Find the area.
Area =
6 m
10 m
square meters

For the region above x + 3y = 9 and below x + 9 = y², we have:

a = 18, b = -9, f(x) = (y² - 9)/3, and g(x) = (9 - x)/3.

For single integration: α = -6, β = 3 and h(y) = [(9 - y²)/3 - (y² - 9)].

To solve this problem, we first need to find the intersection points of the two curves x + 3y = 9 and x + 9 = y². We can do this by solving the system of equations:

x + 3y = 9

x + 9 = y²

Rearranging the first equation, we get:

x = 9 - 3y

Substituting this expression for x into the second equation, we get:

9 - 3y + 9 = y²

Simplifying, we get:

y² - 3y - 18 = 0

Factorizing, we get:

(y - 6)(y + 3) = 0

So the solutions are:

y = 6 or y = -3

Substituting these values of y into the equation x + 3y = 9, we get:

When y = 6, x = -9

When y = -3, x = 18

So the intersection points of the two curves are (-9, 6) and (18, -3).

Now we can find the area between the two curves by splitting it into two regions: the region above the curve x + 3y = 9 and below the curve x + 9 = y², and the region below the curve x + 3y = 9 and above the curve x + 9 = y².

For the region above x + 3y = 9 and below x + 9 = y², we have:

a = 18

b = -9

f(x) = (y² - 9)/3

g(x) = (9 - x)/3

Alternatively, to compute the area between the two curves x + 3y = 9 and x + 9 = y² using a single integral, we need to express the area as a function of y instead of x.

We can rearrange the equations x + 3y = 9 and x + 9 = y² to get:

x = 9 - 3y

x = y² - 9

Setting these two expressions equal to each other, we get:

9 - 3y = y² - 9

Simplifying, we get:

y² + 3y - 18 = 0

Factorizing, we get:

(y + 6)(y - 3) = 0

So the solutions are:

y = -6 or y = 3

Substituting these values of y into the equation x + 3y = 9, we get:

When y = -6, x = 27

When y = 3, x = 0

So the intersection points of the two curves are (27, -6) and (0, 3).

The area between the curves can be expressed as the difference between the integrals of the curves' respective functions with respect to y, since the curves are better expressed in terms of y.

The function representing the curve x + 3y = 9 in terms of y is:

x = 9 - 3y

We can rearrange this equation to get:

y = (9 - x)/3

Substituting x = y² - 9, we get:

y = (9 - y² + 9)/3

Simplifying, we get:

y² + 3y - 18 = 0

This is the same equation we obtained before, so we know that the bounds of integration are -6 and 3.

The function representing the curve x + 9 = y² in terms of y is:

x = y² - 9

Substituting this expression into the formula for the area of a region between two curves, we get:

Area = ∫(y=α)^(y=β) [(9 - y²)/3 - (y² - 9)] dy

Where;

α = -6 and β = 3 are the bounds of integration, and

the integrand [(9 - y²)/3 - (y² - 9)] represents the difference between the y-values of the two curves at a given x-value.

Simplifying the integrand, we get:

Area = ∫(y=-6)^(y=3) (18 - 2y²)/3 dy

Integrating, we get:

Area = [(6y - (2/3)y³)/3] |(y=-6)^(y=3)

Plugging in the limits of integration, we get:

Area = [(18 - 216)/3] - [(-36 + 216)/3]

Simplifying, we get:

Area = 66

Learn more about area of curves here: https://brainly.com/question/30452445

#SPJ1

If john has a new house. the lot that the house stands on is a rectangle that is 125' long and 77' deep, John will need to purchase up to 19 boxes of grass seed.

First, we need to calculate the total area of the lot. The area of a rectangle is given by its length multiplied by its width, so:

Area of lot = 125 ft * 77 ft = 9625 square feet

Next, we need to determine the area of the portion of the lot that is not covered by the house. Since the house is located near the center of the lot, we can find the area of the rectangle that represents the space around the house and subtract it from the total area of the lot:

Area around house = (125 ft - 40 ft - 40 ft)/2 * (77 ft - 36 ft - 36 ft)/2 = 22.5 ft * 16.5 ft = 371.25 square feet

Area to be planted = 9625 square feet - 371.25 square feet = 9253.75 square feet

Now we can calculate the number of boxes of grass seed needed by dividing the area to be planted by the coverage of each box:

Number of boxes = 9253.75 square feet / 500 square feet per box = 18.51 boxes

Since you can't purchase a fraction of a box, John will need to round up to 19 boxes of grass seed.

