List the first 4 terms of a geometric sequence with the first term of 2 and a common ratio of 5.

The distance between point A to point B is 115.91 ft if the boat is heading towards a lighthouse, where Luis is watching from a vertical distance of 107 feet above the water.

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

We have:

A boat is heading towards a lighthouse, where Luis is watching from a vertical distance of 107 feet above the water. Luis measures an angle of depression to the boat at point A to be 10 degrees.

From the above information, we can draw a right-angle triangle.

Let's suppose the distance between point A and point B is x

In right-angle triangle, BCD

tan31 = DC/BC = 107/BC

BC = 107/tan31

BC = 178.07 ft

In right-angle triangle, ACD

tan20 = DC/AC

tan20 = 107/(x + BC)

Plug the value of BC

tan20 = 107/(x+178.07)

x + 178.07 = 293.980

x = 115.91 ft

Thus, the distance between point A to point B is 115.91 ft if the boat is heading towards a lighthouse, where Luis is watching from a vertical distance of 107 feet above the water.

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The polynomial equation is P(x) = (x + 1)(x + 1)(x + 1)(x - 4)

The given parameters are:

A polynomial equation is represented as:

P(x) = (x- Root)

So, we have:

P(x) = (x - (-1))(x - (-1))(x - (-1))(x - 4)

Open the inner brackets

P(x) = (x + 1)(x + 1)(x + 1)(x - 4)

Hence, the polynomial equation is P(x) = (x + 1)(x + 1)(x + 1)(x - 4)

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Answer: number 4 (43º, 62º, 75º)

Step-by-step explanation:

26 + 42 + 106 ≠ 180 so number 1 is not a triangle.

34 + 63 + 79 ≠ 180 so number 2 is not a triangle.

62 + 34 +80 ≠ 180 so number 3 is not a triangle.

43 + 62 + 75 = 180 so number 4 is a triangle.

Because only the angles are given and not the sides, there is an infinite number of triangles. The answer is number 4 (43º, 62º, 75º).

The correct situation for the given condition are as follows:

C) Both proposed placements will light the same sized area.

F) Dylan's proposed placement will light exactly half of the yard.

The area of a triangle is defined as the total space occupied by the three sides of a triangle in a 2-dimensional plane. The basic formula for the area of a triangle is equal to half the product of its base and height, i.e.,  A = 1/2 × b × h.

The area of a triangle =  (base x height) / 2

and,

both lights illuminate the same base and height = (60 x 38) / 2

                                                                                 =  1,140 sq ft

Both Dylan's and Nikki's proposed placement will lit exactly half of the yard.

The yard's total area = 60 x 38 = 2,280 sq ft,

which is twice the area lit by the lights.

Thus, The correct situation for the given condition are as follows:

C) Both proposed placements will light the same sized area.

F) Dylan's proposed placement will light exactly half of the yard.

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Answer:

Step-by-step explanation:

P(A∪B) = 1/6 + 1/2 = 2/3

Answer:

-17, -10, -6, -5, 3, 8 only change is between 3 and 8

Answer:

y = (2x/9) + 1

Step-by-step explanation:

Solving for y we get 3(-2y+x) = 5(-3y+x)+9

Expand the above we get -6y+3x=5(-3y+x)+9

which is -6y+3x = -15y+5x+9

then 9y = 2x+9

which y = (2x/9) + 1

The equation of the line of the best fit on the scatter plot is y = 150x  + 598

From the line in the scatter plot, we have the following points

(x,y) = (3,1048) and (6,1498)

The equation is then calculated using:

[tex]y = \frac{y_2 -y_1}{x_2 -x_1} *(x - x_1) + y_2[/tex]

The equation becomes

[tex]y = \frac{1498 -1048}{6 - 3} *(x - 3) + 1048[/tex]

Evaluate

y = 150 *(x - 3) + 1048

Expand the bracket

y = 150x - 450 + 1048

Evaluate the sum

y = 150x  + 598

Hence, the equation of the line of the best fit is y = 150x  + 598

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The function's behavior at vertical asymptote x = 2 is (b) [tex]\mathbf{ \lim_{x \to 2^-} f(x) = \infty\ and \ \lim_{x \to 2^+} f(x) = -\infty}[/tex]

The attached graph represents the missing information in the question.

