NO LINKS!! URGENT HELP PLEASE!!!

O is the center of the decagon below. Find its area. Round to the nearest tenth if necessary.

If the initial velocity is 75 feet per second, it will take approximately 5.125 seconds for the ball to hit the ground.

The given formula h= -16t²+vt+s represents the height (h) of an object thrown vertically in the air at time (t), with initial velocity (v) and initial height (s). In this case, we are given that the initial height of the softball is 4 feet and the initial velocity is 75 feet per second.

We want to find out how long it will take for the ball to hit the ground, which means we want to find the time (t) when the height (h) is 0.

Substituting the given values into the formula, we get:

0 = -16t² + 75t + 4

This is a quadratic equation in standard form, which we can solve using the quadratic formula:

t = (-b ± √(b² - 4ac)) / 2a

Where a=-16, b=75, and c=4. Substituting these values into the formula, we get:

t = (-75 ± √(75² - 4(-16)(4))) / 2(-16)

t = (-75 ± √(5625 + 256)) / (-32)

t = (-75 ± √(5881)) / (-32)

We can simplify the expression under the square root as follows:

√(5881) = √(49121) = 711 = 77

So we have:

t = (-75 ± 77) / (-32)

Simplifying further, we get two possible solutions:

t = 0.5 seconds or t = 5.125 seconds

Since the softball player hits the ball when it is 4 feet above the ground, we can disregard the solution t=0.5 seconds (which corresponds to when the ball is at its maximum height) and conclude that it will take approximately 5.125 seconds for the ball to hit the ground.

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Answer:

23.8

Step-by-step explanation:

In a right-angled triangle, x ² + b ² = c ²

30.5 is c, we can choose b to be 19.1.

x ² + b ² = c ²

x ² = c ² - b ²

= 30.5² - 19.1²

= 565.44

x = √565.44

= 23.8 (to 3 significant figures)

The required justification for the solution to the equation is shown in the solution part.

As per the given equation, the required solution would be as follows:

Given:

17/3 - (3/4)x = 1(/2)x + 5

Subtraction property of equality:

17/3 - (3/4)x - 17/3 = 1(/2)x + 5 - 17/3

- (3/4)x =  1(/2)x - 2/3

Addition property of equality:

- (3/4)x - 1(/2)x =  1(/2)x - 2/3 - 1(/2)x

-(5/4)x = -2/3

Multiplication property of equality:

-(5/4)x × -4/5 = -2/3 × -4/5

Simplification:

x = 8/15

The required justification for the solution to the equation is shown in the solution part.

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Answer:

Answer shown in picture.

Domain: {-15, 0, 9, 33, 44, 45}

Range: {15, 21, 33, 46, 57, 97}

The domain and range describe the x and y-values of a function.

Domain

The domain of a function shows the x-values covered by a function. Since the function cannot be proved to be continuous, we have to list the domain as a discrete list of values. We cannot say that the values between the listed x-values are a part of the domain. Any x-value included in the function is a part of the domain. As stated in the question, we should list our answer as an ordered list with braces.

Range

The range of a function shows the y-values covered by the function. Similar to the domain, we cannot assume that the y-values between those listed are included in the range. This means that the range will also be a list of values. Range and domain should be listed from least to greatest. So, we can create a list of all the y-values in numerical order.

Answer:2x+1

Step-by-step explanation:

The solution of the given inequality is -3<x<4.

The given inequality is,

|6x-3| < 21

Here absolute function is applied in the given expression,

Therefore,

Case 1

⇒ (6x-3) >  -21

⇒   6x-3 > -21

Add 3 both sides,

⇒         6x > -18

⇒         6x > -3

Divide by 6 both sides we get,

⇒           x > -3

Case 2:

⇒  (6x-3) < 21

⇒    6x-3 <  21

Add 3 both sides,

⇒ 6x-3+3 <  21+3

⇒         6x <  21+3

⇒         6x <  24

Divide by 6 both sides we get,

⇒           x <  4

Now plotting the graph of this inequality we get:

-3<x<4 is the solution.

