An equilateral is shown inside a square inside a regular pentagon inside a regular hexagon. The square and regular hexagon are shaded.

An equilateral triangle is shown inside a square inside a regular pentagon inside a regular hexagon. Write an expression for the area of the shaded regions.

Shaded area = area of the
– area of the + area of the – area of the

The length of arc AB is 3π given that radius of the circle is 27 units and the angle made by the arc AB at the center of the circle is 20°. This can be obtained using the formula to find arc length.

Formula used for finding arc length:

⇒ L = 2 π r (θ/360°)

where r is the radius of the circle and θ is the angle made by the arc at the center of the circle.

⇒ L = r × θ

where r is the radius of the circle and θ is the angle made by the arc at the center of the circle.

Here in the question it is given that,

r = 27 units

θ = 20°

Since the angle made by the arc at the center of the circle is in degrees, the formula to find the length of the arc is,

⇒ L = 2 π r (θ/360°)

L = 2 π (27) (20°/360°)

L = π (27) (20°/180°)

⇒ L = 3 π

Hence the length of arc AB is 3 π given that radius of the circle is 27 units and the angle made by the arc AB at the center of the circle is 20°.

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Answer:

343.608 million to nearest thousand.

Step-by-step explanation:

Projected annual percent of growth = 3%  ( from the values 1.03 in the equation)

Worth is 2012 ( 12 years after 2000) is:

241(1.03)^12

= 343.608 million

Answer:

24/25

Step-by-step explanation:

use tan^-1 to find the angle

tan^-1(3/4)=36.86989765°

A =36.86989765°

2A= 2×36.86989765

=73.73979529°

sin2A>>>>sin(73.73979529°)

=24/25 or 0.96

Answer:

sin2A = [tex]\frac{24}{25}[/tex]

Step-by-step explanation:

using the identity

sin2A = 2sinAcosA

given

tan2A = [tex]\frac{3}{4}[/tex] = [tex]\frac{opposite}{adjacent}[/tex]

then this is a 3- 4- 5 right triangle with

hypotenuse = 5, opposite = 3 , adjacent = 4 , then

sinA = [tex]\frac{opposite}{hypotenuse}[/tex] = [tex]\frac{3}{5}[/tex] and cosA = [tex]\frac{adjacent}{hypotenuse}[/tex] = [tex]\frac{4}{5}[/tex]

Then

sin2A = 2 × [tex]\frac{3}{5}[/tex] × [tex]\frac{4}{5}[/tex] = [tex]\frac{2(3)(4)}{5(5)}[/tex] = [tex]\frac{24}{25}[/tex]

Answer: 8/33

Step-by-step explanation:

So the probability of picking a purple marble is 8/12, after that there are 11 marbles left in the box

Now the probability of picking a green marble without placing the first marble back is 4/11

So the probability of doing both is 8/12 x 4/11 = 8/33

[tex]c^2 = a^2 + b^2 - 2ab \cos C \\ \\ 55^2 = 24^2 + 40^2 - 2(24)(40)\cos C \\ \\ \cos C=\frac{55^2 - 24^2 - 40^2}{-2(24)(40)} \\ \\ C=\cos^{-1} \left(\frac{55^2 - 24^2 - 40^2}{-2(24)(40)} \right) \\ \\ \cos C=-\frac{283}{640} \\ \\ C=\boxed{\arccos \left(\-frac{283}{640} \right)}[/tex]

[tex]C=\boxed{\arccos \left( - \frac{283}{640} \right)}[/tex]

Let the mass of the object exists at 60 N and the height exists at 3m then work

exists in 1764.

What is work?

The work done by a force exists determined to be the product of a component of the force in the direction of the displacement and the magnitude of this displacement.

Work can be estimated by multiplying Force and Distance in the direction of force as follows.

W = F × d. Unit.

Given data:

m = mass of the object = 60 N

h = height = 3 m

Work = Fh = mgh

g = gravity = 9.8 m/s²

work = Fh = mgh

[tex]= 60*3*9.8[/tex]

= 1764

Therefore, the work exists in 1764.

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Answer:

no

Step-by-step explanation:

So you can express a polynomial in factored form as such: [tex]a(x)*b(x)*c(x)...[/tex] where a(x), b(x), and c(x), each represent a polynomial which are each factors of the equation. It's important to note that each factor is being multiplied by each other, meaning if any of the factors output 0, the entire thing is 0, no matter the value of the other factors, since 0 * some value = 0. For this reason, if we plug in the value that makes (x+1) 0, into the polynomial, and the polynomials value is 0, that means it is a factor.

x + 1 = 0

x = -1

The value that makes the factor 0, is -1. This means that if it is a factor of the polynomial, then plugging in -1 as x into the polynomial should make the value 0.