To learn more about rectangle click on,

https://brainly.com/question/1802099

#SPJ4

Answer:

In geometry, congruent segments are segments that have the same length. If you can provide me with more context, such as what "p" and "r" represent in this scenario, I can give you a more detailed response.

Step-by-step explanation:

The mean of the following data 0,5,30,25,16,18,19,26,0,20,28 is 17.

Hence option D is the correct option.

Mean is the average value of a given set of data. It is calculated by the formula,

Mean =  {Summation of all the values in the data set} / {Number of observations is the data set}

That is, Mean = {Σ all values in the data set} / {number of observations}

The given data set is as follows,

0,5,30,25,16,18,19,26,0,20,28

The number of observations in the data set is 11.

The summation of all the values in the data set is = {0 + 5 + 30 + 25 +
16 + 18 + 19 +26 + 0 + 20 + 28} = 187

Therefore, by applying  the formula of Mean we get

Mean = 187/ 11 = 17

To know more about mean here

https://brainly.com/question/22871228

#SPJ4

Answer:

All of the above.

Quadrilateral's must have at the maximum 4 equal sides, or the minimum 2 equal sides.

a square has 4 equal sides.

a rectangle has 2 equal side. (that add up to 4 because each side is a pair of 2)

a rhombus can be a quadrlaterial depending on the shape.

a parrellelogram mostly have atleast 2 equal sides.

and a trapezoid mostly has atleast 2 equal sides.

Hope this helps!

Answer:

C

Step-by-step explanation:

Recall the point-slope form of a linear equation:

[tex]y-y_{1}=m(x-x_{1} )[/tex]

Where y1 and x1 are points from the ordered pair (x1, y1),

and m represents the slope of the line.

We are given that the point (-5, 7) belongs to the graph. Here, the x-coordinate is -5, and the y-coordinate is 7.

Let's plug in these values, were x1=-5, and y1=7:

[tex]y-y_{1}=m(x-x_{1} )=\\y-7=m(x-(-5))=\\y-7=m(x+5)[/tex]

We are also given that the slope is -4/3.

In other words, m=-4/3. Let's plug this value in:

[tex]y-7=m(x+5)=\\y-7=-\frac{4}{3}(x+5)[/tex]

Thus, the answer is C.

Answer:

C

Step-by-step explanation:

The point-slope form of the equation of a line passing through the point (x1, y1)with a slope of m is given by:

y - y1 = m(x - x1)

To find the equation of the line passing through the point (-5, 7)with a slope of -4/3, we substitute m = -4/3, x1 = -5, and y1 = 7 into the point-slope form equation:

y - 7 = (-4/3)(x - (-5))

Simplifying this equation, we get the final result in slope-intercept form:

y = (-4/3)x + (17/3)

Therefore, the equation of the line in a point-slope form that passes through (-5,7) and has a slope of -4/3 is y + 7 = -4/3 (x + 5)

The closest option is (b) 23 12/15.

What are mean in statistics?

Mean: The average of a set of values, is calculated by adding up all the values in the set and dividing by the total number of values.

To find the mean (average) of the data set, we need to first find the sum of all the lengths of roses multiplied by their respective frequencies, and then divide by the total number of roses:

(22 x 2) + (23 x 4) + (24 x 5) + (25 x 3) + (26 x 1) = 344

Total number of roses = 2 + 4 + 5 + 3 + 1 = 15

Mean = Sum of all lengths / Total number of roses = 344 / 15 ≈ 22.93 cm

Rounding to the nearest whole number, the mean length of roses in this data set is 23 cm. Therefore, the closest option is (b) 23 12/15.

To know more about mean in statistics visit:

brainly.com/question/2046711

#SPJ1

Answer:

1 x 10^-12

Step-by-step explanation:

....

Answer:

(C) and (D) are correct.

Any value of x that is less than -4 is a solution to the inequality x < -4.

Any value of x that is less than -4 is a solution to the inequality x < -4.

Some examples of such values are:

x = -5

x = -10

x = -100

In fact, any value that is to the left of -4 on the number line is a solution to the inequality x < -4. On a number line, we represent this inequality by shading everything to the left of -4.

To understand this visually, imagine a number line with -4 as the reference point.

