The leading coefficients of 3x^2-3x-4=0

Answer:

$3 = 2

$6 = 4

$9 = 6

$12 = 8

$15 = 10

To solve the equation \(6sin^2(x)\) + 6sin(x) + 1 = 0, we can use algebraic methods and the unit circle to determine the values of x that satisfy the equation.

1. Start by rearranging the equation to a quadratic form: \(6sin^2(x)\) + 6sin(x) + 1 = 0.

2. Notice that the equation resembles a quadratic equation in terms of sin(x). Let's substitute sin(x) with a variable, such as u: \(6u^2\) + 6u + 1 = 0.

3. Solve this quadratic equation for u. You can use the quadratic formula or factorization methods to find the values of u. The solutions are u = (-3 ± √3) / 6.

4. Since sin(x) = u, substitute back the values of u into sin(x) to obtain the values for sin(x): sin(x) = (-3 ± √3) / 6.

5. To find the values of x, we can use the inverse sine function. Take the inverse sine of both sides: x = arcsin[(-3 ± √3) / 6].

6. The arcsin function has a range of [-π/2, π/2], so the values of x lie within that range. Use a calculator to find the approximate values of x based on the values obtained in step 5.

7. Plot the obtained x-values on the graph to show the solutions of the equation \(6sin^2(x)\) + 6sin(x) + 1 = 0. The graph will illustrate the points where the curve intersects the x-axis.

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The area of the walkway is 24π square meters.

To find the area of the walkway, we need to subtract the area of the inner circle from the area of the outer circle.

The inner circle has a radius of 5 meters, so its area can be calculated using the formula for the area of a circle: A_inner = π * \((r_inner)^{2}\).

A_inner = π * \(5^{2}\) = 25π square meters.

The outer circle has a radius equal to the sum of the inner radius and the width of the walkway. In this case, the outer radius is 5 + 2 = 7 meters.

The area of the outer circle can be calculated in the same way: A_outer = π * \((r_outer)^{2}\).

A_outer = π * \(7^{2}\) = 49π square meters.

Now, we can find the area of the walkway by subtracting the area of the inner circle from the area of the outer circle: A_walkway = A_outer - A_inner.

A_walkway = 49π - 25π = 24π square meters.

The area of the walkway is 24π square meters, where π (pi) is a mathematical constant approximately equal to 3.14159.

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The name of the 3D Shape shown in figure is triangular prism and the surface area of the figure is 111 cm².

The total surface area of a triangular prism is the sum of area of its each face. Total surface area of a triangular prism is calculated with the following formula,

A = bh( s1 + s2 + s3)* l

Here, we have,

(b) is the base of the triangle, h is the height of base of prism, (s1,s2,s3) are the sides or base and l is the length of the prism.

A. The name of the 3D Shape-

The name of the 3D Shape shown in the figure is a right triangular prism.

B. The formula for total surface area for this shape-

The formula to find the total surface area for this shape is,

A = bh( s1 + s2 + s3)* l

C. The surface area of the figure-

The sides of the triangle are 3cm,4cm and 5 cm long.

The length of the prism is 11 cm, the height of the triangular base is 3 cm and base is 4 cm long.

Put these values in the above formula,

calculating we get,

A = 111

Thus, the name of the 3D Shape shown in figure is triangular prism and the surface area of the figure is 111 cm².

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The maximum value of the function f(x, y) = x + y + 4 on the circular disk x^2 + y^2 ≤ 1 is 5, and the minimum value is 3.

The gradient of the function f(x, y):

∇f(x, y) = (df/dx, df/dy) = (1, 1)

The gradient vector (∇f) points in the direction of the steepest ascent of the function and we can say that the maximum value of the function occurs when the gradient vector is perpendicular to the boundary of the circular disk.

The boundary of the circular disk x² + y² ≤ 1 is the circle with a radius of 1 centered at the origin (0, 0).

The gradient vector (1, 1) is not perpendicular

We will evaluate the function at the boundary points of the circular disk.

