 + x = 180, which gives us x = 50 degrees. Thus, A||B when x = 50 degrees.