In simplest radical form, what are the solutions to the quadratic equation 0 =-3x² - 4x + 5?
-b± √b²-4ac
2a
Quadratic formula: x =
O x= -2±√19
3
Ox=-
2+2√19
3
0 x= 2+√15
3
0 x = 2+2√/19
3

Answer:

A scale is just another way of saying what we want to count by on our graph.

Step-by-step explanation:

A "scale" is just another way of saying what we want to count by on our graph. The scale is the range of values that are shown on the axis of a graph. It helps to determine the size and spacing of the intervals or ticks on the axis. The scale can be in different units, such as time, distance, weight, or any other measurable quantity depending on the type of data being represented in the graph.

(a) The magnitude of the rod's angular acceleration is (3g/2L) rad/s^2.

(b) The tangential acceleration of the rod's center of mass is (3g/4) m/s^2.

(c) The tangential acceleration of the rod's free end is (3g/2) m/s^2.

(a) To find the magnitude of the rod's angular acceleration, we can use the formula for rotational motion. The torque acting on the rod is due to the gravitational force acting at its center of mass.

The torque is given by τ = Iα, where τ is the torque, I is the moment of inertia, and α is the angular acceleration.

For a thin rod rotating about one end, the moment of inertia is (1/3)ML^2, where M is the mass of the rod and L is its length.

The torque is equal to the product of the gravitational force and the perpendicular distance from the pivot to the center of mass, which is (1/2)L.

So we have τ = (1/2)MgL, where g is the acceleration due to gravity. Substituting these values into the torque equation, we get (1/2)MgL = (1/3)ML^2 α.

Simplifying the equation, we find α = (3g/2L).

Therefore, the magnitude of the rod's angular acceleration is (3g/2L) rad/s^2.

(b) The tangential acceleration of the rod's center of mass can be found using the formula a = αr, where a is the tangential acceleration, α is the angular acceleration, and r is the distance from the center of mass to the pivot point.

In this case, the distance r is (1/2)L, so substituting the values, we get a = (3g/2L)(1/2)L = (3g/4) m/s^2.

Therefore, the tangential acceleration of the rod's center of mass is (3g/4) m/s^2.

(c) The tangential acceleration of the rod's free end is equal to the sum of the tangential acceleration of the center of mass and the product of the angular acceleration and the distance from the center of mass to the free end.

Since the distance from the center of mass to the free end is (1/2)L, the tangential acceleration of the free end is

a + α(1/2)L = (3g/4) + (3g/2L)(1/2)L = (3g/4) + (3g/4) = (3g/2) m/s^2.

Therefore, the tangential acceleration of the rod's free end is (3g/2) m/s^2.

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The output value is feasible. The input value is not feasible, the possible solution of (6.5, $17.50) does not make sense for this function. The correct answer is No. The input is not feasible.

Jade decided to rent movies for a movie marathon over the weekend.

The function g(x) represents the amount of money spent in dollars, where x is the number of movies.

The given function is g(x) which represents the amount of money spent in dollars, where x is the number of movies.

The solution given is (6.5, $17.50).

We need to find whether the solution makes sense for the given function or not.

The input is given as 6.5 and the output is given as $17.50.

This means that Jade rented 6.5 movies and spent $17.50 on renting those movies.

To check whether the solution makes sense or not, we need to see if the input and output values are feasible or not.

The input value 6.5 is not a feasible value because it is not possible to rent half a movie.

Jade can rent 6 movies or 7 movies but not 6.5 movies.

Therefore, the input value is not feasible.

On the other hand, the output value $17.50 is a feasible value because it is possible for Jade to spend $17.50 on renting 6 movies.

The output value is feasible.

Since the input value is not feasible, the possible solution of (6.5, $17.50) does not make sense for this function. The correct answer is No. The input is not feasible.

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Answer:

40% of 50 is 20

Step-by-step explanation:

[tex]50x=20\\x=\frac{20}{50}=0.4=40\%[/tex]

Answer: 20 is 40% of 50.

Step-by-step explanation:

We can simply divide 20/50

20/50 = 0.4

Now multiply it by 100 to get the percent: 0.4×100 = 40%

Hope this helps!

