3. Find a quadratic polynomial whose one zero is 5 + √3 and sum of the zeroes is 10.

The area of the regular hexagon with a side length of 12.7 and apothem length of 11 is approximately 416.61 square units.

To find the area of a regular hexagon, you can use the formula , where A is the [tex]A =\frac{3\sqrt{3} }{2} (s^{2} )[/tex]area, s is the length of one side, and √3 is the square root of 3.

However, since the apothem length is given, you can also use the formula , where ap is the apothem length and p is the perimeter of the hexagon.

First, let's find the perimeter of the hexagon. Since a hexagon has six sides, the perimeter will be 6 x 12.7 = 76.2.

Next, we can use the apothem length of 11 and the side length of 12.7 to find the length of the radius of the circle inscribed in the hexagon. This is because the apothem is the distance from the center of the hexagon to the midpoint of any side, and the radius is the distance from the center to any vertex.

Using the Pythagorean theorem, we can find the radius:
[tex]r^2 = ap^2 + (\frac{s}{2} )^{2}[/tex]
[tex]r^2 = 11^2 + (\frac{12.2}{7} )^{2}[/tex]
[tex]r^2 = 121 + 40.1225[/tex]
[tex]r^2 = 161.1225[/tex]
[tex]r = \sqrt{161.1225}[/tex]
[tex]r = 12.69[/tex]

Now that we know the radius, we can use the formula for the area of a regular polygon in terms of the radius: A = (1/2) x r x ap x n, where n is the number of sides (which is 6 for a hexagon).

Plugging in the values we have:
[tex]A = \frac{1}{2} (12.69)(11)(6)[/tex]
[tex]A = 416.61[/tex]

Therefore, the area of the regular hexagon with a side length of 12.7 and apothem length of 11 is approximately 416.61 square units.

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Since the derivative of a constant is always 0, we can drop the last term:
f’(x) = -21/x^4 + 4/x^3 + 1/x^2

Using the rules of differentiation, we can find the derivative of f(x) by taking the derivative of each term separately. The power rule and the constant multiple rule will come in handy here.

f(x) = 7/x^3 – 2/x^2 – 1/x + 140

f’(x) = d/dx(7/x^3) – d/dx(2/x^2) – d/dx(1/x) + d/dx(140)

To find the derivative of 7/x^3, we can use the power rule, which states that the derivative of x^n is nx^(n-1).

f’(x) = -21/x^4 – (-4/x^3) – (-1/x^2) + 0

To find the derivative of -2/x^2, we can again use the power rule:

f’(x) = -21/x^4 + 4/x^3 – (-1/x^2) + 0

To find the derivative of -1/x, we use the power rule once more:

f’(x) = -21/x^4 + 4/x^3 + 1/x^2 + 0

And since the derivative of a constant is always 0, we can drop the last term:

f’(x) = -21/x^4 + 4/x^3 + 1/x^2

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To evaluate the integral ∫(3/(√(x² + 8514))) dx, we can use the substitution u = x² + 8514 and du/dx = 2x, which gives us:

∫(3/(√(x² + 8514))) dx = (3/2)∫(1/√u) du
= (3/2) * 2√u + C
= 3√(x² + 8514) + C

Note that we absorbed the arbitrary constant into C as much as possible.
It seems that your question contains some typos and unclear expressions. However, I can help you evaluate a definite integral that includes fractions and an arbitrary constant.

Consider the integral:

∫(3√(x² + 8514) dx)

To solve this integral, let's perform a substitution:

u = x² + 8514
du = 2x dx

Now, we can rewrite the integral as:

(3/2) ∫(√u du)

Now, we can integrate:

(3/2) ∫(u^(1/2) du) = (3/2) * (2/3) * u^(3/2) + C

Now, substitute u back with the original expression:

(3/2) * (2/3) * (x² + 8514)^(3/2) + C = (x² + 8514)^(3/2) + C

So, the evaluated integral is:

(x^2 + 8514)^(3/2) + C

Where C is the arbitrary constant.

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Answer:

The answer to your problem is:

The radius of circle F is 28.

Circle F and circle D are similar.

Step-by-step explanation:

How to find the radius:

A = π × [tex]r^{2}[/tex]

But the radius of a circle from diameter. If you can recall the diameter d, the radius is r = d / 2.

By looking at our facts we can actually see ( if we use the comparing method ) that the circles, F & D are very much similar.

Thus the answer to your problem is:

The radius of circle F is 28.

Circle F and circle D are similar.

Answer:

1/221.

Step-by-step explanation:

Probability(first card is a King) = 4/52 = 1/13 (as there are 4 kings in the pack).

Now there are 51 cards left in the pack, 3 of which are Kings, so:

Probability(second card is a King) = 3/51 = 1/17.