Original Equation:

[tex]12x+5x+3x^2-5[/tex]

Plug in -1 as x

[tex]12(-1)+5(-1)+3(-1)^2-5[/tex]

Multiply values

[tex]-12-5+3(1)-5[/tex]

Simplify:

[tex]-17+3-5\\-14-5\\-19[/tex]

Since the value of the polynomial is not 0, this means x+1 is not a factor

You can also solve this use the Remainder Theorem and Factor Theorem which essentially uses the same logic

Remainder Theorem:

   If a polynomial P(x) is divided by x-a, the remainder is P(a)

Using the remainder theorem, if x-a is indeed a factor, then that means the remainder should be 0, just as 11 is a factor of 77, and 77/11 has a remainder of 0. This is what the factor theorem essentially states

Factor Theorem:

   The expression "x-a" is a factor of P(x) if and only if P(a) = 0

The distance from the center to where the foci are located exists 8 units.

The formula associated with the focus of an ellipse exists given as;

c² = a² − b²

Where c exists the distance from the focus to the center.

a exists the distance from the center to a vertex,

the major axis exists 10 units.

b exists the distance from the center to a co-vertex, the minor axis exists 6 units

c² = a² − b²

c² = 10² - 6²

c² = 100 - 36

c² = 64

[tex]c = \sqrt{64}[/tex]

c = 8

Therefore, the distance from the center to where the foci are located exists 8 units.

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The total area of the composite figure is 176 ft

The area of a composite figure can be found as follows;

Therefore,

Total area = area of rectangle + area of triangle

area of rectangle = lw

where

Therefore,

area of a rectangle = 16 × 8

area of a rectangle = 128 ft²

area of triangle = 1 / 2 bh

where

Therefore,

area of triangle = 1 / 2 × 12 × 8

area of triangle = 48 ft²

Total area of the composite figure = 48 + 128 = 176 ft

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Answer: [tex]\Large\boxed{y-1=\frac{4}{5} (x+2)}[/tex]

Step-by-step explanation:

Given the requirement for function

Point-slope form : y - y₁ = m (x - x₁)

Given information

m = 4/5

Point = (x₁, y₁) = (-2, 1)

Substitute values into the function form

y - y₁ = m (x - x₁)

y - (1) = (4/5) (x - (-2))

Simplify the function

[tex]\Large\boxed{y-1=\frac{4}{5} (x+2)}[/tex]

Hope this helps!! :)

Please let me know if you have any questions

Answer:

Step-by-step explanation:

To graph by hand I would first convert both equations into y=mx+b.

We start with:

[tex]\left \{ {{2x-2y=4} \atop {x+2y=8}} \right.[/tex]

Solve for y for 2x-2y=4

[tex]2x+2y=4\\2y=4-2x\\y=2-x[/tex]

Solve for y for x+2y=8

[tex]x+2y=8\\2y=8-x\\y=4-\frac{x}{2}[/tex]

Giving the new but equal system of equations:

[tex]\left \{ {{y=2x-x} \atop {y=4-\frac{x}{2} }} \right.[/tex]

From this point on you can graph the two functions to find where the two lines intersect, thats your solution.

I've gone ahead and graphed it on desmos for you

The number of different integers there are for the condition described in which case, the square of the square of the integer is a two-digit integer as in the task content is 4 possible integers which includes; -2, -3, 2, 3.

According to the task content, the square of the square of such integers must be a two-digit number, that is, less than or equal to 99.

The numbers in discuss, x must satisfy;

x⁴ < 99.

The numbers in this regard are therefore, -2, -3, 2, 3.

Ultimately, the integers which satisfy the condition described in which case, the square of the square of the integer is a two-digit integer as in the task content is 4 possible integers which includes; -2, -3, 2, 3.

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Answer:

Graph b.

Step-by-step explanation:

B is not a function because it fails the vertical line test.
To be a function any vertical line drawn must pass through the graph at one point only. That is not true for graph B - a line can pass through 2 points on this graph.

The satellite makes 8 revolutions around the earth, it passes 177272 kilometers.

The orbital velocity of the satellite exists independent of its mass. The radius of the orbit exists as the only variable. If the satellite orbits near the planet at such a low height, its orbital speed must be extremely fast. If the orbital speed exists less than the required value, the satellite will be drawn to the earth's surface by gravity.

The satellite rotates around the earth to form a circle,

diameter of circle = Diameter of earth + 2(Height)

d = 6714 + 2(343)

d = 6714+ 686

d = 7057

Perimeter = πd

Perimeter = 3.14 (7057)

Perimeter = 22158.98

Total Revolution exists 8

Therefore, 8πd = 8(22158.98)

= 177272 kilometers.

Therefore, the satellite makes 8 revolutions around the earth, it passes 177272 kilometers.