The polynomial P(x) = x³ + 3x² - 8x + 140 divided by (x + 7), will give a quotient of x² - 3x + 2 and a remainder of 0 using the long division, we can write P(x) = (x + 7)(x² - 4x + 20) + 0

A polynomial is a mathematical expression which have a sum of powers in one or more variables with coefficients. The highest power of the variable in a polynomial is called its degree.

We shall divide the polynomial x³ + 3x² - 8x + 140 by x + 7 as follows;

x³ divided by x equals x²

x + 7 multiplied by x² equals x³ + 7x²

subtract x³ - x² from x³ + 3x² - 8x + 140 will result to -4x² - 8x + 140

-4x² divided by x equals -4x

x + 7 multiplied by -4x equals -4x² - 28x

subtract -4x² - 28x from -4x² - 8x + 140 will result to 20x + 140

20x divided by x equals 20

x + 7 multiplied by 20 equals 20x + 140

subtract 20x + 140 from 20x + 140 will result to a remainder 0

Therefore, the polynomial P(x) = x³ + 3x² - 8x + 140 divided by (x + 7), will give a quotient of x² - 3x + 2 and a remainder of 0 using the long division, we can write P(x) = (x + 7)(x² - 4x + 20) + 0

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The statement about the zeros of function g is that they are located at x = 5 + √2 and x = 5 - √2.

When the vertex of function f is moved 4 units to the right and 2 units down, the equation of function g can be represented as g(x) = -(x-5)^2 + 2.

To determine the statement about the zeros of function g, we need to find the x-values where g(x) equals zero.

Setting g(x) = 0 and solving for x:

[tex]0 = -(x-5)^2 + 2[/tex]

Adding (x-5)^2 to both sides:

[tex](x-5)^2 = 2[/tex]

Taking the square root of both sides (considering both positive and negative roots):

x - 5 = ±√2

Adding 5 to both sides:

x = 5 ± √2

Therefore, the zeros of function g are x = 5 + √2 and x = 5 - √2.

In summary, the statement about the zeros of function g is that they are located at x = 5 + √2 and x = 5 - √2.

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The labeling of bases and height in a trapezium is not fixed and can vary based on the context or problem. It doesn't matter where they are on the trapezium, as long as they are clearly defined and consistent within the given situation.

In a trapezium (or trapezoid), the labeling of the bases and height is not fixed or standardized. It can vary depending on the context or the specific problem being considered. However, there are a few general guidelines to keep in mind when labeling a trapezium.

Bases: The trapezium has two parallel sides, often referred to as the "top base" and the "bottom base." The bases are usually labeled based on their relative lengths or position in the trapezium. The longer parallel side is commonly referred to as the "top base," while the shorter parallel side is referred to as the "bottom base." However, this is not a strict rule and can vary depending on the problem or preference.

Height: The height of a trapezium is the perpendicular distance between the bases. It is generally labeled as a vertical line segment connecting the bases. The placement of the height is not fixed, and it can be drawn from any point on the top base to any point on the bottom base, as long as it forms a perpendicular line. The height is usually labeled with the symbol "h" or sometimes "x" or "y" depending on the context.

It's important to note that the labeling of the bases and height is primarily for communication and clarity. As long as the labeling is consistent and clearly defined within the given problem or context, it does not have to conform to any specific arrangement or be in a rectangular shape. The key is to ensure that the labels are clearly understood and can be used to calculate the desired quantities or solve the problem at hand.

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The third term (a3) of the sequence is -8, the fourth term (a4) is 35, and the fifth term (a5) is -183. These values are obtained by applying the given formula recursively and substituting the previous terms accordingly. The calculations follow a specific pattern and are derived using the provided formula.

The sequence is defined by the following formula:

a1 = 1, a2 = 3,

and

an = (-1)nan - 1 + an - 2 for n ≥ 3.

To find the third term (a3), we substitute n = 3 into the formula:

a3 = (-1)(3)(a3 - 1) + a3 - 2.

Next, we simplify the equation:

a3 = -3(a2) + a1.

Since we know a1 = 1 and a2 = 3, we substitute these values into the equation:

a3 = -3(3) + 1.

Simplifying further:

a3 = -9 + 1.

Therefore, the third term (a3) is equal to -8.

To find the fourth term (a4), we substitute n = 4 into the formula:

a4 = (-1)(4)(a4 - 1) + a4 - 2.

Simplifying the equation:

a4 = -4(a3) + a2.