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The value of a3 in the Arithmetic sequence with a1 = -10 and d = -2 is -14.

The value of a3 in the arithmetic sequence, we can use the formula for the nth term of an arithmetic sequence:

an = a1 + (n - 1) * d

Where:

- an is the nth term in the sequence

- a1 is the first term of the sequence

- d is the common difference between consecutive terms

- n is the position of the term we want to find

In this case, we are given that a1 = -10 and d = -2. We want to find the value of a3, which corresponds to the third term in the sequence (n = 3).

Plugging in the values into the formula, we have:

a3 = a1 + (3 - 1) * d

  = -10 + 2 * (-2)

  = -10 - 4

  = -14

Therefore, the value of a3 in the arithmetic sequence with a1 = -10 and d = -2 is -14.

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Answer:

It's B

Step-by-step explanation:

Look at the sides with the number compare them with each other and you will find they are the most similar ones with each other.

The volume for each cone in this problem is given as follows:

11) V = 94 in³.

12) V = 367 ft³.

13) V = 1005 in³.

The volume of a cone of radius r and height h is given by the equation presented as follows:

V = πr²h/3.

For item 11, the dimensions are r = 3 in and h = 10 in, hence the volume is given as follows:

V = π x 3² x 10/3

V = 94 in³.

For item 12, the dimensions are r = 5 ft and h = 14 ft, hence the volume is given as follows:

V = π x 5² x 14/3

V = 367 ft³.

For item 13, the dimensions are r = 8 in(half the diameter) and h = 15 in, hence the volume is given as follows:

V = π x 8² x 15/3

V = 1005 in³.

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Answer:

80.4 square units.

Step-by-step explanation:

solution Given:

apothem(a)=5

no of side(n)= 12

Area(A)-?

The area of a regular polygon can be found using the following formula:

[tex]\boxed{\bold{Area =\frac{1}{2}* n * s * a}}[/tex]

where:

In this case, we have:

First, we need to find S.

We can find the length of one side using the following formula:

[tex]\boxed{\bold{s = 2 * a * tan(\frac{\pi}{n})}}[/tex]

substituting value:

[tex]\bold{s = 2 * 5 * tan(\frac{\pi}{12})=2.679}[/tex]   here π is 180°

To find the area substituting value in the above area's formula:

[tex]\bold{Area = \frac{1}{2}* 12 * 2.679 * 5=80.37\: sqaure\: units}[/tex]

in nearest tenth 80.4 square units.

Therefore, the area of the regular polygon is 80.4 square units.

Answer:

80.4 square units (nearest tenth)

Step-by-step explanation:

The given diagram shows a regular dodecagon (12-sided polygon) with an apothem of 5 units.

The apothem of a regular polygon is the distance from the center of the polygon to the midpoint of one of its sides.

We can calculate the side length of a regular polygon given its apothem using the following formula:

[tex]\boxed{\begin{minipage}{5.5cm}\underline{Apothem of a regular polygon}\\\\$a=\dfrac{s}{2 \tan\left(\dfrac{180^{\circ}}{n}\right)}$\\\\where:\\\phantom{ww}$\bullet$ $s$ is the side length.\\ \phantom{ww}$\bullet$ $n$ is the number of sides.\\\end{minipage}}[/tex]

Substitute n = 12 and a = 5 into the equation to create an expression for s:

[tex]5=\dfrac{s}{2 \tan \left(\dfrac{180^{\circ}}{12}\right)}[/tex]

[tex]s=10\tan \left(15^{\circ}\right)[/tex]

Now we can use the standard formula for an area of a regular polygon:

[tex]\boxed{\begin{minipage}{6cm}\underline{Area of a regular polygon}\\\\$A=\dfrac{n\cdot s\cdot a}{2}$\\\\where:\\\phantom{ww}$\bullet$ $n$ is the number of sides.\\ \phantom{ww}$\bullet$ $s$ is the length of one side.\\ \phantom{ww}$\bullet$ $a$ is the apothem.\\\end{minipage}}[/tex]