From the attached graph, we have the following highlights:

This means that the limit of f(x) approaches negative infinity and positive infinity at this value of x

Hence, the function's behavior is (b) [tex]\mathbf{ \lim_{x \to 2^-} f(x) = \infty\ and \ \lim_{x \to 2^+} f(x) = -\infty}[/tex]

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The conditions for which it is possible to construct a triangle include:

This is defined as a three-sided polygon which has three edges and three vertices and a total internal angles of 180 degrees.

The triangle with side lengths 4 cm, 5 cm, and 15 cm can't be constructed due to the length of sides not being equal according to pythagoras theorem.

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Using the assumed values, the volume of the cone is [tex]V = \frac {250}3\pi[/tex]

The volume of a cone is calculated using:

[tex]V = \frac 13\pi r^2h[/tex]

The parameters are not given.

So, we use the following assumed values

Radius, r = 5

Height, h =10

Using the assumed values, we have:

[tex]V = \frac 13\pi * 5^2 * 10[/tex]

Evaluate the product

[tex]V = \frac {250}3\pi[/tex]

Hence, using the assumed values, the volume of the cone is [tex]V = \frac {250}3\pi[/tex]

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Answer: C (490/3

Step-by-step explanation:

If j represent the number of jelly beans in each box, then the equation that models the problem is; 6j = 324

We are told that the principal used 6 small boxes of jelly beans to fill a large glass jar.

Now, each box had the same number of jelly beans, for a total of 324 jelly beans.

If j represent the number of jelly beans in each box, then the equation that models the problem is; 6j = 324

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The correct option is option B :    -4 ≤ x ≤ 1

Increasing and decreasing functions are functions whose graphs go upwards and downwards respectively as we move towards the right-hand side of the x-axis. Increasing and decreasing functions are also called non-decreasing and non-increasing functions.

Here, from graph

as we can observe from x = -4 graph starts increases upto x = 1 and after that graph becomes constant.

Thus, between x belongs -4 to 1 the graph is increasing.

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Answer:

x - 2

Step-by-step explanation:

x^3 + 3x^2 - 4x - 12 simplifies to (x + 2)(x - 2)(x + 3)

x^2 + 5x + 6 simplifies to (x + 2)(x + 3)

(x + 2)(x - 2)(x + 3)

 (x + 2)(x + 3)

The (x + 2) and (x + 3) cancel

x - 2

Kayden Kohl

9th Grade Student

(Algebra 2)

============================================================

Explanation:

Add up the four numbers given: 4+8+4+10 = 26 items total

Kick out the 4 black shirts since they are neither blue, nor are they pants.

So we have 26-4 = 22 items that are blue or a pair of pants (or both).

Divide that over the total (26) to get the probability we're after:

22/26 = (11*2)/(13*2) = 11/13

Side note: 11/13 = 0.8462 = 84.62% approximately

For a system of equations to have no real solution, the lines of the equations must be parallel to each other. The value of e and f is -34 and 2 respectively.

What is a system of equations?

Inconsistent System

For a system of equations to have no real solution, the lines of the equations must be parallel to each other.

Consistent System

1. Dependent Consistent System

For a system of the equation to be a Dependent Consistent System, the system must have multiple solutions for which the lines of the equation must be coinciding.

2. Independent Consistent System

For a system of the equation to be an Independent Consistent System, the system must have one unique solution for which the lines of the equation must intersect at a particular.

For the given system of equations, the value of e will be -34, while the value of f will be 2.

Hence, the value of e and f is -34 and 2 respectively.