Since we know a2 = 3 and a3 = -8, we substitute these values into the equation:

a4 = -4(-8) + 3.

Simplifying further:

a4 = 32 + 3.

Therefore, the fourth term (a4) is equal to 35.

To find the fifth term (a5), we substitute n = 5 into the formula:

a5 = (-1)(5)(a5 - 1) + a5 - 2.

Simplifying the equation:

a5 = -5(a4) + a3.

Since we know a4 = 35 and a3 = -8, we substitute these values into the equation:

a5 = -5(35) + (-8).

Simplifying further:

a5 = -175 - 8.

Therefore, the fifth term (a5) is equal to -183.

In summary, the third term (a3) is -8, the fourth term (a4) is 35, and the fifth term (a5) is -183.

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When x = 3, the expression 2x - 50 evaluates to -44.

To demonstrate an example using the expression 2(x + 5) - 5 × 12, let's simplify it step by step:

Start with the given expression.

2(x + 5) - 5 × 12

Apply the distributive property.

2x + 2(5) - 5 × 12

Simplify within parentheses and perform multiplication.

2x + 10 - 60

Combine like terms.

2x - 50

The simplified form of the expression 2(x + 5) - 5 × 12 is 2x - 50.

Let's consider an example for substituting a value for the variable x:

Suppose we want to evaluate the expression when x = 3. We substitute x = 3 into the simplified expression:

2(3) - 50

Now, perform the calculations:

6 - 50

The result is -44.

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Question

evaluate the expression 2(x+5)-5 x 12.

Step-by-step explanation:

100% = 575

1% = 575÷100 = 5.75

60% = 5.75 × 60 = 345

The polynomial with real coefficients from the zeros is P(x) = 2x³ - 18x² + 2x + 58

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

zeros =  5+2i, 5-2i, -1

One such polynomial P(x) can be defined as

P(x) = x³ - 9x² + x + 29.

When this polynomial is multiplied by a costant, the roots and zeros remain the same

Let the constant be 2

So, we have

New P(x) = 2(x³ - 9x² + x + 29)

Evaluate

New P(x) = 2x³ - 18x² + 2x + 58

Hence, the function is P(x) = 2x³ - 18x² + 2x + 58

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The number of minutes spent higher than 38 meters above the ground on the Ferris wheel ride is approximately 1.0918 minutes.

To solve this problem, we need to determine the angular position of the Ferris wheel when it is 38 meters above the ground.

The Ferris wheel has a diameter of 50 meters, which means its radius is half of that, or 25 meters.

When the Ferris wheel is at its highest point, the radius and the height from the ground are aligned, forming a right triangle.

The height of this right triangle is the sum of the radius (25 meters) and the platform height (4 meters), which equals 29 meters.

To find the angle at which the Ferris wheel is 38 meters above the ground, we can use the inverse sine (arcsine) function.

The formula is:

θ = arcsin(h / r)

where θ is the angle in radians, h is the height above the ground (38 meters), and r is the radius of the Ferris wheel (25 meters).

θ = arcsin(38 / 29) ≈ 1.0918 radians

Now, we know the angle at which the Ferris wheel is 38 meters above the ground.

To calculate the time spent higher than 38 meters, we need to find the fraction of the total revolution that corresponds to this angle.

The Ferris wheel completes one full revolution in 2 minutes, which is equivalent to 2π radians.

Therefore, the fraction of the revolution corresponding to an angle of 1.0918 radians is:

Fraction = θ / (2π) ≈ 1.0918 / (2π)

Finally, we can calculate the time spent higher than 38 meters by multiplying the fraction of the revolution by the total time for one revolution:

Time = Fraction [tex]\times[/tex] Total time per revolution = (1.0918 / (2π)) [tex]\times[/tex] 2 minutes

Calculating this expression will give us the answer in minutes.

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Answer:

The area of the complex figure is approximately 210.92 square units.

Step-by-step explanation:

Let's calculate the area of the complex figure with the given information.

We can break the figure down into three components: an equilateral triangle, a right triangle, and a rectangle.

1. Equilateral Triangle:

The height of the equilateral triangle is given as 4.33 units. We can calculate the area using the formula:

Area of Equilateral Triangle = (base^2 * √3) / 4

In this case, the base of the equilateral triangle is also the length of side d, which is given as 13 units.