On the boundary of the circular disk, x² + y² = 1, we have the following points:

When x = 1 and y = 0: f(1, 0) = 1 + 0 + 4 = 5

When x = 0 and y = 1: f(0, 1) = 0 + 1 + 4 = 5

When x = -1 and y = 0: f(-1, 0) = -1 + 0 + 4 = 3

When x = 0 and y = -1: f(0, -1) = 0 + (-1) + 4 = 3

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complete question:

For each of the following functions, find the maximum and minimum values of the function on the circular disk: x^2+y^2≤1. Do this by looking at the level curves and gradients.

f(x,y)=x+y+4

maximum value =

In the figure, mGE = 97 and mHF = 43. Since GPEQ is a parallelogram, opposite angles are congruent. Therefore, m<GPE = m<EQG = mGE = 97.

m<GPEQ = 97

Answer:

Yes, its true that 30 is 6 times as much as 5.

6×5=30.

Answer:

yes

Step-by-step explanation:

because 6x5=30

Answer:

3/4 hour-72

1 hour- 92

Step-by-step explanation:

3/4-

24 x 3= 72

1-

24 x 4 =92

The relationship that has a zero slope is option a, he first column, x, has the entries, negative 3, negative 1, 1, 3. The second column, y, has the entries, 2, 2, 2, 2.

Positive slopes and negative slopes are absent from horizontal lines. A horizontal line's slope is always zero. This is due to the fact that it has a constant height—if we use the rise over run technique, rise will always be 0 regardless of what run is.

Option A is the connection with a zero slope.

Regardless of the x-values, option A's y-values are all fixed at (2). This implies that for any change in x (run), the change in y (rise) is always zero, resulting in a slope of zero.

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Answer:

$1717.80

Step-by-step explanation:

We are given one clue: He pays $572.60 each year to cover everyone and his family.

We are asked to find how much does Phil have to pay after 3 years. So, we must multiply 572.60 by 3 to find the total cost Phil has to pay after 3 years.

572.60 x 3 = Total cost to pay after 3 years.

=> $1717.80 = Total cost to pay after 3 years.

We can conclude that Phil will have to pay $1717.80 after 3 years.

On average, it takes approximately 14 minutes for a plane to complete the entire arriving process, from radioing the control tower to landing on the runway, in the morning at Nogan Airport.

To determine the average time that elapses between a plane radioing the control tower and its completion of the entire arriving process in the morning, we need to consider the different steps involved in the process.

Radioing the control tower: The time between two consecutive arriving requests follows an exponential distribution with an average of 10 minutes. Hence, on average, it takes 10 minutes for a plane to radio the control tower after the previous plane.

Assigning position in queue: The air traffic controller assigns the plane a position in the queue on a first-come-first-serve basis, implying that there is no additional delay for this step.

Landing on the runway: Once the plane reaches the front of the queue, it lands on the runway. The time it takes for a plane to use a runway, either for landing or departing, follows an exponentially distributed process.

Since the runway dedicated to arrival can serve 15 flights per hour, the average time it takes for a plane to complete the landing process is 1/15 hour, or 4 minutes.

Considering these steps, the average time that elapses between a plane radioing the control tower and completing the entire arriving process in the morning can be calculated as follows:

Average time = Time to radio the control tower + Time to land on the runway

= 10 minutes + 4 minutes

= 14 minutes

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A square's diagonal has a length equal to √(2) times the length of its sides. So if the side length is x, then the diagonal is such that

√(2) x = 10 cm

→   x = 10/√(2) cm ≈ 7.07 cm

The perimeter of a square is 4 times its side length, so the perimeter is

4 (10/√(2) cm) = 40/√(2) cm ≈ 28.3 cm

which makes 28.4 cm the closest answer.

Answer:

28.4

Step-by-step explanation:

The factors illustrate they the sides of the rectangles are:

The first equation given is x² - 3x + 2.

= x² - 3x + 2.

= x² - x - 2x + 2

= x(x - 1) - 2(x - 1)

= (x - 1)(x - 2)

Therefore, the side lengths are (x - 1) and (x - 2).

In the rectangular figure, the length and width should be the expressions above.

The second equation given is 2x² + x - 6.

= 2x² + x - 6.

= 2x² + 4x - 3x - 6

= 2x(x + 2) - 3(x + 2)

= (2x - 3)(x + 2)

Therefore, the side lengths are (2x - 3) and (x + 2).

In the rectangular figure, the length and width should be the expressions above.

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Answer:

88cm^2

Step-by-step explanation:

Area of the rectangle: base x height

Area of parallelogram: base x height

Area of the shaded part: area of rectangle -area of parallelogram:

12x10-4x8=120-32=88

If only two out of the five people show up for the meeting, it is possible in 10 different ways.

