Find the circumference of a circle with radius of 18 in. Leave your answer in terms of π

Answer with explanation:

The pre image which is in blue color is parallelogram.

There are four blue parallelograms here,congruent to each other,each one of them when rotated by certain angle ,gives parallelogram in brown color.

When we rotate a polygon,after rotation neither the shape nor the size of polygon changes.The two shapes are congruent to each other.

→The Polygon being rotated to create the brown quilt block pattern is

Option C: Parallelogram

Answer:

Area to be developed = 269.23 acres

Step-by-step explanation:

Let there is A acres natural area to be developed.

If 35% of A acres is developed then untouched area will be (100 - 35 = 65%)

Now it has been given in the question that 65% of A (untouched area) = 500 acres

[tex]A.\frac{65}{100}=500[/tex]

[tex]A=\frac{500}{0.65}=769.23[/tex]

So area of the natural field = 769.23 acres

Now 35% of the natural area which is to be developed = A×35%

[tex]=769.23.\frac{35}{100}=(769.23)(.35)=269.23[/tex]

Area of the natural area to be developed is 269.23 acres

The number of acres that are to be developed is 269 acres.

Using this formula

Number of acres=(Number of acres untouched/(100%-Percentage of natural area)×Percentage of natural area

Let plug in the formula

Number of acres=500 acres/(100%-35%)×35%

Number of acres=(500 acres/65%)×35%

Number of acres=769.23×35%

Number of acres=269 acres

Inconclusion the number of acres that are to be developed is 269 acres.

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Answer:

The degree of [tex]12x^4-8x+4x^2-3[/tex] is 4.

Step-by-step explanation:

The given polynomial is [tex]12x^4-8x+4x^2-3[/tex]

This polynomial is of one variable which is x. Hence, the degree of the polynomial is the highest exponent.

For the given polynomial, the highest exponent is 4.

Therefore, the degree of [tex]12x^4-8x+4x^2-3[/tex] is 4.

Answer:

The other answer is correct here except it is missing the answer 4pi/3

other wise its correct. The answers are 0, 2pi/3, and 4pi/3

Step-by-step explanation:

see previous answer

the greatest possible error when measuring in feet is 1/2 foot

 answer is B

We are given the equation:

x (y + 6) – 5 (y + 6)                           ---> 1

We are to look for the missing factor in the equation: (_) (y + 6) from the given values.

Knowing the rules of the polynomial multiplicity, we can have an idea that the given equation can also be written in the form of:

(x – 5) (y + 6)                                      ---> 2

wherein the whole factor (y + 6) was simply distributed to the values in the factor (x – 5). To prove that equations 1 and 2 are equal:

x (y + 6) – 5 (y + 6) = (x – 5) (y + 6)

Expanding:         

x y + 6 x - 5 y – 30 = x y + 6 x – 5 y – 30     (EQUAL!)

Therefore our missing factor is:

(x – 5)

The roots of the polynomial equation x³ - 7x = 6x - 12 is x = 1, 3, -4 and graph is shown in the picture.

Polynomial is the combination of variables and constants systematically with "n" number of power in ascending or descending order.

[tex]\rm a_1x+a_2x^2+a_3x^3+a_4x^4..........a_nx^n[/tex]

We have a polynomial equation:

x³ - 7x = 6x - 12

[tex]\rm x^3-7x+12=6x[/tex]

x³ - 13x + 2 = 0

(x - 1)(x -3)(x + 4) = 0

x = 1, 3, -4

Thus, the roots of the polynomial equation x³ - 7x = 6x - 12 is x = 1, 3, -4 and graph is shown in the picture.

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Answer:

[tex]\sqrt{7x}(\sqrt{x}-7\sqrt{7})\Rightarrow x\sqrt{7}-49\sqrt{x}[/tex]

Step-by-step explanation:

Given: [tex]\sqrt{7x}(\sqrt{x}-7\sqrt{7})[/tex]

Simplify the expression.