Area of Equilateral Triangle = (13^2 * √3) / 4

Area of Equilateral Triangle ≈ 42.42 square units

2. Right Triangle:

The right triangle has two sides with lengths a (5 units) and b (5 units), and its hypotenuse has a length of side c (also 5 units).

Area of Right Triangle = (base * height) / 2

In this case, both the base and height of the right triangle are the same and equal to a or b (5 units).

Area of Right Triangle = (5 * 5) / 2

Area of Right Triangle = 12.5 square units

3. Rectangle:

The rectangle has a length equal to side d (13 units) and a width equal to side e (12 units).

Area of Rectangle = length * width

Area of Rectangle = 13 * 12

Area of Rectangle = 156 square units

Now, to get the total area of the complex figure, we add the areas of each component:

Total Area = Area of Equilateral Triangle + Area of Right Triangle + Area of Rectangle

Total Area = 42.42 + 12.5 + 156

Total Area ≈ 210.92 square units

Therefore, the area of the complex figure is approximately 210.92 square units.

Answer:

33.33%

Step-by-step explanation:

We Take

(35 ÷ 105) x 100 ≈ 33.33%

So, 35 is 33.33% of 105

1) The probability that 5 will be working is: 0.187

2) The probability that at least one machine would be working is: 0.006

3) The probability that all would be working is : 1

We are given the parameters as:

Total number of machines = 200

Probability that a Machine is working = 12% = 0.12

1) Now, you want to pick 40 machines and want to find the probability that 5 will be working.

This probability is given by the expression:

P(5 working) = C(40,5) * 0.12⁵·0.88³⁵ ≈ 0.187

where C(n, k) = n!/(k!(n-k)!)

2) The probability that at least one machine would be working is:

0.88⁴⁰ ≈ 0.006

3) The probability that all would be working is the complement of the probability that all have failed. Thus:

P(all working) = 1 - 0.12⁴⁰ ≈ 1

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To graph the function g(x) = 7x + 10, we shift the graph of f(x) = 7x vertically by adding a constant term of +10. This means every y-coordinate on the graph increases by 10 units. The slope of the line remains the same at 7. The resulting graph is a straight line passing through (0, 10) with a slope of 7.

To graph the function g(x) = 7x + 10, you need to make the following change to the graph of f(x) = 7x:
1. Translation: The graph of f(x) = 7x can be shifted vertically by adding a constant term to the equation. In this case, the constant term is +10.
Here's how you can do it step by step:
1. Start with the graph of f(x) = 7x, which is a straight line passing through the origin (0,0) with a slope of 7.
2. To shift the graph vertically, add the constant term +10 to the equation. Now, the equation becomes g(x) = 7x + 10.
3. The constant term of +10 means that every y-coordinate of the points on the graph will increase by 10 units. For example, the point (0,0) on the original graph will shift to (0,10) on the new graph.
4. Similarly, if you take any other point on the original graph, such as (1,7), the corresponding point on the new graph will be (1,17) since you add 10 to the y-coordinate.
5. Keep in mind that the slope of the line remains the same, as only the y-values are affected. So, the new graph will still have a slope of 7.
By making this change, you will have successfully graphed the function g(x) = 7x + 10.

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Answer: Step-by-step work:

40,328

77

3,105 (Carry the 3)

27,468

302,976

1,609,432

Add the numbers horizontally:

2,943,941

So, 40,328 * 77 = 2,943,941

The remainder when divided by 10 is:

2,943,941 % 10 = 1

Therefore, the remainder is 1.

More concisely:

40,328 * 77 = 2,943,941

2,943,941 % 10 = 1

So the remainder when 2,943,941 is divided by 10 is 1.

Hope this helps! Let me know if you have any other questions

Step-by-step explanation:

The negative value indicates that the policy is providing a net benefit of approximately $9,742.21 over the 10-year period.

To calculate the net cost of insurance, we need to compare the return on investment from investing the premium elsewhere with the cash value of the policy.

First, let's calculate the amount of money you would have if you invested the $2,000 premium elsewhere for 10 years with a 5% annual yield. We can use the compound interest formula:

A = P * (1 + r)^n

Where:

A is the final amount.

P is the principal amount (premium).

r is the interest rate per period (5% or 0.05).

n is the number of periods (10 years).

