if the diameter of a circle is 4x+12 then find the area?


please solve this question...this question is based on "multiplying binomials by binomials" ​

(a)To solve the system of equations, x^2 - y^2 = 16 and x^2 - y = 7, we can use substitution or elimination method to find the values of x and y.

(b) To graph the solution set of the system of inequalities, x^2 - y^2 > 7 and x^2 - y < 0, we need to plot the boundaries and shade the appropriate regions based on the given inequalities.

(a)Let's use the substitution method to solve the system of equations:

From the second equation, we can rewrite it as x^2 = y + 7.

Substituting this value of x^2 in the first equation, we get (y + 7) - y^2 = 16.

Rearranging the equation, we have -y^2 + y + 7 - 16 = 0.

Simplifying further, we get -y^2 + y - 9 = 0.

Now, we can solve this quadratic equation for y by factoring or using the quadratic formula.

After finding the values of y, we can substitute them back into the second equation to find the corresponding values of x.

(b)To graph the solution set, we first graph the boundaries of the inequalities. For x^2 - y^2 > 7, we draw the curve of the equation x^2 - y^2 = 7, which represents a hyperbola. For x^2 - y < 0, we graph the curve of the equation x^2 - y = 0, which represents a parabola opening upwards.

Next, we need to determine which regions satisfy the given inequalities. For x^2 - y^2 > 7, the shaded region lies outside the hyperbola. For x^2 - y < 0, the shaded region lies below the parabola.

By combining the shaded regions of both inequalities, we find the solution set of the system of inequalities. It includes the regions outside the hyperbola and below the parabola. We label the corners of the shaded region to indicate the solution set accurately.

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Distance values always the positive or absolute value of the difference between two values on a number line.

It should be noted that a number line is simply the straight line that's used to add or subtract the given set of numbers.

In this case, distance values always the positive or absolute value of the difference between two values on a number line.

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Answer:

B.

Step-by-step explanation:

The measure of the major arc along the perimeter of the circle between Stanley and Frank is given as follows:

200º.

The measure of the major arc is obtained applying the proportions in the context of the problem.

The entire circumference (perimeter) of the circle has an angle measure of 360º, there are 10 friends and nine spaces, hence the angle measure of each space is given as follows:

360/9 = 40º.

Between Stanley and Frank, there are three people = four spaces, hence the arc lengths are given as follows:

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Answer:

The hand moved \(\bf \frac{3}{4}\) of a complete turn.

Step-by-step explanation:

The hand moved from 3 to 12, that is, it moved:

12 - 3 = 9 hours

In a clock, 12 hours represent a complete turn.

∴ Using the unitary method:

12 hours    ⇒     1 turn

1 hour        ⇒     \(\frac{1}{12}\) turns

9 hours     ⇒     \(\frac{1}{12}\)  × 9 = \(\frac{9}{12}\)

                                     = \(\bf \frac{3}{4}\) turns    (simplified)

∴ The hand moved \(\bf \frac{3}{4}\) of a complete turn.

The answer is  \(\boxed{\frac{3}{4}}\).

To find the fraction of a complete turn it moved in this case, take the ratio between hours covered between 3 and 12, and the hours covered in a complete turn.

Answer:

42×12/4

=42×3

=126

........

Answer:

x=1y

Step-by-step explanation:

The limit lim(x→∞) x/√(x^2 + 3) is 1, and there is no need to apply L'Hospital's Rule in this case.

When trying to use L'Hospital's Rule to find the limit lim(x→∞) x/√(x^2 + 3), it is important to note that L'Hospital's Rule can only be applied if the function is continuous and differentiable. In this case, the function is continuous and differentiable, but applying L'Hospital's Rule is not necessary as the limit can be evaluated using another method.
First, let's rewrite the given function by dividing both the numerator and the denominator by x:
lim(x→∞) (x/x) / (√(x^2 + 3)/x) = lim(x→∞) 1 / √(1 + 3/x^2)
As x approaches infinity, the term 3/x^2 approaches 0, so the limit becomes:
lim(x→∞) 1 / √(1 + 0) = 1 / √(1) = 1
Therefore, the limit lim(x→∞) x/√(x^2 + 3) is 1, and there is no need to apply L'Hospital's Rule in this case.