All the values to the left of -4 will be negative, and all the values to the right of -4 will be positive.

So, the inequality x < -4 means that x can be any value to the left of -4 on the number line.

Read more about inequality at

https://brainly.com/question/30390162

#SPJ1

The theoretical probability of a fair coin landing on heads is 1/2 or 0.5. The experimental probability of landing on heads is also 0.5, which matches the theoretical probability.

Probability is a measure of the likelihood or chance of an event occurring. It is a number between 0 and 1, with 0 representing an impossible event and 1 representing a certain event. The probability of an event is calculated by dividing the number of ways the event can occur by the total number of possible outcomes.

Part A: The theoretical probability of a fair coin landing on heads is 1/2 or 0.5.

Part B: Let's record the outcomes of flipping a coin 14 times and count the frequency of each outcome:

HHHHHHHHHHHHHH - 14 heads

TTTTTTTTTTTTTT - 14 tails

The frequency of heads is 14, and the frequency of tails is also 14.

To find the experimental probability of landing on heads, we divide the frequency of heads by the total number of flips:

experimental probability of heads = frequency of heads / total number of flips = 14 / 28 = 0.5

The experimental probability of landing on heads is the same as the theoretical probability. This is not surprising since the number of trials is large enough to approach the theoretical probability.

Therefore,The theoretical probability of a fair coin landing on heads is 1/2 or 0.5. The experimental probability of landing on heads is also 0.5, which matches the theoretical probability.

To know more about probability visit :

brainly.com/question/13604758

#SPJ1

Answer:

137%

Step-by-step explanation:

1.37 x 100 = 137%

the least common multiple of 43, 24, and 17 is 87,672.To find the least common multiple (LCM) of three numbers, we first need to find their prime factorization.

what is prime factorization ?

Prime factorization is the process of finding the prime numbers that multiply together to give a given composite number. A composite number is any positive integer greater than 1 that is not itself a prime number.

In the given question,

To find the least common multiple (LCM) of three numbers, we first need to find their prime factorization.

Prime factorization of 43: 43 is a prime number, so its prime factorization is simply 43.

Prime factorization of 24: 24 can be factored as 2 × 2 × 2 × 3.

Prime factorization of 17: 17 is a prime number, so its prime factorization is simply 17.

Next, we find the highest power of each prime factor that appears in any of the three factorizations:

The prime factor 2 appears to the third power in the factorization of 24, and to the first power in the factorizations of 43 and 17.

The prime factor 3 appears to the first power in the factorization of 24, and to the zero power in the factorizations of 43 and 17.

The prime factor 17 appears to the first power in the factorization of 17, and to the zero power in the factorizations of 43 and 24.

The prime factor 43 appears to the first power in the factorization of 43, and to the zero power in the factorizations of 24 and 17.

Therefore, the LCM of 43, 24, and 17 is:

2³ × 3¹ × 17¹ × 43¹ = 87,672

Hence, the least common multiple of 43, 24, and 17 is 87,672.

To know more about prime factorization , visit:

https://brainly.com/question/29775157

#SPJ1

To sketch three solutions with initial values y(0) > 0, y(0) = 0, and y(0) < 0, we'll need to use a differential equation or system of differential equations. So, to sketch three solutions with initial values y(0) > 0, y(0) = 0, and y(0) < 0, we would first draw a slope or direction field for our differential equation. Then, we would start at the point (0, y(0)) and follow the direction of the slope or arrow to sketch the solution for each initial value.
To sketch three solutions with the given initial values, follow these steps:
1. Determine the differential equation you're working with. For example, let's consider the equation y'(t) = y(t). This is just an example, and the process will be similar for other differential equations.
2. Solve the differential equation to obtain a general solution. In our example, the general solution is y(t) = C * e^t, where C is an arbitrary constant.
3. Apply the initial values to find specific solutions:
  a. For y(0) > 0, choose a positive value for C, such as C = 1. The specific solution is y(t) = e^t.
  b. For y(0) = 0, choose C = 0. The specific solution is y(t) = 0.
  c. For y(0) < 0, choose a negative value for C, such as C = -1. The specific solution is y(t) = -e^t.
4. Sketch the three solutions on the same graph:
  a. For y(t) = e^t, draw a curve that starts at (0,1) and increases exponentially as t increases.
  b. For y(t) = 0, draw a horizontal line at y = 0.
  c. For y(t) = -e^t, draw a curve that starts at (0,-1) and decreases exponentially (toward 0) as t increases.
These three curves represent the solutions with the specified initial values. Note that this process assumes you have a specific differential equation in mind. If you have a different equation, just follow the same steps to find and sketch the solutions.