Calculating the investment amount:

A = 2,000 * (1 + 0.05)^10

A ≈ 2,000 * 1.628895

A ≈ 3,257.79

Therefore, if you invested the premium elsewhere, you would have approximately $3,257.79 after 10 years.

Now, let's calculate the net cost of insurance:

Net cost of insurance = Annual premium - Cash value of the policy + Investment return

Net cost of insurance = 2,000 - 15,000 + 3,257.79

Net cost of insurance ≈ -$9,742.21

The negative value indicates that the policy is providing a net benefit of approximately $9,742.21 over the 10-year period.

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The value of x, representing the length of the hypotenuse AC, is 3√2 units.

In a right triangle ABC, with angle ABC measuring 45 degrees and side AB having a length of 3 units, we can use trigonometric ratios to find the length of the hypotenuse AC, represented by x.

Since angle ABC is 45 degrees, we know that it is a special right triangle, specifically a 45-45-90 triangle.

In such a triangle, the lengths of the sides are in a specific ratio: 1:1:√2.

In this case, side AB is 3 units, which represents the length of one of the legs. By the ratio mentioned earlier, the hypotenuse AC (x) will be √2 times the length of AB.

Therefore, we have:

AC = AB [tex]\times[/tex] √2

AC = 3 [tex]\times[/tex] √2

AC = 3√2 units

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Answer:

y = (2x + 5)(2x + 3)

Step-by-step explanation:

y = 4x² + 16x + 15

consider the factors of the product of the coefficient of the x² term and the constant term which sum to give the coefficient of the x- term

product = 4 × 15 = 60 and sum = + 16

the factors are + 10 and + 6

use these factors to split the x- term

y = 4x² + 10x + 6x + 15 ( factor the first/second and third/fourth terms )

y = 2x(2x + 5) + 3(2x + 5) ← factor out (2x + 5) from each term

y = (2x + 5)(2x + 3)

since multiplication is commutative , then could be

y = (2x + 3)(2x + 5)

Answer:

f(x)=5x

g(x)=1/x-5

f(g)=5(1/x-5)

f(x)=5/x- 25

therefore domain is x=0

The lengths of the three sides of the pie-shaped lake-front lot are:

Shortest side: 100 feet

Second side: 400 feet

Third side: 600 feet

Let's denote the lengths of the three sides of the triangular lake-front lot as x, x + 300, and x + 500.

The perimeter of a triangle is the sum of its three sides, so we can set up an equation to represent the given information:

x+ (x + 300) + (x + 500) = 1,100

Simplifying the equation:

3x + 800 = 1,100

Subtracting 800 from both sides:

3x = 300

Dividing both sides by 3:

x = 100

Now that we have found the length of the shortest side, we can substitute this value back into the expressions for the other two sides:

Shortest side (x) = 100 feet

Second side (x + 300) = 100 + 300 = 400 feet

Third side (x + 500) = 100 + 500 = 600 feet

Therefore, the lengths of the three sides of the pie-shaped lake-front lot are:

Shortest side: 100 feet

Second side: 400 feet

Third side: 600 feet

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The probability of landing on the dark blue target is 2/5.

Probability is the ratio of required to the total possible outcomes of an event.

P(dark blue ) = 40/100

divide through by 20

P(dark blue ) = 2/5

Therefore, the probability of landing on target is 2/5

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Answer:

A

Step-by-step explanation:

the axis of symmetry passes through the vertex

its equation x = - 5 is the x- coordinate of the vertex

substitute x = - 5 into f(x) for corresponding y- coordinate

f(- 5) = - (- 5)² - 10(- 5) + 16

       = - 25 + 50 + 16

      = - 25 + 66

     = 41

coordinates of vertex = (- 5, 41 )

According to the information we can infer that it will take approximately 31 years for the wolf population to reach 500.

The given function, w(x) = 14 * 1.08^x, models the number of wolves (w) in the years since 1995 (x).

To find the number of years it will take for the population to reach 500 wolves, we can set up the equation:

Dividing both sides by 14, we get:

Taking the logarithm (base 1.08) of both sides to solve for x:

Using a calculator, we find that x ≈ 31.

According to the above it will take approximately 31 years for the wolf population to reach 500 based on the given model.

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Answer:

answer is 42

Step-by-step explanation:

use the distance formula and it's simple afterwards. I am pretty sure the answer is correct but let me know if you need more help