There is a lighthouse that is 25 meters tall and a boat is sinking 204 meters away from the lighthouse. To the nearest whole degree, what is the angle of depression from the top of the lighthouse to the sinking boat?

Yes, it is possible to have a perfect square binomial. The detailed information is given below.

In trinomial, there are three terms and in binomial, there are two terms.

Let the perfect square of the binomial will be given as

⇒ (a + b)²

There are only two terms a and b and has a square on it. So the expression (a + b)² is a perfect square binomial.

Open the bracket, then we have

(a + b)² = a² + b² + 2ab

There are only three terms a², 2ab and b² and derived from a perfect binomial square. So the expression a² + b² + 2ab is a perfect square trinomial.

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The total number of roots of the given polynomial function is 6.

The given polynomial is [tex]f(x)=3x^{6}+2x^{5}+x^{4} -2x^{3}[/tex].

We need to determine the total number of roots of the given polynomial function.

What is the total number of roots of the polynomial function?

The number of roots of any polynomial is depended on the degree of that polynomial. Suppose n is the degree of a polynomial f(x), then fx) has n number of roots.

Here, the degree of the given polynomial function is 6.

Therefore, the given polynomial function will be having 6 roots.

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The range of the relation is {0, 2, 4}

The range of the relation are the y values

From the table, we have:

y values = 0, 2, 4, 2, 0

Remove the repetition

y values = 0, 2, 4

Hence, the range of the relation is {0, 2, 4}

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The surface area of the composite figure is given by 730 sq.in

Composites are solid figures made up of basic shapes like rectangle , square and even of three dimensional figures like cube , cuboid etc.

It is given in the question to determine the area of the composite figure

Area of Cube is

Area = 6 * side²

Area = 6 * 4² = 96 sq.in

The surface area of the cuboid is equal to

Sum of surface area of all the sides

As the opposite sides are same

7x10x2 + 15x10x2 + 7x15x2

650 sq.in

As the surface area of the base of the cube is counted twice

Therefore it will subtracted from the total

96 + 650 - 4*4

=730 sq.in

Therefore the surface area of the composite figure is given by 730 sq.in

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Not sure how to explain

its 5 white and 15 red

Answer:

26 gm

Step-by-step explanation:

Tin is   1   out of (9+1)   = 1/10 th

1/10th * 260 gm  =   26 gm

Answer:

A. a = 2s - b -c

Step-by-step explanation:

Rearrange the equation in a way that you have only a on one side. When solving equations you can add, subtract, multiply or divide by the same number/variable/expression on the both sides.

[tex]s = \frac{a + b + c}{2}[/tex]

Multiply by 2 to get rid of the fraction.

[tex]s \cdot 2 = \frac{a + b + c}{2} \cdot 2[/tex]

On the right side the 2 cancels out:

[tex]s \cdot 2 = a + b + c[/tex]

On the right side next to a are still b and c. But we want a alone. Subtract b.

[tex]s \cdot 2 - b = a + b + c - b[/tex]

b - b on right side gives 0.

[tex]s \cdot 2 - b = a + c + 0[/tex]

The step above is usually skipped, because number + 0 = number.

[tex]s \cdot 2 - b = a + c[/tex]

Next to a there is still c. Subtract c.

[tex]s \cdot 2 - b - c = a + c - c[/tex]

c - c on the left is 0.

[tex]s \cdot 2 - b - c = a[/tex]

So our answer is:

[tex]s \cdot 2 - b - c = a[/tex]

It can be rewritten to (change sides):

[tex]a = s \cdot 2 - b - c[/tex]

And s · 2 can be rewritten to 2s:

[tex]a = 2s - b - c[/tex]

Answer:

169, 152, 135

Step-by-step explanation:

186-17=169

169-17=152

152-17=135

Answer:

5/7 or D

Step-by-step explanation:

i just know

The correct answer is option D which is p ³+ 2; when p = 3 the number of plants is 29.

The complete question is given below:-

liana cubed the number of flowering plants in her garden, then added 2 vegetable plants. Let p represent the original number of plants in her garden. Which shows an expression to represent the total number of plants in her garden and the total number of plants if p = 3? 3 p minus 2; when p = 3 the number of plants is 7 3 p + 2; when p = 3 the number of plants is 11 p cubed minus 2; when p = 3 the number of plants is 25 p cubed + 2; when p = 3 the number of plants is 29

Expression in maths is defined as the collection of the numbers variables and functions by using signs like addition, subtraction, multiplication, and division.