Substitute the found expression for s, n = 12 and a = 5 into the formula and solve for A:

[tex]A=\dfrac{12 \cdot 10\tan \left(15^{\circ}\right) \cdot 5}{2}[/tex]

[tex]A=\dfrac{600\tan \left(15^{\circ}\right)}{2}[/tex]

[tex]A=300\tan \left(15^{\circ}\right)[/tex]

[tex]A=80.3847577...[/tex]

[tex]A=80.4\; \sf square\;units\;(nearest\;tenth)[/tex]

Therefore, the area of a regular dodecagon with an apothem of 5 units is 80.4 square units, rounded to the nearest tenth.

Answer:

Step-by-step explanation:

Answer:   B y = ±[tex]\sqrt{x+36}[/tex]

Step-by-step explanation:

To find the inverse of any equation.  Switch the x and the y then solve for y.

y = x² - 36                      >switch variables

x = y² - 36                      >add 36 to both sides

x+36=y²                         >take square root of both sides

y = ±[tex]\sqrt{x+36}[/tex]  

B

Answer:

It is true that in algebraic expressions there could have all four arithmetic operations

The general format of the solution to the system of equations in this problem is given as follows:

(x, -1/5x).

Considering the augmented matrix for the system, the system of equations in the context of this problem is defined as follows:

The second equation is true for any ordered pair (x,y), hence the system has an infinite number of solutions.

The infinite number of solutions has the format given as follows:

x + 5y =  0

5y = -x

y = -x/5.

Hence the ordered pair is:

(x, -1/5x).

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The number of 1/3 inch cubes required to fill the box is 62.

Volume = length × width × height

Height = 7/3

Length = 10/3

width = 8/3

Hence ,

Volume = 7/3 × 10/3 × 8/3 = 560/27

Size of cube = 1/3

Number of cubes required = Volume of box / size of cube

Number of cubes = 560/27 × 3/1

Number of cubes = 1680/27 = 62.22

Therefore, it will take 62 1/3 cubes to fill the box

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The answers to all parts are shown below.

The law of uninhibited decay is a first-order chemical reaction, which means that the rate of the reaction is proportional to the concentration of compound A.

The rate law can be written as:

rate = k[A]

where k is the rate constant and [A] is the concentration of compound A.

From the given data, we can use the following equation to determine the rate constant:

ln([A]t/[A]0) = -kt

where [A]t is the concentration of compound A at time t, [A]0 is the initial concentration of compound A, k is the rate constant, and t is the time.

Using the given data:

[A]t = 0.37 M

[A]0 = 0.40 M

t = 30 minutes = 0.5 hours

ln(0.37/0.40) = -k(0.5)

k = 0.0486 h⁻¹

(a) How much of compound A will remain after 2 hours?

Using the same equation and substituting the known values:

ln([A]t/[A]0) = -kt

ln([A]t/0.40) = -0.0486 x 2

[A]t/0.40 = e⁻(⁹⁷² /¹⁰⁰⁰⁰)

[A]t = 0.25 M

Therefore, after 2 hours, 0.25 M of compound A will remain.

(b) How long will it take until 0.10 M of compound A remains?

Substituting the known values into the equation again:

ln([A]t/[A]0) = -kt

ln(0.10/0.40) = -0.0486t

t = 4.26 hours

Therefore, it will take approximately 4.26 hours until 0.10 M of compound A remains.

(c) After 2 hours, the amount of compound A remaining will be 0.25 M.

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The sample size needed to be 99​% confident that the sample proportion will not differ from the true proportion by more than ​4% is given as follows:

n = 1037.