These 2 events are independent so we multiply the probabilities:

Required probability =

1/13 * 1/17

= 1/221.

The value of the trigonometric expression sin c - cos c is: s - r

The three most common trigonometric ratios are:

sin x = opposite/hypotenuse

cos x = adjacent/hypotenuse

tan x = opposite/adjacent

We are given that:

sinb = r and cos b = s

Thus, from the diagram attached, we can see that:

sin B = rh/h = r

cos B = sh/h = s

Thus, using trigonometric ratios, we can equally say that:

cos C = rh/h = r

sin C = sh/h = s

Thus:

sin c - cos c = s - r

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12+13 = 25, therefor the answer is correct

The x-coordinates of all inflection points a f of the function[tex]f(x) = -x^4 - 8x^3 + 6x - 2[/tex]are (-4, f(-4)) and (0, f(0)).

To find the intervals of concavity and the inflection points of the function[tex]f(x) = -x^4 - 8x^3 + 6x - 2,[/tex] we need to find the second derivative and analyze its sign.

First, we find the first derivative:

[tex]f'(x) = -4x^3 - 24x^2 + 6[/tex]

Then, we find the second derivative:

[tex]f''(x) = -12x^2 - 48x[/tex]

To determine the intervals of concavity, we need to find where f''(x) is positive or negative.

[tex]f''(x) = -12x^2 - 48x = -12x(x + 4)[/tex]

f''(x) is negative for x < -4 and x > 0, and positive for -4 < x < 0.

Therefore, the function f(x) is concave down on the intervals (-∞, -4) and (0, ∞), and concave up on the interval (-4, 0).

To find the inflection points, we need to find where the concavity changes. This occurs at x = -4 and x = 0.

At x = -4, the function changes from concave down to concave up. Therefore, (-4, f(-4)) is an inflection point.

At x = 0, the function changes from concave up to concave down. Therefore, (0, f(0)) is also an inflection point.

Thus, the inflection points of f(x) are (-4, f(-4)) and (0, f(0)).

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The degree of the monomial expression -3xy²z(-2x²yz) is derived to be equal to 8.

A monomial is a type of algebraic expression that consists of only one term. It is an expression in which the variables and their exponents are multiplied together, with no addition or subtraction involved. The degree of a monomial is the sum of the exponents of its variables.

Given the monomial:

-3xy²z(-2x²yz)

We can simplify it by multiplying the coefficients and adding the exponents of the variables:

-3(-2)x^(2+1) y^(2+1) z^(1+1)

= 6x³y³ z²

Therefore, the degree of the given monomial expression is: 3 + 3 + 2 = 8.

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The truck would have lost 36% of its initial value.

The value in dollars, v(x), of a certain truck after x years can be represented by a mathematical function or equation. In the absence of a specific equation, it is difficult to provide an answer.

However, I can provide an example of a possible equation that represents the depreciation of a truck's value over time.

Let's assume that the truck loses 20% of its value every year. If the initial value of the truck is V0 dollars, then the value of the truck after x years, Vx, can be represented by the following equation:

Vx = [tex]V0(0.8)^x[/tex]

In this equation, the term [tex](0.8)^x[/tex] represents the percentage of the truck's value that remains after x years of depreciation. For example, after one year, the truck's value would be V1 = [tex]V0(0.8)^1[/tex] = 0.8V0,

which means that the truck would have lost 20% of its initial value. After two years, the truck's value would be V2 = V0[tex](0.8)^2[/tex]= 0.64V0,

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Hello, I am Alyssa Ann Verrett.

Put the numbers in order:

City A: {2, 3.5, 4, 4, 5, 5.5}

City B: {3.5, 4, 5, 5.5, 6, 6}

a)

The mean monthly rainfall amount for city A: 4 in;

The mean monthly rainfall amount for city B: 5 in;

b)

The MAD monthly rainfall amount for city A: 0.8 in;

The MAD monthly rainfall amount for city B: 0.8 in;

c)

The median monthly rainfall amount for city A: 4 in;

The median monthly rainfall amount for city A: 5.25 in;

Step-by-step explanation:

a) The general definition of mean of a set X is:

mean = (x₁ + x₂ + x₃ + ... xₙ)/n

For City a:

mean = (4+3.5+5+5.5+4+2)/6 = 4

For City b:

mean = (5+6+3.5+5.5+4+6)/6 = 5

b) The general definition of mean absolute deviation of a set X is:

MAD = (|x₁-mean| + |x₂-mean| + |x₃-mean| + ... + |xₙ-mean|)/n

For City a:

MAD = ( |4-4| + |3.5-4| + |5-4| + |5.5-4| + |4-4| + |2-4| )/6 = (0 + 0.5 + 1 + 1.5 + 0 + 2)/6 = 5/6 =0.8

For City b:

MAD = ( |5-5| + |6-5| + |3.5-5| + |5.5-5| + |4-5| + |6-5| )/6 = (0 + 1 + 1.5 + 0.5 + 1 + 1)/6 = 5/6 = 0.8

c) The general definition of median depends on the quantity of elements in the set X and it represents the middlemost value of the set:

When the quantity is odd:

median= x₍ₙ₊₁₎/₂

When the quantity is even:

median= (xₙ/₂ + x ₙ₊₂/₂) /2

For City A:

median = 2, 3.5, 4, 4, 5, 5.5 = (4 + 4) / 2 = 4

For City B:

median = 3.5, 4, 5, 5.5, 6, 6 = (5 + 5.5) / 2 = 5.25

Answer:

Step-by-step explanation:

Solution: -4

The graph gets closer and closer to the line x=-4 but never touches it.

The divergence of vector fields at all points where they are defined ar 4x - 2xcos(xz) for all points in R3.

The divergence of the given vector field F = (2x^2 - sin(xz)) i + 5j - (sin (xz)) k can be found using the formula for divergence:

div(F) = (∂Fx/∂x) + (∂Fy/∂y) + (∂Fz/∂z)

Here, Fx = (2x² - sin(xz)), Fy = 5, and Fz = -sin(xz). Taking the partial derivatives, we get:

∂Fx/∂x = 4x - zcos(xz)

∂Fy/∂y = 0

∂Fz/∂z = -xcos(xz)

Therefore, the divergence of F is:

div(F) = (∂Fx/∂x) + (∂Fy/∂y) + (∂Fz/∂z) = 4x - zcos(xz) - xcos(xz) = 4x - 2xcos(xz)

The divergence of F is defined for all points where F is defined, which is the entire 3-dimensional space. So, the divergence of F is 4x - 2xcos(xz) for all points in R3.

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Saturn is approximately 9.52 times further from the sun than Earth.

To find out how many times further from the sun Saturn is compared to Earth, we need to divide Saturn's distance from the sun by Earth's distance from the sun.

First, let's correct the distances given:
- Earth's distance from the sun: 1.496 x 10^8 km
- Saturn's distance from the sun: 1.4246 x 10^9 km (I assume you missed the exponent)

Now, let's calculate the ratio:

Ratio = (Saturn's distance) / (Earth's distance)
Ratio = (1.4246 x 10^9 km) / (1.496 x 10^8 km)

To make the calculation easier, let's factor out the common exponent (10^8):

Ratio = (1.4246 x 10) / (1.496)
Ratio ≈ 9.52

So, Saturn is approximately 9.52 times further from the sun than Earth.

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The length of segment BC is given as follows:

BC = 47.2 km.

The Law of Cosines is a trigonometric formula that relates the lengths of the sides of a triangle to the cosine of one of its angles. It is also known as the Cosine Rule.

The Law of Cosines states that for any triangle with sides a, b, and c and angle C opposite to side c, the following equation holds true:

c² = a² + b² - 2ab cos(C)

The parameters for this problem are given as follows:

a = 27.8, b = 24.7, C = 129.1

Hence the length of segment BC is given as follows:

(BC)² = 27.8² + 24.7² - 2 x 27.8 x 24.7 x cosine of 129.1 degrees

(BC)² = 2249.0497

[tex]BC = \sqrt{2249.0497}[/tex]

BC = 47.2 km.

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Answer:

To convert the equation 3x - 15y = 11 into slope-intercept form, we need to solve for y.

First, we'll subtract 3x from both sides:

-15y = -3x + 11

Next, we'll divide both sides by -15:

y = (3/15)x - (11/15)

Simplifying the fraction:

y = (1/5)x - (11/15)

This is the slope-intercept form, where the slope is 1/5 and the y-intercept is -11/15.

Answer:

y=9

Step-by-step explanation:

The opposite angles of 2 intersecting lines are equal.

11y-36⁰=63⁰

11y=63⁰+36⁰

11y=99⁰

y=9

Hope this helps!

Answer:

12

Step-by-step explanation:

The numbers increase by 4 on each row.

The critical value for this hypothesis test is 1.676.

To test the claim that manufacturing workers in Racine and Kenosha had the same salary as workers across the state, we can conduct a hypothesis test with the following null and alternative hypotheses:

We can use a t-test for the sample mean to test this hypothesis. At a 90% confidence level, we have a significance level of alpha = 0.10. Since this is a two-tailed test (we are testing for a difference in either direction), we will split the significance level evenly between the two tails, so alpha/2 = 0.05.

We need to calculate the critical value of the t-distribution with n-1 degrees of freedom, where n is the sample size. In this case, n = 54, so the degrees of freedom is 53. We can use a t-distribution table or a calculator to find the critical value. For a two-tailed test with alpha/2 = 0.05 and 53 degrees of freedom, the critical value is approximately 1.676.