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Given:

To solve it, follow the steps below.

Step 01: Use the given hint (512 = 32*16).

Step 02: Use the product rule for logarithms.

According to the product rule:

Then,

Step 03: Use the definition of the log to solve the problem.

Given the definition:

So, let's solve each part of the equation.

In order to find x, let's factor 32.

32 | 2

16 | 2

8 | 2

4 | 2

2 | 2

1

2⁵ = 32

And,

Now, let's solve the second term.

Let's factor 16:

16 | 2

8 | 2

4 | 2

2 | 2

1

2⁴ = 16

Substituting it in the equation:

Then,

Step 04: Substitute the solutions and solve the equations.

Answer: 9.

The value of g(5) can be determined by integrating the given derivative function and using the initial condition g(2) = -7.  The value of g(5) is approximately 57.955.

To find the value of g(5), we need to integrate the derivative function g'(x). The antiderivative of √\(x^3\) + x with respect to x will give us the original function g(x). Let's perform the integration:

∫√\(x^3 + x dx\) = ∫\((x^(3/2) + x) dx = (2/5)x^(5/2) + (1/2)x^2 + C\)

Now, using the initial condition g(2) = -7, we can determine the constant of integration C:

\((2/5)(2)^(5/2) + (1/2)(2)^2 + C = -7\)

Simplifying the equation, we can solve for C:

(8/5) + 2 + C = -7

C = -7 - (8/5) - 2

C = -7 - (16/5) - (10/5)

C = -7 - (26/5)

C = -35/5 - 26/5

C = -61/5

Now that we have the value of C, we can substitute it back into the original function and evaluate g(5):

g(5) = \((2/5)(5)^(5/2) + (1/2)(5)^2 - (61/5)\)

Calculating this expression will give us the value of g(5).

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It's important to remember that using the binomial approximation assumes a large population size, which may not be the case here.

To answer your questions, we will use R commands to calculate the probabilities.

(a) To find the probability that exactly 6 of the students will be full-time, we can use the "dhyper" function in R. The parameters are x = 6, m = 30 (number of full-time students), n = 20 (number of part-time students), and k = 10 (sample size).

R command:
```R
dhyper(x = 6, m = 30, n = 20, k = 10)
```

(b) To find the probability that at most 8 of the students will be full-time, we can use the "phyper" function in R, which calculates the cumulative probability. We need to calculate P(X ≤ 8).

R command:
```R
phyper(q = 8, m = 30, n = 20, k = 10)
```

(c) To use the binomial approximation, we can use the "dbinom" function in R with p = 0.6 (probability of full-time student) and n = 10 (sample size). We want to calculate P(X = 6).

R command:
```R
dbinom(x = 6, size = 10, prob = 0.6)
```

Compare this result with the answer in part (a). If the difference is relatively small, it's appropriate to use the binomial approximation in this scenario.

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The required solutions are:

a)  i. The system has no solution when m ≠ 0 and m ≠ -2.

ii. The system has infinitely many solutions when m = 0 or m = -2.

iii. The system has a unique solution when m = -2, the system has a unique solution: x = 6, y = -2, z = 0.

Given that the system of linear equations are x +2y-6z= 2,

x+3y+mz = 0 and y + \(m^2\)z= m.

To analyze the given system of linear equations,  rewrite it in matrix form:

The linear equation is expressed as matrix form.

\(\left[\begin{array}{ccc}1&2&-6\\1&3&m\\0&1&m^2\end{array}\right]\) x \(\left[\begin{array}{c}x\\y\\z\end{array}\right]\) = \(\left[\begin{array}{c}2\\0\\m\end{array}\right]\)

a) To determine the value(s) of m for which the system has:

i. no solution: The system will have no solution if the coefficient matrix's rank is not equal to the augmented matrix's rank. In other words, if the determinant of the coefficient matrix is zero and the determinant of the augmented matrix is nonzero.

ii. infinitely many solutions: The system will have infinitely many solutions if the coefficient matrix's rank is equal to the augmented matrix's rank, and the determinant of the coefficient matrix is zero.

iii. a unique solution: The system will have a unique solution if the coefficient matrix's rank is equal to the augmented matrix's rank, and the determinant of the coefficient matrix is nonzero.

b) To solve the system when m = -2, we substitute -2 for m in the equations and solve for x, y, and z.

a) i. For the system to have no solution, the determinant of the coefficient matrix must be zero while the determinant of the augmented matrix is nonzero.