The given expression is liana cubed the number of flowering plants in her garden, then added 2 vegetable plants.

If she cubed the number of the plants will be:- P³

Now she added two vegetable plants:- 2

Then the equation will be: - p³ + 2. Now we will put the value of p = 3 in the equation.

Total number of the plants = ( 3 )³ + 2 = 27 + 2 = 29

Therefore the correct answer is option D which is p³+ 2; when p = 3 the number of plants is 29.

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Total number of plants is p³ +2 ; when p = 3 the number of plants is 29 , Option D is the right answer.

Equation is mathematical statement formed when two algebraic expressions are equated using an equal sign.

It is given that  

Let p represent the original number of plants in her garden.

then  total number of plants in her garden =  p³ +2

the total number of plants if p = 3 is

=3³ +2

= 29

p³ +2 ; when p = 3 the number of plants is 29 , Option D is the right answer.

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Answer:

Scientific Method:

Step-by-step explanation:

Scientific method is the set of basic rules that must be followed for the production of knowledge that has the rigor of science, that is, it is a method used for research and verification of a certain content. For several authors, the scientific method is the logic applied to science.

i hope this

Step-by-step explanation:

Answer:

Volume = 7WH - (1/2)W^2H

Step-by-step explanation:

The base consists of the length (L) and the width (W).  It is rectangular, so the perimeter would be the sum of all four sides:

Perimeter = L + W + L +W,

or      Perimeter = 2L + 2W

We are told that 2L + 2W = 28cm     [The perimeter is 28 cm]

------

The volume of the box is given by:  

Volume = L*W*H     [Length x Width x Height]

=====

Let's rearrange the first equation and use it in the second:

2L + 2W = 28cm

2L = 28cm - 2W

L = (28cm - 2W)/2

L = (14 - W)

Now use this definition of L (14 - W) in the second equation:

Volume = L*W*H

Volume = (14 - W)/2)*W*H

Volume = (7-(1/2)W)*W*H

Volume = 7WH - (1/2)W^2H

This can also be written as:  Volume = WH(7 - (1/2)W)

Answer:

x = -2

y = -6

Step-by-step explanation:

Equating the equations :

Equate both

And

Graph attached

The answers are as follows:

3000- standard notation

4.2*10 raised to 4 - scientific notation

1.05 × 10 raised to power –7  - scientific notation

0.0013 - standard notation

6,500,000 - standard notation

6.2 × 10 raised to power 19 - scientific notation

Concept: Standard notation is a way of writing a number so it is easier to read. It is often used for very large or very small numbers.

Scientific notation is a way of writing very large or very small numbers. A number is written in scientific notation when a number between 1 and 10 is multiplied by a power of 10.

In the given questions,

3000- standard notation

4.2*10 raised to 4 - scientific notation

1.05 × 10 raised to power –7  - scientific notation

0.0013 - standard notation

6,500,000 - standard notation

6.2 × 10 raised to power 19 - scientific notation

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Due to length restrictions, we kindly invite to see the explanation below to know the answer with respect to each component of the question concerning linear equations.

In this question we need to derive an expression of the daily distance as a function of time. Now we proceed to complete the components:

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We have been given (4 + 4i) - (13 + 17i) .after solving we get the correct option is A ) -9 - 13 i.

Complex numbers are those numbers that contain the imaginary and the real part.

We have been given (4 + 4i) - (13 + 17i) .

On removing the parenthesis

4 + 4 i - 13 - 17i.

On combine the real part and complex parts, we get

= 4 - 13 + 4i - 17 i.

= -9 - 13 i.

Therefore, The correct option is A ) -9 - 13 i.

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Answer:

John is 19 and his sister is 23.

Step-by-step explanation:

See attached image.

Answer:

15

Step-by-step explanation:

Answer:

if you mean the formula it is (1/2) · b · (6 · h + sqrt(3) · b)

Step-by-step explanation:

cylindrical-shaped aquarium is to be filled with water for the newly bought salt water fishes. How much salt water is needed if the aquarium has a 2 ft radius of its base and a height of 3 ft?

Volume = πr²h

V = (3.14) (2)² (3)

V = (3.14) (4) (3)

V = 37.68 ft³

37.68 ft³ of salt water is needed to fill the cylindrical aquarium.