Therefore, the critical value for this hypothesis test is 1.676.

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Able Cable offers the fastest mean downloading speed among the three providers with a speed of 4.0 Mbps.

We can calculate the mean (average) download speed for each provider and compare them to determine which company offers the fastest mean downloading speed.

Based on the given data, the mean download speed for each provider is:

City Net: (3.6 + 3.7 + 3.7 + 3.6 + 3.9) / 5 = 3.7 megabits per second (Mbps)

Able Cable: (3.9 + 3.9 + 4.1 + 4.0 + 4.1) / 5 = 4.0 Mbps

Tel-N-Net: (3.9 + 3.7 + 4.0 + 3.6 + 3.8) / 5 = 3.8 Mbps

Therefore, Able Cable offers the fastest mean downloading speed among the three providers with a speed of 4.0 Mbps.

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Rectangles are relatable to factors because of their areas and perimeter equations

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

Explaining why rectangles are relatable to factors

Rectangles are relatable to factors because of the following reasons

Perimeter = 2 * (Length + width)

Area = Length * width

This means that in calculating the areas and the perimeters of a rectangles, we make use of arithmetic expressions

These arithmetic expressions, when expanded form terms and factors of  expression

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The expression |y-x| without absolute value is simply: y-x

In mathematics, the absolute value refers to the magnitude or numerical value of a real number without considering its sign. It gives the distance of the number from zero on the number line. The absolute value of a number x is denoted by |x| and is defined as follows:

If x is positive or zero, then |x| = x.

If x is negative, then |x| = -x (the negative sign is removed).

Since y > x, the difference (y-x) will be positive. The absolute value of a positive number is the number itself. Therefore, the expression |y-x| without absolute value is simply: y-x

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The system of inequalities that models this scenario are:

Part A: Based on the question, we take x be the number of hours that Paula spends watering plants and also we take y be the number of hours she spends sweeping the nursery. Hence system of inequalities equation will be:

x + y ≤ 12 (she is unable to work more than 12 hours each week)

5x + 10y ≥ 60 (she need to make about $60 per week)

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Answer:

9.42 meters

Step-by-step explanation:

radius= 1.5

double the radius to get the diameter

diameter= 3

to find the circumference the equation is π × d

3.14 × 3= 9.42

circumference= 9.42

Answer: B

The guy above is wrong! The correct answer is 7.07, and I double checked with a circumference calculator.

Step-by-step explanation:

-To find the circumference of a circle, you can use the formula C = πd.

-By using this formula the answer found is 7.07

This is 100% the right answer, trust me.

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Graph of g(x) translated right direction and h(x) translated downwards direction with respect to f(x).

The given functions are;

f(x) = |x| where a > 0

g(x) = |x-a|

h(x) = |x|-a

Plot the graph of f(x)

We get vertex point (0, 0)

Now plot the graph of g(x) = |x-a|

This graph is translated towards right direction by a unit with respect to f(x)

Now plot the graph of h(x) = |x|-a

This graph is translated downwards with respect to f(x) by a unit.

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The following table shows the weight of a cat in pounds and the corresponding number of cans of cat food to be given each day.

To complete the table, we need to use the information that the directions on the small cans of cat food say to feed a cat 1 can of food each day for every 4 pounds of body weight.

For example, for a cat weighing 4 pounds, we need to give 1 can of food each day.

For a cat weighing 5 pounds, we need to give more than 1 can but less than 2 cans of food each day.

To find the exact number of cans, we can use the formula:

cans per day = weight in pounds / 4

Substituting the given values, we get:

cans per day = 5 / 4

cans per day = 1.25

Therefore, for a cat weighing 5 pounds, we need to give 1.25 cans of food each day. We can round this to the nearest tenth to get 1.3 cans per day.

Similarly, we can use the formula to complete the rest of the table:

KIT-E-KAT weight in pounds cans per day

4   1

5   1.3

6   1.5

7   1.8

8   2

9   2.3

10  2.5

11   2.8

12  3

13  3.3

14  3.5

15  3.8

Therefore, the completed table shows the weight of a cat in pounds and the corresponding number of cans of cat food to be given each day.

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Answer:

u = 2

Step-by-step explanation:

The bearing of U from T in the image is 32 degrees South by West of T

In mathematics, bearings refer to the direction of an object or location in relation to two points. It is determined by the angle between the line joining them and that of the north.

Measured typically in degrees, it follows a cardinal system where 0° or 360° signifies North; East stands for 90°, South denotes at 180° while West represents 270°.

Thus, it can be seen that the bearing of U from T in the image is 32 degrees South by West of T

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