[tex]\Rightarrow \sqrt{7x}(\sqrt{x}-7\sqrt{7})[/tex]

Distribute  [tex]\sqrt{7x}[/tex] over parentheses

[tex]\Rightarrow \sqrt{7x}\cdot\sqrt{x}-\sqrt{7x}\cdot7\sqrt{7}[/tex]

[tex]\Rightarrow \sqrt{7x^2}-7\sqrt{7^2x}[/tex]

square term take out from square root

[tex]\Rightarrow x\sqrt{7}-7\cdot 7\sqrt{x}[/tex]

[tex]\Rightarrow x\sqrt{7}-49\sqrt{x}[/tex]

[tex]\sqrt{7x}(\sqrt{x}-7\sqrt{7})\Rightarrow x\sqrt{7}-49\sqrt{x}[/tex]

The We have given that the pairs of values of f(x) and g(x) with the corresponding values of h(x) s given below.

(x^2-9)/(x-3)

x^2-4x+3/x-3

x^2+4x-5/x-1

x^2-16/x-4

We have to match the pairs  of values of f(x) and g(x) with the corresponding values of h(x) if h(x) = f(x) ÷ g(x).

A function from a set X to a set Y assigns to each element of X exactly one element of Y. The set X is called the domain of the function and the set Y is called the codomain of the function. Functions were originally the idealization of how a varying quantity depends on another quantity.

1)f(x)/g(x)=(x^2-9)/(x-3)=x+3

2)f(x)/g(x)=x^2-4x+3/x-3=x+1

3)f(x)/g(x)=x^2+4x-5/x-1=x+5

4)f(x)/g(x)=x^2-16/x-4=x+4

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Answer:

The prime factors are:

a. 5 and 5 (5 × 5 = 25)

b. 2 and 19 (2 × 19 = 38)

c. 2, 2, 3, and 3 (2 × 2 × 3 × 3 = 36)

d. 3, 5, and 19 (3 × 5× 19 = 285)

e. 2, 5, 5, and 13 (2 × 5 × 5 × 13 = 650)

f. 2, 2, 3, 5, and 29 (2 × 2 × 3 × 5 × 29 = 1,740)

Step-by-step explanation:

straight from Penn

Answer: The correct option is (D) y = -x + 2.

Step-by-step explanation:  We are to select the correct equation that describes the given graph.

We can see that the graph is a straight line passing through the points (0, 2) and (1, 1).

So, the slope of the line will be

[tex]m=\dfrac{2-1}{0-1}=-1.[/tex]

Therefore, the equation of the line with slope m = -1 and passing through the point (0, 2) is given by

[tex]y-2=m(x-0)\\\\\Rightarrow y-2=-1\times x\\\\\Rightarrow y-2=-x\\\\\Rightarrow y=-x+2.[/tex]

Hence, the equation that describes the graph is  y = -x + 2.

Thus, (D) is the correct option.

The value of y, calculated using the difference between the intercepted arcs, is 69.5° when rounded to the tenths place.

The figure provided depicts a circle with a secant (line GC) and a tangent (line GB) intersecting at point G, forming an angle. There are several angle measures given in the figure: angle ECA is 30°, angle ADB is 58°, and angle EAB is 161°. The angles x° and y° are what we need to find.

Here's how to find x and y:

1. To find x:

  - The angle formed by a tangent and a chord (GB and BA in this case) is equal to the angle in the alternate segment of the circle. Therefore, x is equal to the angle in the alternate segment, which is angle ADB (58°). So, x = 58°.

2. To find y:

  - The angle formed by a tangent and a secant (GB and GC in this case) from the external point G is equal to the difference between the measure of the intercepted arc (the large arc EAC) and the measure of the adjacent arc (the small arc EC). This can be calculated by the formula [tex]\( y = \frac{1}{2}(\text{large arc} - \text{small arc}) \).[/tex]

  - The large arc EAC is the full circle (360°) minus the small arc EBC (161°), so the measure of arc EAC is 360° - 161° = 199°.

  - The small arc EC is twice the angle ECA (which is an inscribed angle) because the measure of an arc is twice the measure of an inscribed angle that subtends it. So, the measure of arc EC is 2 * 30° = 60°.

  - Now we can calculate y using the formula: [tex]\( y = \frac{1}{2}(199 - 60) \).[/tex]

Let's calculate the exact values for x and y.

The value of x is equal to the angle ADB, which is 58°.