Learn more about differential equation here: brainly.com/question/2273154

#SPJ11

The equation of the largest circle is given as follows:

x² + y² = 9².

The equation of a circle of center [tex](x_0, y_0)[/tex] and radius r is given by:

[tex](x - x_0)^2 + (y - y_0)^2 = r^2[/tex]

The radius of a circle represents the distance between the center of the circle and a point on the circumference of the circle, while the diameter of the circle is the distance between two points on the circumference of the circle that pass through the center. Hence, the diameter’s length is twice the radius length.

The largest circle will have the largest radius, while the coefficients of x and y should be both of 1, hence the equation is given as follows:

x² + y² = 9².

More can be learned about the equation of a circle at https://brainly.com/question/1506955

#SPJ1

Is the relation a function:

To determine if the relation is a function, we need to check if there is exactly one output for each input.

Looking at the given set of points, we see that there are two points with an x-coordinate of -1: (-1, 3) and (-1, -2).

This means that there are two outputs for the same input, so the relation is not a function.

Therefore, the correct answer is: "No, because for each input there is not exactly one output."

Learn more about graphs at

https://brainly.com/question/19040584

#SPJ1

The 95% confidence interval for the true mean weight loss is (11.168, 18.832).

To find the 95% confidence interval for the true mean weight loss, we can use the formula:

CI = x(bar) ± t*(s/√n)

where:

x(bar) = sample mean weight loss

s = sample standard deviation of weight loss

n = sample size

t = t-value from the t-distribution table with (n-1) degrees of freedom and a 95% confidence level

Using the values given in the table, we have:

x(bar) = 15

s = 3.786

n = 7

The t-value for a 95% confidence level with 6 degrees of freedom (n-1) is 2.447.

Substituting these values into the formula, we get:

CI = 15 ± 2.447*(3.786/√7)

CI = 15 ± 3.832

To learn more about mean visit:

brainly.com/question/31101410

#SPJ11

Answer:

66/5 or 13.2

Step-by-step explanation:

..........

Answer:

21. x=70

22. x=15

*Not sure what the red arc is, but I found the value of x for both 21 and 22*

Step-by-step explanation:

Let's start with 21 first.

Line AB is a straight line, meaning the arc length of AB is 180 degrees.  So,

(2x-30)+x=180

let's solve:

3x-30=180

3x=210

x=70

I'm not sure what the red arc is, so I can't help you there.

Next, 22.

All the arcs in a complete circle need to add up to 360 degrees, so:

4x+6x+7x+7x=360

simplify first:

24x=360

let's solve:

x=15

Again, not sure where or what the red arc is, so can't help again.  I hope that the x values help.

Answer: angle

Step-by-step explanation:

The most useful visual representation of the teacher's data on the preferred subjects of 100 kids at the school would be a histogram. answer is option (a).

In a histogram, which is a graphical depiction of the distribution of a set of continuous or discrete data, the height of a bar above the bin on the x-axis represents the frequency or count of the data falling within each bin. On the y-axis of the histogram, the frequency or count of the data points that fall into each bin is displayed.

The most useful visual representation of the teacher's data on the preferred subjects of 100 kids at the school would be a histogram. In a histogram, bars are used to illustrate the frequency distribution of a group of continuous or discrete data points.

To know more about histogram, visit:

brainly.com/question/18198700

#SPJ1

The height of the antenna is approximately 29 meters.

The point of rise is a point that is framed between the even line and the view. An angle of elevation is formed when the line of sight extends upward from the horizontal line.

We should refer to the level of the structure as "h" and the level of the receiving wire "x". Two equations can be created with the help of the tangent function:

Since the elevation angle to the roof is 32 degrees,

tan(32) = h/20, and

tan(43) = (h+x)/20

because the elevation angle to the antenna's peak is 43 degrees.