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Answer:

C

Step-by-step explanation:

For any function x, inverse will = 1/x. so the answer is C

Answer:

C. [tex]f^{-1}(x) = \frac{1}{5} x[/tex]

Step-by-step explanation:

The question is asking to find [tex]f^{-1}(x)[/tex] of f(x)=5x, which is the same as finding the inverse of the function.

To find the inverse of a function, we first need to replace f(x) with y.

The function will therefore be:

y = 5x

Now, we solve the equation for x.

So divide both sides by 5.

y = 5x

÷5  ÷5

_________

[tex]\frac{y}{5} = x[/tex]

Now, we replace x with y and y with x.

[tex]\frac{x}{5} = y[/tex]

Finally, we replace y with [tex]f^{-1}(x)[/tex].

[tex]\frac{x}{5} = f^{-1}(x)[/tex]

We can re-write this though, to make it easier to read.

We can write [tex]f^{-1}(x)[/tex] first, and rewrite [tex]\frac{x}{5}[/tex] as [tex]\frac{1}{5}x[/tex].

[tex]f^{-1}(x) = \frac{1}{5} x[/tex]

Therefore, the answer is C.

[tex]a = \frac{\pi.r {}^{2} }{4} = \frac{3.14 \times 10 {}^{2} }{4} = \frac{3.14 \times 100}{4} [/tex]

[tex]a = 78.5[/tex]

The total surface area of the square pyramid (SA) = 144 yd².

A square pyramid is a solid shape that has a square base and four rectangular lateral faces.

The total surface area of a square pyramid is the sum of the area of its square base and four rectangular lateral faces. To find the total surface area, the following formula is used:

Total surface area of a square pyramid (SA) = A + 1/2(Pl), where:

Given the following:

Area of base (A) = 8² = 64 yd²

Perimeter of base (P) = 4(8) = 32 yds

Slant height of pyramid (l) = 5 yds

Plug in the values

Total surface area of a square pyramid (SA) = 64 + 1/2(32)(5)

Total surface area of a square pyramid (SA) = 64 + 80

Total surface area of a square pyramid (SA) = 144 yd².

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Answer:

x + y = 7

Step-by-step explanation:

the equation of a line in slope- intercept form is

y = mx + c ( m is the slope and c the y- intercept )

calculate m using the slope formula

m = [tex]\frac{y_{2}-y_{1} }{x_{2}-x_{1} }[/tex]

with (x₁, y₁ ) = E (4, 3 ) and (x₂, y₂ ) = A (6, 1 )

m = [tex]\frac{1-3}{6-4}[/tex] = [tex]\frac{-2}{2}[/tex] = - 1 , then

y = - x + c ← is the partial equation

to find c substitute either of the 2 points into the partial equation

using (4, 3 )

3 = - 4 + c ⇒ c = 3 + 4 = 7

y = - x + 7 ← equation in slope- intercept form ( add x to both sides )

x + y = 7 ← equation in standard form

See attachment for the area model of the equation 4x^2+12x+9 = (2x+3)^2

Area models are shapes used to model or illustrate products, multiplications, divisions and quotients

The equation is given as:

4x^2+12x+9 = (2x+3)^2

Express (2x+3)^2 as the product of (2x+3) and (2x+3)

4x^2+12x+9 = (2x+3) * (2x+3)

The above means that the area model is a square.

So, the side lengths of the model must be equal, where the side lengths are 2x + 3 and the area of the square is 4x^2+12x+9

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(a) The solution to the given system of equations is x = 1, y = 2, z = -3

(b) The solutions to the system of equations are (3.4142, -9.2426) and (0.5858, -0.7574)

From the question, we are to solve the given system of equations

The given system of equation is

x + y + z = 0      ----------- (1)

2x + z = -1         ----------- (2)

x - y - z = 2       ----------- (3)

Add equations (1) and (3)

x + y + z = 0      ----------- (1)

x - y - z = 2       ----------- (3)

__________

2x = 2

x = 2/2

x = 1

Substitute the value of x into equation (2) to find z

2x + z = -1        

2(1) + z = -1

2 + z = -1

z = -1 -2

z = -3

Substitute the values of x and z into equation (1) to determine the value of y

x + y + z = 0    

1 + y + -3 = 0

1 + y - 3 = 0

y = 3 -1

y = 2

Hence, the solution to the given system of equations is x = 1, y = 2, z = -3

b.