If five people plan to meet after school and there will be one group of five people if they all show up, but only two people show up, we need to determine the number of ways this can happen.

To find the number of ways two people can show up out of the five, we can use combinations. In a combination, the order of selection does not matter.

The number of ways to choose two people out of five can be calculated using the formula for combinations, denoted as "nCr", where n is the total number of people and r is the number of people we want to choose.

In this case, we want to choose 2 people out of 5, so the calculation would be:

5C2 = (5!)/(2!(5-2)!) = (5!)/(2!3!) = (5 \(\times\) 4)/(2 \(\times\) 1) = 10

Therefore, there are 10 possible ways for two people to show up out of the five if all of them plan to meet after school.

These 10 possibilities could be different combinations of any two individuals out of the five.

To determine the specific combinations, you can list all the pairs or use a combination formula calculator.

It's important to note that the order in which the two people show up does not matter, as long as they are two out of the five originally planning to meet.

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Answer:

-3

Step-by-step explanation:

first do -22-2= -24

then do 1/8 of -24= -3

Answer:

0.75

Step-by-step explanation:

Answer: what you would do is 20 x 12 and see what you get and the subtract it from 900 and then see what number would take you to 900 on the graph

Step-by-step explanation:

Answer:

A

Step-by-step explanation:

20x +12y= 900

Let's start by finding the y-intercept.

When x= 0,

20(0) +12y= 900

12y= 900

y= 900 ÷12

y= 75

The y-intercept is thus at point (0, 75).

This means that the graph would pass through the vertical axis at the point (0, 75). Looking at the provided graphs, the answer could either be option A or C as they have the point (0, 75) as the y-intercept. The y-intercept for both options B and D is (0, 45) and thus they are incorrect.

Now, let's find the x-intercept.

When y= 0,

20x +12(0)= 900

20x= 900

x= 900 ÷20

x= 45

Thus, the x-intercept is (45, 0). Since the x- intercept of the graph in option A is also (45, 0), option A is correct.

The y-intercept of graphs B, C and D are (75, 0), (60, 0) and about (28, 0) respectively.

Answer:

No

Step-by-step explanation:

Answer:

84 m

Step-by-step explanation:

Perimeter of the park = perimeter of rectangle + perimeter of 2 semicircles

62

The cost of the printer paper at 15 cases, can be found to be $ 337. 50

To find the cost of 15 cases of printer paper, you first need to find the cost of a single case of printer paper which would be:

= Cost of two cases / Number of cases

= 45 / 2

= $ 22. 50

The cost of 15 cases of printer paper would then be:

= Cost per case of printer paper x Number of cases

= 22. 5 x 15

= $ 337. 50

We can therefore conclude that the cost of 15 cases of printer paper would cost $ 337. 50.

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Answer:

2593 ml= 2.593 L

Step-by-step explanation:

Solution,

We know that,

1000 ml= 1L

1 ml= 1/1000 L

2593 ml= (1/1000)×2593 L

= 2593/1000 L

= 2.593 L

The correct answer is Option B.10 . The constant of variation for this relation is k=10.

When two variables are directly proportional, they are related by the equation y=kx, where k is the constant of variation.

This means that as x increases, y increases proportionally.

On the other hand, if x decreases, then y decreases proportionally.

Hence, we are to determine the constant of variation for the given relation: If y varies directly as x, and y is 12 when x is 1.2,

We are given that y varies directly as x, which means we can write this as:y=kx, where k is the constant of variation.

We are also given that y is 12 when x is 1.2.

Thus:12=k(1.2)

Dividing both sides by 1.2, we get:k=10

Hence, the constant of variation for this relation is k=10.

The correct answer is Option B. 10

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Answer:

B

Step-by-step explanation:

39 subjects were tested in this simple one-way ANOVA.

The df for F distribution is (treatment df, error df)

Using given information

Treatment df = 7

Error df = 31

Total df= 7+31 = 38

Again, total df = N-1, N= number of subjects tested

Then, N-1 = 38

=> N= 39

One-way ANOVA is typically used when there is a single independent variable or factor and the goal is to see whether variation or different levels of that factor have a measurable effect on the dependent variable.

The t-test is a method of determining whether two populations are statistically different from each other, and ANOVA determines whether three or more populations are statistically different from each other.

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Let's assume that each van and each bus can carry "x" number of students.