A confidence interval of proportions has the bounds given by the rule presented as follows:

[tex]\pi \pm z\sqrt{\frac{\pi(1-\pi)}{n}}[/tex]

In which the variables used to calculated these bounds are listed as follows:

The margin of error is given as follows:

[tex]M = z\sqrt{\frac{\pi(1-\pi)}{n}}[/tex]

The confidence level is of 99%, hence the critical value z is the value of Z that has a p-value of [tex]\frac{1+0.99}{2} = 0.995[/tex], so the critical value is z = 2.575.

As we have no estimate, the parameter is given as follows:

[tex]\pi = 0.5[/tex]

Then the sample size for M = 0.04 is obtained as follows:

[tex]M = z\sqrt{\frac{\pi(1-\pi)}{n}}[/tex]

[tex]0.04 = 2.575\sqrt{\frac{0.5(0.5)}{n}}[/tex]

[tex]0.04\sqrt{n} = 2.575 \times 0.5[/tex]

[tex]\sqrt{n} = \frac{2.575 \times 0.5}{0.04}[/tex]

[tex](\sqrt{n})^2 = \left(\frac{2.575 \times 0.5}{0.04}\right)^2[/tex]

n = 1037.

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The volume of the cylinder A = 1006.76 m³

The volume of the cylinder B = 2893.82 ft³

The volume of the cylinder C = 2712.96 in³

The volume of the cylinder D = 111.78 in³

The Volume of the cylinder = πr²h

Where r = radius , h = height

A) r = 15/2 = 7.5

h = 5.7

Volume = 3.14 × (7.5)² × 5.7

Volume = 1006.76

B) r = 8

height = 14.4

Volume = 3.14 × (8)² × 14.4

Volume = 2893.82

C) r = 6

h = 24

Volume = 3.14 × (6)² × 24

Volume = 2712.96

D) r = 2

h = 8.9

Volume = 3.14 × (2)² × 8.9

Volume = 111.78

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Answer:

96 cubic inches

Step-by-step explanation:

To calculate the empty space that will be left in the box once the book is inside, we need to find the difference between the volume of the box and the volume of the book.

Volume of the box:

20" x 12" x 2 1/2" = 600 cubic inches

Volume of the book:

18" x 3 1/2" x 8" = 504 cubic inches

Empty space in the box:

600 cubic inches - 504 cubic inches = 96 cubic inches

Therefore, there will be 96 cubic inches of empty space left in the box once Kylie puts the book inside.

You are approximately 3.4 miles from your starting point.

We  have,

To solve this problem, we need to use the Pythagorean theorem, which states that the sum of the squares of the two shorter sides of a right triangle is equal to the square of the length of the hypotenuse.

 |\

8 | \

 |  \

 |___\

    3

We can see that the three blocks north and 10 blocks south cancel each other out, so we only need to consider the 8 blocks west.

Using the distance formula, we can find that the distance traveled west is:

8 blocks × 2/10 mile per block = 1.6 miles

Now we can use the Pythagorean theorem to find the distance from the starting point:

distance = √(3² + 1.6²)

distance ≈ 3.4 miles

Therefore,

You are approximately 3.4 miles from your starting point.

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The relationship between graph of functions is described below.

Since we can see that,

Both equations are quadratic functions, meaning that their graphs are parabolic.

The first equation,

f(x) = (x - a)(x - b),

It represents a parabola that opens upwards or downwards depending on the values of a and b.

If a < b,

the parabola opens upwards,

and if a > b, it opens downwards.

To graph f(x),

we can first find its x-intercepts by setting f(x) = 0,

⇒ 0 = (x - a)(x - b)(x - c)

This gives us three x-intercepts,

⇒ x = a, x = b, and x = c.

The value of c is important because it determines the direction in which the parabola opens.

If c is greater than both a and b,

the parabola opens upwards, and if c is less than both a and b,

the parabola opens downwards.

If c is between a and b, the parabola has a minimum or maximum point.

Now, we can find the y-intercept by setting x = 0,

⇒  f(0) = (0 - a)(0 - b)(0 - c) = -abc

This tells us that the y-intercept is -abc.

