A ship is stationary at sea.
A tugboat is 36 km away at a bearing of 130°, and a yacht is 27 km from the tugboat at a bearing of 260°.
Draw a scale diagram showing the positions of the three vessels.
Use a scale of 1 : 450,000.
Measure the distance from the ship to the yacht to the nearest km.

Answer:

  -1/2

Step-by-step explanation:

Zeros of a polynomial function are its x-intercepts, the values of x that make the polynomial zero. Each zero x=p corresponds to a linear factor (x-p) of the polynomial.

A monic polynomial is one that has a leading coefficient of 1. For a monic polynomial of degree n, the coefficient of the term of degree n-1 is the opposite of the sum of all of the zeros. The constant term of any odd-degree monic polynomial is the opposite of the product of the zeros.

The given polynomial can be made monic by dividing by its leading coefficient:

  (2x^3 -x^2 -5x -2)/2 = x^3 -(1/2)x^2 -(5/2)x -1

The given polynomial has degree 3, so we're interested in the coefficient of the x^2 term. That coefficient is -1/2, so the sum of zeros will be ...

  sum of zeros = -(-1/2) = 1/2

If z represents the third zero, then we have the sum ...

  1/2 = -1 +2 +z

  z = -1/2 . . . . . . subtract 1 from both sides

The third zero is -1/2.

The given polynomial is of odd degree, so the product of the zeros is the opposite of the constant.

  (-1)(2)(z) = -(-1)

  z = 1/(-2) = -1/2 . . . . . divide by the coefficient of z

The third zero is -1/2.

Of course, a graph will show all of the (real) zeros. The attached graph from a graphing calculator shows the third zero is -1/2.

Answer:

1/2x^3

Step-by-step explanation:

The formula for the volume of a rectangular prism is v = b x w x h (volume is base times width times height).

Just plug the numbers (or in this case variables) into the formula:

v = x times x times 1/2x

v = 1/2 times x^3

v = 1/2x^3

Volume

Option A

The triangle ABE and triangle DEC are similar by AAA option third is correct.

It is defined as the law to prove that the two triangles have the same shape, but it is not compulsory to have the same size. The ratio of the corresponding sides is in the same proportions and the corresponding angles are congruent.

We have given two triangles in the picture.

As we can see in the triangle ABE

Angle ABE = 90 degree or right angle

Similarly, in a triangle DEC

Angle DEC = 90 degree or right angle

Angle ABE = Angle DEC

Angle EAB = Angle CDE

If the corresponding two angles are the same as two triangles then the third the angle will be the same.

Angle AEB = Angle DCE

The triangle ABE and triangle DEC are similar to AAA

Thus, the triangle ABE and triangle DEC are similar by AAA option third is correct.

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The actual height of the building is 67 1/2 feet

The courthouse is the tallest building in the city. If it is 7 1/2 inches tall in the model, how tall is the actual building?

Scale factor: 1 inch = 9 feet

The given parameters are:

This means that:

7 1/2 inches : Actual = 1 inch = 9 feet

So, we have:

Actual =7 1/2 * 9 feet

Evaluate the product

Actual = 67 1/2 feet

Hence, the actual height of the building is 67 1/2 feet

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The location of point B that partitions A(3, 4) and C(5, 11) in the ratio 2:3 is (3.8, 6.8).

An equation is an expression that shows the relationship between two or more numbers and variables.

An independent variable is a variable that does not depend on other variables while a dependent variable is a variable that depends on other variables.

Let b = (x, y) represent the location of the point B, hence:

x = (2 / (2 + 3))(5 - 3) + 3 = 3.8

y = (2 / (2 + 3))(11 - 4) + 4 = 6.8

The location of point B that partitions A(3, 4) and C(5, 11) in the ratio 2:3 is (3.8, 6.8).

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We have following associations:

In this question we need to fill the blanks of a given proof by understanding and taking advantage of the most important axioms and theorems of Euclidean geometry and real algebra. In this case, a linear pair is the combination of two angles whose sum equals 180°, and those angles are always supplementary.

Thus, we have following associations:

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Answer:

D

Step-by-step explanation:

The graph in the picture given is obviously a function of f(x) = x^3 which answers whether the graph is a function or not. In addition, the answer the part on why it's a graph, it's because it passes the vertical line test.

Answer:

no

Step-by-step explanation:

the bet displays 3 hexagonal bases when in the figure there is only 2 bases.

Answer:

No.