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Answer:

he value of e and f is -34 and 2

Answer:

(-3±√61)÷2

Step-by-step explanation:

First we expand the brackets to give us :

x²+5x-14 = -1 +2x

Now we make this into the quadratic format (x²+ax+b=0) by subtract -1 and 2x from both sides :

x²+3x-13 = 0

This quadratic cannot be factorized so we must use the quadratic formula :

x = [tex]\frac{-b+\sqrt{b^{2} -4ac} }{2a}[/tex]   or   x = [tex]\frac{-b-\sqrt{b^{2} -4ac} }{2a}[/tex]

a = 1 , b = 3 , c = -13

Now we simplify as much as possible by first substituting values known :

x = [tex]\frac{-3+\sqrt{3^{2} -4(1)(-13)} }{2(1)}[/tex]    or   x = [tex]\frac{-3-\sqrt{3^{2} -4(1)(-13)} }{2(1)}[/tex]

Now we evaluate the exponent :

x = [tex]\frac{-3+\sqrt{9 -4(1)(-13)} }{2(1)}[/tex]   or     x = [tex]\frac{-3-\sqrt{9 -4(1)(-13)} }{2(1)}[/tex]

Now we multiply the numbers :

x = [tex]\frac{-3+\sqrt{9 +52 } }{2(1)}[/tex]    or   x = [tex]\frac{-3-\sqrt{9 +52 } }{2(1)}[/tex]

Now we add the numbers :

x = [tex]\frac{-3+\sqrt{61} }{2(1)}[/tex]   or   x = [tex]\frac{-3-\sqrt{61} }{2(1)}[/tex]

Now we multiply the denominator:

x = [tex]\frac{-3+\sqrt{61} }{2}[/tex]   or   x = [tex]\frac{-3-\sqrt{61} }{2}[/tex]

So our final answer is (-3±√61)÷2

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Answer:

15

Step-by-step explanation:

Just substitute the x for 5
In this case:

Original function: f(x) = [tex]x^{2}[/tex] - 2x

Substitute function: f(5) = [tex](5)^{2}[/tex] - 2(5)

Now solve for the substitute function

[tex](5)^{2}[/tex] - 2(5)

25 - 10

15

Therefore, f(5) is equal to 15

Answer:

  20

Step-by-step explanation:

To find the value at the blue dot, you must identify the scale of the markings of the number line.

__

12 is 2 marks to the right of 8, so we know 2 marks has a value of 12-8 = 4.

That means the second mark to the right of 12 will be 12+4 = 16.

The second mark to the right of that is 16+4 = 20, which is where the blue dot is.

The value at the blue dot is 20.

By definition of perimeter and consecutive side, we conclude that the side lengths of the triangle with perimeter of 141 centimeters are 46, 47 and 48 centimeters.

The three sides of a triangle are consecutive if and only if they are represented by three consecutive natural numbers. The perimeter is the sum of the three side lengths, whose formula is presented below:

x + (x + 1) + (x + 2) = 141

3 · x + 3 = 141

3 · (x + 1) = 141

x + 1 = 47

x = 46

By definition of perimeter and consecutive side, we conclude that the side lengths of the triangle with perimeter of 141 centimeters are 46, 47 and 48 centimeters.

The statement is complete, the correct statement is the following:

The triangle has three consecutive sides and its perimeter is 141 centimeters. Work out the value of each side.