The coefficient matrix's determinant is:

det(A) = (1 x (3 x \(m^2\)) - (-6) x (1 x (m))) = (3 \(m^2\) + 6m) = 3m(m + 2)

The augmented matrix's determinant is:

det(A') = (2 x (3 x  \(m^2\) ) - (-6) x (0 x (m))) = (6 \(m^2\))

To have no solution, det(A) = 3m(m + 2) must be zero, but det(A') = 6 \(m^2\) must be nonzero. Therefore, for the system to have no solution, m ≠ 0 and m ≠ -2.

ii. For the system to have infinitely many solutions, both the determinant of the coefficient matrix and the augmented matrix must be zero.

From part i, we know that det(A) = 3m(m + 2). To have infinitely many solutions, det(A) = 3m(m + 2) = 0, and thus m = 0 or m = -2.

iii. For the system to have a unique solution, the determinant of the coefficient matrix must be nonzero.

From part i, we know that det(A) = 3m(m + 2).

To have a unique solution, det(A) = 3m(m + 2) must be nonzero, which means m ≠ 0 and m ≠ -2.

b) Substitute m = -2 into the equations and solve for x, y, and z:

\(\left[\begin{array}{ccc}1&2&-6\\1&3&-2\\0&1&4\end{array}\right]\) x \(\left[\begin{array}{c}x\\y\\z\end{array}\right]\) = \(\left[\begin{array}{c}2\\0\\-2\end{array}\right]\)

Use row elementary methods gives,

\(\left[\begin{array}{ccc}1&0&0\\0&1&0\\0&0&1\end{array}\right]\)x \(\left[\begin{array}{c}x\\y\\z\end{array}\right]\) = \(\left[\begin{array}{c}6\\-2\\0\end{array}\right]\)

Therefore, when m = -2, the system is consistent and has a unique solution:x = 6, y = -2, z = 0.

The required solutions are:

a)  i. The system has no solution when m ≠ 0 and m ≠ -2.

ii. The system has infinitely many solutions when m = 0 or m = -2.

iii. The system has a unique solution when m = -2, the system has a unique solution: x = 6, y = -2, z = 0.

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Answer:

Y intercept is 8

Step-by-step explanation:

Not sure about the slope sorry

Ivan has created 9 sculptures.

We know, ratio is a comparison between two quantities or numbers. It expresses how many times one quantity is contained in another or how the two quantities relate to each other.

To find the number of sculptures he has created, we need to divide the number of paintings by the ratio of paintings to sculptures.

Number of paintings: 54

Ratio of paintings to sculptures: 6 paintings : 1 sculpture

Number of sculptures

= Number of paintings / Ratio of paintings to sculptures

= 54 / (6/1)

= 54 / 6

= 9

Therefore, Ivan has created 9 sculptures.

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It takes approximately 0.000628 seconds for the potential energy stored by the circuit to be equally distributed between the capacitor and inductor.

When a capacitor and an inductor are combined in a circuit, it creates an LC circuit. An LC circuit stores energy back and forth between the inductor and capacitor at a certain frequency. When the energy in the circuit is equally distributed between the capacitor and the inductor, it is said to be in resonance.

The time taken for the potential energy stored by the circuit to be equally distributed between the capacitor and inductor in resonance can be calculated using the following equation:

T = 2π√LC  Where T is the time period and L and C are the inductance and capacitance of the circuit respectively.

Let’s assume that the circuit has an inductance of 100mH and a capacitance of 10nF.

The time taken for the potential energy stored by the circuit to be equally distributed between the capacitor and inductor can be calculated as follows:

T = 2π√(L*C)

T = 2π√((100*10⁻³)*(10*10⁻⁹))

T = 2π√(10⁻⁹)

T = 2π*10⁻⁵

T = 0.000628 s (approx.)