To graph the parabola, we can plot the x-intercepts and the y-intercept, and then use the shape of the parabola to connect the points.

If the parabola opens upwards, it will have a minimum point at the vertex, and if it opens downwards, it will have a maximum point.

The second equation, f(x) = (x - a)(x - b)(x - c),

represents a cubic function,

meaning that its graph is a curve with either a local minimum or maximum.

To graph f(x), we can use the same process as above to find the x-intercepts and y-intercept, and then use the shape of the curve to connect the points.

After plotting can see, the cubic function has two local minima and one local maximum.

It also has a point of inflection at x = (a + b + c)/3.

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There are 75 triangles that can be formed using these 9 vertices.

Here we have,

We have 9 vertices arranged in a pattern where 5 vertices are above and 4 vertices are below in a parallel direction.

And we want to know how many triangles can be formed using these vertices.

In order to this,

Count the number of ways to choose 3 vertices from the 9 vertices.

This can be done using the combination formula, which is:

[tex]^{9}C_{3}[/tex] = 9! / (3! * (9-3)!)

      = 84.

Since,

A degenerate triangle is one where all three vertices lie on the same line. To count the number of degenerate triangles,

We need to count how many ways we can choose 3 vertices that lie on the same line.

There are 5 lines with 3 points each (the 5 lines with the upper vertices). So the number of degenerate triangles is:

5 [tex]^{3}C_{3}[/tex] + 4  [tex]^{3}C_{3}[/tex] = 9.

Subtract the number of degenerate triangles from the total number of triangles to get the number of non-degenerate triangles.

Therefore, the number of non-degenerate triangles is:

84 - 9 = 75.

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value of the sides of the triangle are given as follows;

shorter leg = 5

longer leg = 12

hypotenuse = 13

Pythagoras Theorem states that the sum of the squares on the legs of a right triangle is equal to the square on the hypotenuse.

If the short leg = x

the longer length = x+7

the hypotenuse = x+7+1 = x+8

Using Pythagorean theorem

(x+8)² = x² + (x+7)²

x² +16x +64 = x²+ x² + 14x +49

collecting like terms

x²-2x²+16x -14x+64 -49= 0

-x² + 22x +15 = 0

x² -2x -15 = 0

x² -5x +3x -15 = 0

(x² -5x) (3x -15) = 0

x(x-5) +3(x-5)

(x+3)(x-5) = 0

x= -3 or +5

Since length is discreet we choose the positive answer

therefore x = 5

shorter leg = 5

longer leg = 5+7 = 12

hypotenuse = 5+7+1 = 13

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The algebraic equation of the cubic function set on Cartesian plane is f(x) = (x + 6) · (x - 1) · (x - 4). (Correct choice: 3)

In this problem we find the representation of a cubic function set on Cartesian plane, whose definition as algebraic equation is shown below:

f(x) = a · (x - r₁) · (x - r₂) · (x - r₃)

Where:

Graphically speaking, the roots of the polynomials are the points of the curve on x-axis. If we know that a = 1, r₁ = - 6, r₂ = 1 and r₃ = 4, then the algebraic equation of the cubic function is:

f(x) = (x + 6) · (x - 1) · (x - 4)

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Answer:

3)  f(x) = (x - 4)(x - 1)(x + 6)

Step-by-step explanation:

The x-intercepts of a function are the points at which the curve crosses the x-axis, so when f(x) = 0.

From inspection of the given graph, the curve crosses the x-axis at:

According to the Factor Theorem, if f(x) is a polynomial and f(a) = 0, then (x - a) is a factor of f(x).

Therefore, as f(x) = 0 when x = -6, x = 1 and x = 4, then (x + 6) and (x - 1) and (x - 4) are factors of the polynomial.

Therefore, the equation of the function is:

The coordinates you would be standing on would be coordinate (-5.71, -3.57).

To discover the arrangement of point "K" that partitions the line section interfacing the beginning point to the coffee shop in a proportion of 5:2, we are able to utilize the concept of the area equation.