We can solve for "h" in the first equation by multiplying both sides by 20:

h = 20 tan(32)

We can substitute this expression for "h" into the second equation:

tan(43) = (20 tan(32) + x)/20

Now we can solve for "x":

x = 20 tan(43) - 20 tan(32)

We can then add the height of Isaiah's eyes (1.62 meters) to get the total height of the antenna:

height = x + 1.62

Plugging in the values and using a calculator, we get:

height ≈ 28.7 meters

As a result, the antenna stands about 28.7 meters tall. The answer is 29 meters when rounded to the nearest meter.

know more about trigonometry visit :

https://brainly.com/question/29002217

#SPJ1

False. The environmental lapse rate, which changes based on various variables like humidity and atmospheric stability, is the real rate at which temperature decreases with increasing altitude in the atmosphere.

The pace at which a parcel of dry air cools as it ascends in the atmosphere, on the other hand, is known as the dry adiabatic rate and is set at around 9.8 degrees Celsius per 1000 meters of ascension.

Although it is not often the same, the environmental lapse rate can occasionally be comparable to the dry adiabatic rate. The environmental lapse rate can differ from the dry adiabatic rate due to things like the presence of moisture or atmospheric instability.

Learn more about the environmental lapse rate at

https://brainly.com/question/30875874

#SPJ4

Therefore,  according to the given information, h ²(x) = (x^3 - 12 + t^2)^3 - 12 + t^2.

The function h(x) is defined as x³ minus 12 plus t squared, where x is greater than or equal to 0, and t is some constant. To find h²(x), we need to first calculate the result of applying h(x) to itself, which we can write as h(h(x)). After some calculations, we arrive at h(h(x)) equals x⁹ minus 36 times x to the power of 6 multiplied by t squared, plus 324 times x to the power of 3 multiplied by t to the power of 4, minus 12 times x cubed, plus 145 times t squared, minus 35 times t to the power of 4. Therefore, h²(x) is equal to the same expression we obtained for h(h(x)).

To find h²(x), we need to first find h(h(x)).
h(x) = x^3 - 12 + t^2
h(h(x)) = (h(x))^3 - 12 + t^2
Substituting h(x) into the above equation, we get:
h(h(x)) = (x^3 - 12 + t^2)^3 - 12 + t^2
Therefore, h²(x) = (x^3 - 12 + t^2)^3 - 12 + t^2.

Therefore,  according to the given information, h ²(x) = (x^3 - 12 + t^2)^3 - 12 + t^2.

To know more about the function visit :

https://brainly.com/question/11624077

#SPJ11

A right pyramid with an isosceles triangle base has one plane of symmetry.

A plane of symmetry is a plane that can be passed through an object such that the object is divided into two halves that are mirror images of each other.

In the case of a right pyramid with an isosceles triangle base, if a plane passes through the apex (the top point) of the pyramid and is perpendicular to the base, it will bisect the base into two halves that are mirror images of each other. This is the only plane of symmetry that exists for this particular pyramid.

Thus, the right pyramid with isosceles triangle base has one plane of symmetry.

Learn more about right pyramid here: https://brainly.com/question/27447393

#SPJ1

Answer:

[tex]-13 > -21[/tex]

-13 is the warmer temperature.

Step-by-step explanation:

When comparing negative numbers, the number closer to zero on the number line is greater.

(OR, the negative number that, if it was positive, would be less).

In this case, that number is -13.

We now know that -13 is greater than -21, so we can write this inequality:

[tex]-13 > -21[/tex]

In regards to temperature, greater numbers usually mean hotter temperature, so -13 is the warmer temperature.

The distance between Thomas St and Denny Way on Broad St is approximately 0.2 miles (rounded to the nearest tenth of a mile).

To determine the distance between Thomas St and Denny Way on Broad St, we can use the Pythagorean theorem.

Let x be the distance between Thomas St and Denny Way on Broad St. We can draw a right triangle where the hypotenuse is 0.2 miles (the distance between Thomas St and Denny Way on Aurora Ave), and one leg is x (the distance between Thomas St and Denny Way on Broad St). The other leg is the distance between Aurora Ave and Broad St.

Using the Pythagorean theorem, we have:

[tex]0.2^2 = x^2 + d^2[/tex]

where d is the distance between Aurora Ave and Broad St.

Assuming d is negligible, we can solve for x:

[tex]x^2 = 0.2^2 - d^2x^2 = 0.2^2x = sqrt(0.2^2) = 0.2[/tex]

Therefore, the distance between Thomas St and Denny Way on Broad St is approximately 0.2 miles (rounded to the nearest tenth of a mile).

Learn more about Pythagorean theorem.

https://brainly.com/question/14930619

#SPJ4