The value of y, calculated using the difference between the intercepted arcs, is 69.5° when rounded to the tenths place.

Therefore, [tex]\( x = 58 \) and \( y = 69.5 \).[/tex]

The value of cos 53 degrees in terms of sine is,

⇒ sin 37 degree

An angle is a combination of two rays (half-lines) with a common endpoint. The latter is known as the vertex of the angle and the rays as the sides, sometimes as the legs and sometimes the arms of the angle.

We have to given that;

⇒ cos 53 degree

Hence, We can change it into sine as;

⇒ cos 53 degree

⇒ sin (90 - 53)

⇒ sin 37 degree

Thus, The value of cos 53 degrees in terms of sine is,

⇒ sin 37 degree

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To find the equations of the directrices for a hyperbola centered at the origin with a vertex at (3, 0) and a focus at (9, 0), we use the formula x = ±a/e. The hyperbola's directrices are x = ± 1.

The student asked about the equations of the directrices for a hyperbola that is centered at the origin, with a vertex at (3, 0) and a focus at (9, 0). A hyperbola has two directrices, and each is a line that is perpendicular to the transverse axis and equidistant from the center as the foci are, but on the opposite side. The equation of a directrix can be found using the formula x = ±a/e, where 'a' is the distance from the center to the vertex and 'e' is the eccentricity, which is the ratio of the distance from the center to a focus (c) over 'a'.

In this case, the hyperbola is aligned along the x-axis. Given a vertex at (3, 0), it implies that 'a' is equal to 3. Since the focus is at (9, 0), it suggests 'c' is equal to 9. The eccentricity 'e' can be found by e = c/a, which is 9/3 = 3. Using the directrix formula x = ±a/e, the two directrices of the hyperbola would be x = ±(3/3), which simplifies to x = ± 1.

Answer:

The missing term is x.

Step-by-step explanation:

Given expression is,

[tex]\frac{x}{x^2-4x+4}-\frac{x}{x^2-3x+2}------(1)[/tex]

Since, [tex]x^2-4x+4=(x)^2-2\times (2x)+(2)^2[/tex]

[tex]\implies x^2-4x+4=(x-2)^2------(2)[/tex]    ( (a-b)² = a² - 2ab + b² )

Now,   [tex]x^2-3x+2=x^2-2x-x+2[/tex]    ( By middle term splitting )

[tex]=x(x-2)-1(x-2)[/tex]

[tex]\implies x^2-3x+2=(x-1)(x-2)------(3)[/tex]

From equation (1), (2) and (3),

[tex]\frac{x}{x^2-4x+4}-\frac{x}{x^2-3x+2}=\frac{x}{(x-2)^2}-\frac{x}{(x-2)(x-1)}[/tex]

[tex]=\frac{x(x-1)-x(x-2)}{(x-2)^2(x-1)}[/tex]

[tex]=\frac{x(x-1-x+2)}{(x-2)^2(x-1)}[/tex]

[tex]=\frac{x(1)}{(x-2)^2(x-1)}[/tex]

[tex]=\frac{x}{(x-2)^2(x-1)}[/tex]

Hence, the missing term in the equation is x.

This problem is better understood with a given figure. Assuming that the flight is in a perfect northwest direction such that the angle is 45°, therefore I believe I have the correct figure to simulate the situation (see attached).

Now we are asked to find for the value of the hypotenuse (flight speed) given the angle and the side opposite to the angle. In this case, we use the sin function:

sin θ = opposite side / hypotenuse

sin 45 = 68 miles per hr / flight

flight = 68 miles per hr / sin 45

flight = 96.17 miles per hr

Since no one was getting the the answer that is on the assignment I plugged  the problem into an algebra calculator, and got A 0.6616

The apothem of the square is equal to half the length of a side of the square, which can be calculated by doubling the radius. In this case, the apothem is 3√2.

The apothem of a square is a line segment drawn from the center of the square to any side of the square, perpendicular to that side. The apothem is equal to half the length of a side of the square.

Given that the square has a radius of 3√2, we can determine the length of a side of the square by doubling the radius. So, the length of a side is 2 * 3√2 = 6√2.

Therefore, the apothem of the square is half the length of a side, which is (6√2)/2 = 3√2.