We should expect the starting point to be meant as A with orchestrates (- x1, - y1), and the café is implied as B with works with (- x2, - y2). The ratio of 5:2 suggests that segment AB is divided into two parts and five parts, each accounting for 7 percent of the length.

The x-direction of point K can be determined as:

xK = (5 * x2 + 2 * x1)/7

Basically, the y-direction of point K can be determined as:

yK = (5 * y2 + 2 * y1) / 7

Stopping within the arranges of the coffee shop (-8, -5) as (-x2, -y2) and accepting the beginning point as the beginning (0, 0), we have:

xK = (5 * (-8) + 2 * 0) / 7 = -40/7 ≈ -5.71

yK = (5 * (-5) + 2 * 0) / 7 = -25/7 ≈ -3.57

Hence, in case you stood on point K, you'd be around at coordinate (-5.71, -3.57).

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The distance that describes how long his route was is: 168 miles.

To determine how long the route was, we need to first represent the entire unknown distance covered by this individual with s.

5/7 s + 40 minutes + (0.75s - 118) = s

5/7s + 75/100s + 40 - 118 = s

5/7s + 75/100s - 78 = s

5/7s + 75/100s - s = 78

325s = 54600

s = 168 miles.

So, the entire distance covered by the cyclist is 168 miles.

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The distance that describes how long his route was is: 168 miles.

How to determine the length of the route.

To determine how long the route was, we need to first represent the entire unknown distance covered by this individual with s.

5/7 s + 40 minutes + (0.75s - 118) = s

5/7s + 75/100s + 40 - 118 = s

5/7s + 75/100s - 78 = s

5/7s + 75/100s - s = 78

325s = 54600

s = 168 miles.

So, the entire distance covered by the cyclist is 168 miles.

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The volume of the solid is given as follows:

55 ft³.

The volume of a rectangular prism, with dimensions length, width and height, is given by the multiplication of these dimensions, according to the equation presented as follows:

Volume = length x width x height.

The total volume would be given as follows:

V = 9 x 6 x 1.25

V = 67.5 ft³.

The volume of the removed part is given as follows:

V = 1.25 x 2.5 x (9 - 3 - 2)

V = 12.5 ft³.

Hence the volume of the solid is given as follows:

67.5 - 12.5 = 55 ft³.

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Answer:

55.0ml is answer = 22.05

Step-by-step explanation:

Each number should be dragged to a box to complete the table as follows;

Kilometers     Meters

1                        1,000

2                       2,000

3                       3,000

5                       5,000

8                       8,000

In Science and Mathematics, a conversion factor is a number that is used to convert a number in one set of units to another, either by dividing or multiplying.

Generally speaking, there are one (1) kilometer in one thousand (1,000) meters. This ultimately implies that, a proportion or ratio for the conversion of kilometer to meters would be written as follows;

Conversion:

1 kilometer = 1,000 meters

2 kilometer = 2,000 meters

3 kilometer = 3,000 meters

4 kilometer = 4,000 meters

5 kilometer = 5,000 meters

6 kilometer = 6,000 meters

7 kilometer = 7,000 meters

8 kilometer = 8,000 meters

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Missing information:

The question is incomplete and the complete question is shown in the attached picture.

The quadratic equation with the given roots is:

y = 0.5x² + 1.5x - 5

For a quadratic equation with a leading coefficient a, and roots:

x = h and x = k, we will get general formula:

y = a*(x - h)*(x - k)

Here we know that the roots are x = 2 and x = -5, replacing that we will get:

y = a*(x - 2)*(x + 5)

And we know that this quadratic passes through (1, -3), replacing these values:

-3 = a*(1 - 2)*(1 + 5)

-3 = a*(-1)*(6)

-3 = -6a

-3/-6 = a

0.5 = a

Replacing that:

y = 0.5*(x - 2)*(x + 5)

Expanding the quadratic we will get:

y = 0.5x² + 1.5x - 5

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