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Another way to write the absolute value inequality lp|≤12 is -12≤p≤12

Inequality are expression not separated by an equal sign. Given the inequality expression

lp|≤12

The modulus can be positive or negative

If positive, p ≤12 and if negative -p≤12 or p ≥- 12

Combine both solutions

-12≤p≤12

Hence another way to write the absolute value inequality lp|≤12 is -12≤p≤12

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Answer:The data set that is represented in the histogram is {5, 6, 5, 11, 12, 13, 12, 13, 14, 15, 11, 18, 17, 13} Definition of a histogram An histogram is a graph that organises numerical data. The histogram is made up of rectangles whose area is equal to the frequency of the data and whose width is equal to the class interval. the frequency is usually on the vertical axis while the class interval is usually on the horizontal axis.Explaining the graphLooking at the histogram, the age group of 5 - 10 have 3 children in the carpool. the age group of 11 - 13 have 7 children in the carpool. the age group of 14 - 18 have 4 children in the carpool. This means that there are 14 children in the carpool. The correct option should have 14 ages that range between 5 and 18. Here are the options of this question: A. {3, 3, 3, 7, 7, 7, 7, 7, 7, 7, 4, 4, 4, 4} B. {5, 10, 4, 11, 12, 13, 12, 13, 12, 11, 14, 14, 19, 18} C. {5, 6, 5, 11, 12, 13, 12, 13, 14, 15, 11, 18, 17, 13} D. {3, 5, 10, 11, 13, 7, 18, 14, 4}

Step-by-step explanation:

Answer:

C. 8/17

Step-by-step explanation:

Given:

Hypotenuse = 17

BC = 8

Cos (B) = leg adjacent to ∠B / hypotenuse

= BC/BA

Substitute

Cos (B) = 8/17

Hence option C is correct

Answer:

i) Her claim is incorrect

ii) see below

iii)  44 cm

Step-by-step explanation:

Given:

If the picture is enlarged by a scale factor of 3 to form a poster, then the dimensions of the poster will be:

Area of rectangle = width × length

⇒ Area of poster = (3x) × 3(x + 4)

                             = 9x(x + 4)

                             = 9x² + 36x  cm²

Inputting x = 31 into the area of poster formula found above:

⇒ 9(31)² + 36(31)

= 8649 + 1116

= 9765 cm²

Therefore, as 9765 ≠ 1053 her claim in incorrect.

Using the formula for the area of poster found in part (i).

Area of poster = 1053 cm²

⇒ 9x² + 36x = 1053

⇒ 9x² + 36x - 1053 = 0

⇒ 9(x² + 4x - 117) = 0

⇒ x² + 4x - 117 = 0

First find x by solving the equation from part (ii):

⇒ x² + 4x - 117 = 0

⇒ x² + 13x - 9x - 117 = 0

⇒ x(x + 13) - 9(x + 13) = 0

⇒ (x - 9)(x + 13) = 0

⇒ x = 9,  x = -13

As width cannot be negative, x = 9 only

Perimeter of picture = 2(width + length)

                                 = 2(x + x + 4)

                                 = 2(2x + 4)

                                 = 4x + 8

Input found value of x into the expression for the perimeter:

⇒ Perimeter of picture = 4(9) + 8

                                      = 36 + 8

                                      = 44 cm

The units on a base area calculations is  known to be cm² or  m² while units on your volume calculations is known to be m³ or cm³.

The unit above is used because in base area calculation, only 2 sides are calculated while in volume calculation, 3 sides are involved.

Note that in base area, square unit is often used in its calculations via the use of two dimensions length and breadth (cm² or  m² ).

In terms of volume, cubic unit is used in its calculations through the use of three dimensions length, breadth and height ( m³ or cm³.).

Note also that Area is seen as the space taken by a two dimensional flat object while volume is seen as the space taken by the three-dimensional object and as such The units on a base area calculations is  known to be cm² or  m² while units on your volume calculations is known to be m³ or cm³.

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In the proof given, BC║AD and CD║BA because: B. slopes of opposite sides are equal.

If two lines are parallel, they will have the same slope value,.

Slope = rise/run.

Slope of BC = rise/run = -2/5

Slope of AD = -2/5

Slope of BA = rise/run = -6/1 = -6

Slope of BA = rise/run = -6/1 = -6

Therefore, we can conclude that BC║AD and CD║BA because: B. slopes of opposite sides are equal.

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