Let's assume there are "x" students in each van and each bus. Therefore, the total number of students in High School A's senior class is 8x + 8x = 16x. We know that the total number of students in High School A's senior class is 240, so we can set up an equation:

16x = 240

Solving for x, we get:

x = 15

So, each van and each bus had 15 students in it for High School A's senior class.

Similarly, for High School B, the total number of students is 4x + 1x = 5x. We know that the total number of students in High School B's senior class is 54, so we can set up an equation:

5x = 54

Solving for x, we get:

x = 10.8

Since the number of students must be a whole number, we can round up to 11. Therefore, each van and each bus had 11 students in it for High School B's senior class.

Therefore, the total number of students in High School A's senior class is 1x + 6x = 7x. We know that the total number of students in High School A's senior class is 372, so we can set up an equation:

7x = 372

Solving for x, we get:

x = 53

Therefore, each van and each bus can carry 53 students for High School A's senior class.

Similarly, for High School B, the total number of students is 4x + 12x = 16x. We know that the total number of students in High School B's senior class is 780, so we can set up an equation:

16x = 780

Solving for x, we get:

x = 48.75

Since the number of students must be a whole number, we can round up to 49. Therefore, each van and each bus can carry 49 students for High School B's senior class.

Let's assume that the price of one senior citizen ticket is "s" and the price of one child ticket is "c". Therefore, we can set up two equations based on the given information:

\(3s + 9c = 75\)

\(8s + 5c = 67\)

We can solve these equations simultaneously to find the values of "s" and "c". One way to do this is to multiply the first equation by 8 and the second equation by 3, so that we can eliminate "c" and solve for "s":

\(24s + 72c = 600\)

\(24s + 15c = 201\)

Subtracting the second equation from the first, we get:

57c = 399

Solving for "c", we get:

c = 7

Substituting this value into one of the original equations, we can solve for "s":

\(3s + 9(7) = 75\)

\(3s + 63 = 75\)

\(3s = 12\)

\(s = 4\)

Therefore, one senior citizen ticket costs $4 and one child ticket costs $7.

Let's assume that the speed of the boat in still water is "b" and the speed of the current is "c".

Therefore, we can set up two equations based on the given information:

\(336 = (b + c) * 12\)

\(336 = (b - c) * 14\)

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a) To calculate the overall mean, you must take the total wages divided by the total number of workers. What Stacy is doing is calculating the average of the means, which is incorrect as both the total wages and the quantity of workers are both different (or she's just using the wrong method of calculation)

b) First, we find the total wages of the 56 workers : 42 x 9.5 + 14 x 13.5 = 588 (pounds)

So, the overall mean is : 588 : 56 = 10.5 (pounds/h)

Answer:

£ 10.50

Step-by-step explanation:

a) Stacy is wrong because she found the mean of the £9.50 and £13.50. She has to find the mean of wage of 42 packers and wage of 14 truck drivers.

\(\sf b) Overall \ mean \ wage = \dfrac{sum \ of \ wages \ of \ 42 \ packers+ Sum \ of \ wages \ of \ 14 \ truckers}{number \ of \ packers + numbers \ of \ truck \ drivers}\)

Sum of wages of 42 packers = 42 * 9.50

                                                = £ 399

Sum of wages of 14 truck drivers = 14 * 13.50

                                                       = £ 189

\(\sf Overall \ mean \ wage = \dfrac{399+189}{42+14}\\\\\)

                            \(\sf = \dfrac{588}{56}\\\\\)

                            = £ 10.50

Answer:

Im not too sure what the question is

Step-by-step explanation:

but when finding the percent of any number, 10% will always move the decimal over to the left once. So 10% of 300 is 30.0 This also works for 1%, you just move the decimal over twice. So 1% of 300 is 3

The fifth term of the arithmetic sequence is -1190.

An arithmetic sequence is a sequence of numbers in which the difference between consecutive terms remains constant. To find the fifth term, we can use the formula for the nth term of an arithmetic sequence:

aₙ = a₁ + (n - 1) * d

where aₙ represents the nth term, a₁ is the first term, n is the position of the term, and d is the common difference.

Given that the 100th term is -1240 and the common difference is -25, we can substitute these values into the formula.

Since the fifth term corresponds to n = 5, we can calculate:

a₅ = -1240 + (5 - 1) * (-25)

= -1240 + 4 * (-25)

= -1240 - 100

= -1340

Therefore, the fifth term of the arithmetic sequence is -1190.

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