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a. The response variable in this experiment is the binding strength. b. The experimental conditions are determined by the type of glue. c. The extraneous variables mentioned are the number of pages and the book's binding type, and other variables to consider include temperature, humidity, application technique, pressure, and drying time.

a. The response variable in this experiment is the binding strength. It is the variable of response variablethat will be measured to determine the effect of different glues.

b. The explanatory variable that will determine the experimental conditions is the type of glue. It is the variable that is manipulated by the experimenter to observe its impact on the binding strength.

c. The two extraneous variables mentioned in the problem description are the number of pages in the book and whether the book is being bound as a paperback or a hardback. These variables are not the focus of the experiment but are mentioned as factors that may potentially affect the binding strength.

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Answer:

The length of each side of Kamila’s square bedroom is;

For the Living room;

For the bedroom;

Recall that the area of Kamila’s rectangular living room is 2.5 times the area of her square bedroom;

Explanation:

Given that the area of Kamila’s rectangular living room is 2.5 times the area of her square bedroom. The length of the living room is 18 feet and its width is 1.25 times the length of a side of the bedroom.

Recall that the area of a rectangle can be calculated using the formula;

For the Living room;

For the bedroom;

Recall that the area of Kamila’s rectangular living room is 2.5 times the area of her square bedroom;

substituting equations 1 and 2 into equation 3;

Therefore, the length of each side of the square bedroom is;

We need to use the fact that the percentages of all three categories must add up to 100%. Therefore, the percentage of independent voters can be found by subtracting the percentages of democrat and republican voters from 100%.
Percentage of independent voters = 100% - 35% - 40% = 25%
So, 25% of the registered voters are independent.
In conclusion, the percentage of independent voters is 25%. This is because the percentages of democrat, republican, and independent voters must add up to 100%. The percentages of democrat and republican voters are given, so we can find the percentage of independent voters by subtracting those from 100%.
Based on the given information, 35% of registered voters are classified as Democrats, and 40% are classified as Republicans. To find the percentage of registered voters who are independent, we need to subtract the total percentage of Democrats and Republicans from 100%.
100% - (35% + 40%) = 100% - 75% = 25%
Therefore, 25% of the registered voters are classified as independent.

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A correlational result can be used to infer causality, but only if the value of r is greater than 0.

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If the cost for 10 ounce of organic blueberry is $2. 70, the cost of 30 ounce of organic blueberry is represented by the equation x = 20y + 2.70 where y is the cost in dollars for one ounce of organic blueberry.

As x is the cost in dollar for 30 ounce of organic blueberry. For y is the cost in dollars for one ounce of organic blueberry, then

x = 30y + c

where c is the fixed cost

We know for 10 ounce of organic blueberry it costs $2.70. That is

2.70 = 10y + c

c = 2.70 - 10y

So x = 30y + 2.70 - 10y

x = 20y + 2.70

-- The question is incomplete, the complete question is as follows--

"The cost for 10 ounce of organic blueberry is $2. 70 which equation can be used to determine x the cost in dollars, for 30 ounces of organic blueberries.?"

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Answer:y= -5

X=-6

-5/6

Step-by-step explanation:

Answer:

y= -3x+24

Step-by-step explanation:

First find the slope of the line

-x + 3y = -6

Add x to each side

3y = x-6

Divide by 3

3y/3 = 1/3 x -6/3

y = 1/3x -2

The slope is 1/3 since it is in the form y = mx+b where m is the slope

Perpendicular lines have slopes that multiply to -1

1/3 * m = -1

m = -1 * 3/1

m = -3

The slope of the perpendicular line is -3

Slope intercept form is

y = mx+b where m is the slope and b is the y interceot

y = -3x+b

We have a point ( 6,6)

6 = -3(6) +b

6 = -18+b

Add 18 to each side

6+18 = -18+b+18

24 = b

y= -3x+24

Answer:

y= -3x+24

Step-by-step explanation:

hope this helps!

