Solve the polynomial equation. state the multiplicity of each root. 8x3 - 12x2 + 6x - 1 = 0

Kevin and Randy have 50 quarters and 18 nickels.

To solve this problem, we can set up a system of equations. Let's use the variables x for the number of quarters and y for the number of nickels. We can then write two equations based on the given information:

Equation 1: x + y = 68 (the total number of coins is 68)

Equation 2: 0.25x + 0.05y = 13.40 (the total value of the coins is $13.40).

We can start by solving Equation 1 for x in terms of y:

x = 68 - y. Now we can substitute this expression for x into Equation 2:

0.25(68 - y) + 0.05y = 13.40

Simplifying, we get 17 - 0.25y + 0.05y = 13.40.

Combining like terms, we have 0.20y = 3.60.

Dividing both sides by 0.20, we find y = 18. Plugging this value back into Equation 1, we can solve for x:

x + 18 = 68

x = 68 - 18 = 50.

Therefore, Kevin and Randy have 50 quarters and 18 nickels.

Here, we need to find the length of the hose which is diagonally placed in the rectangular garden.

The length is given as = 72 meters

The width is given as = 60 meters

We will use Pythagoras theorem here.

Hypotenuse² = Perpendicular² + Base²

Hypotenuse² = 72² + 60²

Hypotenuse² = √8,784 meters²

Hypotenuse = 93.72 meters

Thus, the length of diagonal hose will be = 93.72 meters

The correct option is (C)

109 adult tickets were sold for the school play.

Let's assume the number of adult tickets sold is x.

According to the given information, the number of student tickets sold is 2 times the number of adult tickets sold. So, the number of student tickets sold is 2x.

Since the total number of tickets sold is 327, we can write the equation x + 2x = 327. Simplifying this equation gives us 3x = 327. Dividing both sides by 3, we get x = 109.

Therefore, 109 adult tickets were sold.

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This question is about exponential growth and the rabbit population on an island.

The subject of this question is Mathematics. Specifically, it involves exponential growth and a function that represents the rabbit population on the island over time. Let's define the function f(x) to represent the population of rabbits at year x.

Based on the information given, the initial population is 20 rabbits. The population triples every year, which means that for each year x, the population is f(x) = 20 * 3^x.

For example, after 1 year, the population would be f(1) = 20 * 3^1 = 60 rabbits. After 2 years, the population would be f(2) = 20 * 3^2 = 180 rabbits, and so on.

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Correct Answer is B which is $ 358.47 for monthly payment

The complete question is :

The total height of the Statue of Liberty and its pedestal is 305 feet. This is 153 more than the height of the statue. Write and solve an equation to find the height h (in feet) of the statue.

Question says 153, so we add 153 with the height of the statue

The total height of the Statue of Liberty = Height of the statue + 153

305 = h + 153

To find out h we subtract 153 on both sides

305 - 153 = h + 153 - 153

h = 152

The height of the statue = 152 ft

The height of the statue is 152 feet.

Let's call the height of the statue "h" in feet. According to the problem, the total height of the Statue of Liberty and its pedestal is 305 feet, and this is 153 more than the height of the statue. So, you can write the equation as:

Total Height = Statue Height + Pedestal Height

305 feet = h + 153 feet

Now, to find the height "h" of the statue, you can isolate it on one side of the equation. To do that, subtract 153 feet from both sides of the equation:

305 feet - 153 feet = h

152 feet = h

So, the height of the statue is 152 feet.

To know more about equation:

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The complete question is:

The total height of the Statue of Liberty and its pedestal is 305 feet. This is 153 more than the height of the statue. Write and solve an equation to find the height h (in feet) of the statue.

Answer:

the measure of the tangent-tangent angle is 56 degrees.

Step-by-step explanation:

apex

Answer:

B) -1

Step-by-step explanation:

The ball hits the ground after approximately 4.16 seconds.

To find the time at which the ball strikes the ground, we need to determine when h(t) = 0. Given the equation for height:

[tex]\[ h(t) = -16t^2 - 21t + 190 \][/tex]

we can set h(t) to 0 and solve for t:

[tex]\[ -16t^2 - 21t + 190 = 0 \][/tex]

Using the quadratic formula, we can find the roots of this equation:

[tex]\[ t = \frac{-b \pm \sqrt{b^2 - 4ac}}{2a} \][/tex]

where a = -16 , b = -21, and c = 190. Plugging in the values, we get:

1. Find the discriminating value [tex]\( \Delta = b^2 - 4 \times a \times c \)[/tex]:

[tex]\[ \Delta = (-21)^2 - 4 \times (-16) \times 190 = 441 + 12160 = 12601 \][/tex]

2. Calculate the roots:

[tex]\[ t = \frac{-(-21) \pm \sqrt{12601}}{2 \times -16} \\ \[ t = \frac{21 \pm \sqrt{12601}}{-32} \][/tex]

Since we're interested in the positive value (representing the time when the ball hits the ground), we'll only consider the root with the "minus" sign:

[tex]\[ t = \frac{21 - \sqrt{12601}}{-32} \approx \frac{-21 + \sqrt{12601}}{32} \approx \frac{21 - \sqrt{12601}}{32} \][/tex]

Using a calculator, let's approximate the result:

[tex]1. Compute \( \sqrt{12601} \approx 112.24 \),\\2. Then calculate \( 21 + 112.24 \approx 133.24 \),\\3. Divide by 32 to get \( t \approx \frac{133.24}{32} \approx 4.16375 \).[/tex]

Rounding to a more readable result, we can say that the ball hits the ground after approximately 4.16 seconds.

It is given that:

Kali earns $ 8 per hour.

This means that if she works for n hours then this earning for n hours will be given by: $ 8n

She works x hours on both Monday and Tuesday.

This means that the earning of x hours is: $ 8x

and hence the earning for both Monday and Tuesday is:$ 2(8x)

She also worked for 5 hours on Thursday.

Hence, the earning for Thursday is: 5×8=40

The total earning of the week is given by:

                            2(8x)+5(8)