Mr. Lee is buying a spherical water tank for his tomato plantation. How much water could be stored if the water tank has a radius of 2 meters?

Volume = (4/3) πr³

V = (4/3) (3.14) (2)³

V = (4/3) (3.14) (8)

V = (4/3) (25.12)

V = 33.493 m³

Mr. Lee can store 33.493 m³ of water in the spherical tank.

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Answer:

860.71m³

Step-by-step explanation:

V(cuboid) = bhd

V(cylinder) = h(pi)r²

V(shape) = cuboid - cylinder

cuboid = 10 x 10 x 12

cuboid = 1200m³

cylinder = 12(pi)3²

cylinder = 12(pi)9

cylinder = 339.292m³

shape = 1200 - 339.292

shape = 860.71m³

Answer:

860.9 -ish

Step-by-step explanation:

To find that volume we need to find the volume of the rectangular prism and subtract the volume of the cylinder.  

First, lets find the volume of the prism.  

V=lwh  

V=10*10*12  

V=1200

Now, find the volume of the cylinder.  

V=Pie*Rsquared*h

V=3.14*3squared*12

V is about 339.12  

Now do  

1200-339.12=860.88

So it is about 860.9  

The constant of proportionality will be 3.

The complete question ks given below:-

Explain how to find the constant of proportionality for the ratio of robins to cardinals. A 2-column table with 4 rows. Column1 is labelled Cardinals with entries 5, 6, 9, and 10. Column 2 is labelled Robins with entries 15, 18, 27, and 30.

In mathematics, ratios are used to determine the relationship between two numbers it indicates how many times is one number to another number.

Given data will be arranged as follows:-

robins              15, 18, 27,  30.

cardinals         5, 6, 9, 10.

The constant of proportionality will be calculated by taking a ratio of the data:-

[tex]\dfrac{Cardinals}{Robins} =\dfrac{15}{5}=\dfrac{18}{6}=\dfrac{27}{9}=\dfrac{30}{10}=3[/tex]

Therefore the constant of proportionality will be 3.

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Answer: B. When the nail became magnetized the iron atoms in the nail were temporarily aligned and caused a physical change in the nail.

Step-by-step explanation:

Electrons behave like little magnets and when they flow through a wire, they create a magnetic field, which turns the nail into a magnet

[tex]\quad \huge \quad \quad \boxed{ \tt \:Answer }[/tex]

[tex]\qquad \tt \rightarrow \:x = 16 [/tex]

____________________________________

[tex] \large \tt Solution \: : [/tex]

If two polygons are similar, their corresponding sides ratios will be equal to each other.

[tex]\qquad \tt \rightarrow \: \cfrac{8}{16} = \cfrac{2x - 20}{24} [/tex]

[tex]\qquad \tt \rightarrow \: \cfrac{1}{2} = \cfrac{2x - 20}{24} [/tex]

[tex]\qquad \tt \rightarrow \: 2x - 20 = \cfrac{24}{2} [/tex]

[tex]\qquad \tt \rightarrow \: 2x = 12 + 20[/tex]

[tex]\qquad \tt \rightarrow \: 2x = 32[/tex]

[tex]\qquad \tt \rightarrow \: x = 16[/tex]

Answered by : ❝ AǫᴜᴀWɪᴢ ❞

Answer:

D. None of the above.

Step-by-step explanation:

Supplementary angles must add up to 180 degrees.

Complementary angles must add up to 90 degrees.

Vertical angles are opposite of each other.

Hope this helps!

If not, I am sorry.

An isosceles triangle is one with two equal-length sides. The ΔBCD is an isosceles triangle.

An isosceles triangle is one with two equal-length sides. It is sometimes stated as having exactly two equal-length sides, and sometimes as having at least two equal-length sides, with the latter form containing the equilateral triangle as a particular case.

Given ΔABC is an isosceles triangle with side AB = AC. Therefore, as per the base angle theorem,

∠A = ∠C = 36°

Also, in ΔABC, the sum of the angles can be written as,

∠ABC + ∠BAC + ∠BCA = 180°

∠ABC + 36° + 36° = 180°

∠ABC = 108°

For ∠ABC we can write,

∠ABC = ∠ABD + ∠CBD

108° = 72° + ∠CBD

∠CBD = 36°

Now, in ΔBCD, the measure of ∠CBD and ∠DCB both equals to 36°. Therefore, we can write, that the ΔBCD is an isosceles triangle.

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