The net change in the value of the function between x = 1 and x = 6 is 30.

To find the net change in the value of the function between the inputs of 1 and 6, we need to find the difference between the output values of the function at x = 1 and x = 6, and then take the absolute value of that difference.

First, we can find the output value of the function at x = 1:

f(1) = 6(1) - 5 = 1

Next, we can find the output value of the function at x = 6:

f(6) = 6(6) - 5 = 31

The net change in the value of the function between x = 1 and x = 6 is the absolute value of the difference between these two output values:

|f(6) - f(1)| = |31 - 1| = 30

Therefore, the net change in the value of the function between x = 1 and x = 6 is 30.

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True. A vector in space can be described by specifying its magnitude and its direction angles. The magnitude of a vector represents its length or size, while the direction angles determine the orientation of the vector with respect to a reference axis system.

In three-dimensional space, a vector can be decomposed into its components along the x, y, and z axes. By using trigonometric functions, the direction angles of the vector can be determined. The direction angles are typically measured with respect to the positive x-axis, the positive y-axis, and the positive z-axis.

Once the magnitude and direction angles of a vector are known, the vector can be fully described. This description allows for precise calculations and analysis of vector quantities, such as displacement, velocity, and force, in various physical and mathematical contexts.

It's worth noting that there are alternative ways to describe vectors, such as using Cartesian coordinates or unit vectors. However, specifying the magnitude and direction angles provides a convenient and comprehensive representation of a vector in space.

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Answer:

w = 21.4

Step-by-step explanation:

π(2ft)2(10ft) + π(2ft)2(13ft − 10ft) is used to calculate the total volume of grains that can be stored in the silo.(option-c)

The total volume of grains that can be kept in the silo is calculated as (2ft)2(10ft) + (2ft)2(13ft 10ft).(option-c)

The formula $V = gives the volume of a cylinder.

$, where $r$ denotes the base's radius and $h$ denotes its height. The equation $V = gives the volume of a cone.

$, where $r$ denotes the base's radius and $h$ denotes its height.

The silo is made up of a cone with a height of 3 feet and a radius of 2 feet, as well as a 10 foot tall cylinder with the same dimensions. Consequently, the silo's overall volume is V =

V = \(\pi (2ft)^2 (10ft) + \frac{1}{3} \pi (2ft)^2 (3ft)\)

V =\(\pi (4ft^2) (10ft) + \frac{1}{3} \pi (4ft^2) (3ft)\)

V = \(40 \pi ft^3 + 4 \pi ft^3\)

V = \(44 \pi ft^3\)(option-c)

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Perimeter = 2 x length + 2 x width

Perimeter = 2 x 10 + 2 x 4 = 20 + 8 = 28 cm

Area = length x width

Area = 10 x 4 = 40 square cm

There are several different sampling methods that could be employed for this study, including:

Simple random sampling: This method involves randomly selecting a certain number of students from each campus and measuring the distance between their hometowns and their campuses.

Stratified random sampling: This method involves dividing the student population at each campus into different strata (e.g. by major or year in school) and then randomly selecting a certain number of students from each stratum.

Cluster sampling: This method involves randomly selecting a certain number of campuses and then measuring the distance between the hometowns of all students at those campuses and their respective campuses.

Multi-stage sampling: This method involves using a combination of the above methods, such as first using cluster sampling to select a certain number of campuses and then using stratified random sampling to select a certain number of students from each campus.

This study would be an enumerative study because it seeks to measure the characteristics of a population, in this case, the average distance between the hometowns of students and their campuses, by counting and measuring them.

It is not an analytic study because it doesn't involve testing a hypothesis or making causal inferences.

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The equation that can be used to compute the number of pieces of jewellery is ($120 + $15q)/q = $20 .

Average cost is total cost divided by the quantity of jewellery sold.

Average cost = total cost / quantity

Total cost is the sum of fixed cost and variable cost.

Total cost = fixed cost + variable cost

The fixed cost is the cost of renting the stall. The variable cost is the cost of the materials.

Total cost = $120 + ($15 x q)

T = $120 + $15q

Average cost = ($120 + $15q)/q = $20

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