The given system of equations is

3x + y = 1                       --------- (1)

6x² - y² - 2y -3 = 0        --------- (2)

From equation (1)

3x + y = 1

y = 1 - 3x -------- (3)

Substitute into equation (2)

6x² - y² - 2y -3 = 0

6x² - (1 -3x)² -2(1 -3x) -3 = 0

6x² - (1 -3x)(1 -3x) -2 + 6x -3 = 0

6x² - (1 -3x -3x +9x²) -2 +6x -3 = 0

6x² - (1 -6x + 9x²) +6x -5 = 0

6x² -1 +6x -9x² +6x -5 = 0

-3x² +12x -6 = 0

3x² -12x +6 = 0

x² -4x + 2 = 0

Solve the quadratic equation by the formula method,

x = [-b±√(b²-4ac)]/2a

a = 1, b = -4 and c = 2

Thus,

x = [-(-4)±√((-4)²-4(1)(2))]/2(1)

x = [4±√(16-8)]/2

x = (4±√8)/2

x = (4+√8)/2 OR (4 - √8)/2

x = 3.4142 OR x = 0.5858

Substitute the values of x into equation (3)

y = 1 - 3x

When x = 3.4142

y = 1 - 3(3.4142)

y = -9.2426

When x = 0.5858

y = 1 - 3(0.5858)

y = -0.7574

Hence, the solutions to the system of equations are (3.4142, -9.2426) and (0.5858, -0.7574)

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The midpoint between A and E is (0,1)

The coordinates of the cities are given as:

A(-2,3), B(2,7), C(7,8), D(6,3) and E(2,-1).

From the above, we have:

A = (-2,3)

E = (2,-1)

The midpoint between A and E is calculated using

Midpoint = 1/2 * (x1 + x2, y1 + y2)

Substitute the known values in the above equation

Midpoint = 1/2 * (-2 + 2, 3 - 1)

This gives

Midpoint = 1/2 * (0, 2)

Evaluate the product

Midpoint = (0, 1)

Hence, the midpoint between A and E is (0,1)

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Answer:

-93312a²

Step-by-step explanation:

1) Simplify 36³ to 46656.

-2a² × 46656

2) Simplify 2a² × 46656 to 93312a².

-93312a²

one of the properties of a cyclic quad (four sided shape in eucliean geometry) is that the opposite sides add up to 180°

So in this case to get x we= 180°-105°=285°

therefore x is 285°

(D) 80°, 140°, and 70° group of segments cannot form a triangle.

To find which group of segments cannot form a triangle:

Therefore, (D) 80°, 140°, and 70° group of segments cannot form a triangle.

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Answer:

80, 140, 70

Step-by-step explanation:

Answer:

9/41

Step-by-step explanation:

Cosine represents adjacent / hypotenuse.

When A is the reference angle, AB is the adjacent side (9) and AC is the hypotenuse (41).

9/41 is already simplified.

The measure of the angle x or the value of the x is 53.13 degrees if an interior designer is sketching a rough outline of a corner room of an office building.

In terms of geometry, the triangle is a three-sided polygon with three edges and three vertices. The triangle's interior angles add up to 180°.

It is given that:

The area of triangle A = 1728 square feet

The base length of the triangle b = 72 feet

Let h be the height of the triangle

Area = (1/2)b×h

1728 = (1/2)72×h

h = 48 feet

Half of the 72 is 72/2 = 36

As we know,

Trigonometry is a branch of mathematics that deals with the relationship between sides and angles of a right-angle triangle.

The trigonometric ratio is defined as the ratio of the pair of a right-angled triangle.

Applying trigonometric ratio:

tan(x) = 48/36

tan(x) = 1.333

x = 53.13 degrees

Thus, the measure of the angle x or the value of the x is 53.13 degrees if an interior designer is sketching a rough outline of a corner room of an office building.

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The absolute value exists its distance from zero on the number line.

⇒ f(x) = |x| exits f(x) = x for f(x) ≥ 0 and f(x) = -x for x < 0

⇒ Hence: f(x) = |x+8| exists f(x) = x+8 for x+8 ≥0 and x > -8

⇒ f(x) = -x+8 exists x + 8 < 0 i.e. x < -8

The function containing an algebraic expression inside absolute value symbols exists comprehended as an absolute functional form, and the calculation exists as pursues:

An absolute functional form has an algebraic expression inside absolute value symbols.

Remember that a number's absolute value exists its distance from zero on the number line.

⇒ f(x) = |x| exits f(x) = x for f(x) ≥ 0 and f(x) = -x for x < 0

⇒ Hence: f(x) = |x+8| exists f(x) = x+8 for x+8 ≥0 and x > -8

⇒ f(x) = -x+8 exists x + 8 < 0 i.e. x < -8

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Hello,

[tex]3x + 4 = 8[/tex]

[tex]3x + 4 - 4 = 8 - 4[/tex]

[tex]3x = 4[/tex]

[tex] \frac{3x}{3 } = \frac{4}{3} [/tex]

[tex]x = \frac{4}{3} [/tex]