Step-by-step explanation:

Examples of three-dimensional figures are: Cuboid, Cube, Cylinder, Sphere, Pyramid, and a Cone.

Answer:

[tex]\frac{x-22}{(x+2)(x-4)}[/tex]

Step-by-step explanation:

multiply the numerator/denominator of the first fraction by (x - 4)

multiply the numerator/denominator of the second fraction by (x + 2)

this ensures that the fractions have a common denominator

[tex]\frac{4}{x+2}[/tex] - [tex]\frac{3}{x-4}[/tex]

= [tex]\frac{4(x-4)}{(x+2)(x-4)}[/tex] - [tex]\frac{3(x+2)}{(x+2)(x-4)}[/tex] ← subtract numerators leaving the common denominator

= [tex]\frac{4x-16-3x-6}{(x+2)(x-4)}[/tex]

=[tex]\frac{x-22}{(x+2)(x-4)}[/tex]

Answer:

-2.5 < x < 71

Step-by-step explanation:

I don't see a 'z' here, so I'll use x from the picture.

You would line up your values as such:

0 < 2x+5 < 71

You have a zero at the beginning because even without having an x value, your outcome would still be 5.

Subtract 5 from all sides.

-5 < 2x < 66

You now divide by two on both sides.

-2.5 < x < 33.

Which is your final answer.

You cannot go over 33, since 71 is your largest angle, and having something like say, 34, would give you 73.

-2.5 is your lowest value since if you went lower, you would have a negative angle, which isn't possible.

Answer:

(3x^2 - 1) * (4x - 3)

Step-by-step explanation:

Answer:

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

[tex]\text{L.H.S}\\\\=\dfrac{\cos A}{1-\sin A} + \dfrac{\sin A}{1-\cos A} +1\\\\\\=\dfrac{\cos A(1-\cos A) + \sin A(1-\sin A) + (1-\sin A)(1 - \cos A)}{(1-\sin A)(1 -\cos A)}\\\\\\=\dfrac{\cos A - \cos^2 A + \sin A - \sin^2 A + 1 - \cos A - \sin A + \sin A \cos A}{(1 -\sin A)(1 - \cos A)}\\\\\\=\dfrac{-(\sin^2 A + \cos^2A) +1 + \sin A \cos A}{(1 - \sin A)(1 - \cos A)}\\\\\\=\dfrac{-1 + 1 + \sin A \cos A }{(1 - \sin A)((1 - \cos A)}\\\\\\=\dfrac{0+ \sin A \cos A}{(1 - \sin A)(1 - \cos A)}\\[/tex]

[tex]=\dfrac{\sin A \cos A}{(1 - \sin A)(1 - \cos A)}\\\\\\=\text{R.H.S}\\\\\text{Proved.}[/tex]

1) -15+4r=-9

-15+4r=-9

We move all terms to the left:

-15+4r-(-9)=0

We add all the numbers together, and all the variables

4r-6=0

We move all terms containing r to the left, all other terms to the right

4r=6

r=6/4

r=1+1/2

2) 5-y/3=-1

5-y/3=-1

We move all terms to the left:

5-y/3-(-1)=0

We add all the numbers together, and all the variables

-y/3+6=0

We multiply all the terms by the denominator

-y+6*3=0

We add all the numbers together, and all the variables

-1y+18=0

We move all terms containing y to the left, all other terms to the right

-y=-18

y=-18/-1

y=+18

3) 42=-5x-8

42=-5x-8

We move all terms to the left:

42-(-5x-8)=0

We get rid of parentheses

5x+8+42=0

We add all the numbers together, and all the variables

5x+50=0

We move all terms containing x to the left, all other terms to the right

5x=-50

x=-50/5

x=-10

I don't understand your question

Sorry!!! :)

a. The survey method is unlikely to result in a representative sample

b. Interview people on all days of the week.

A representative sample is a sub-section of a larger population and has similar characteristics of the main group population.

a. The population of the study is the entire consumers that shop at the supermarkets who shop all days of the weeks. Therefore, asking only shoppers who shopped on Monday will most likely give you a bias response as most customers may select Wednesday. The sample doesn't represent the entire population.

b. A better survey method is picking samples on all days of the week and ask them.

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Answer:

Step-by-step explanation:

Answer:

A. Another way to write g(h(x)) is (g×h)(x)

Step-by-step explanation:

Hope this helps!

If not, I am sorry.

The function is called an exponential function became the exponent is a variable.

The function is called an exponential function became the exponent is a variable.

An exponential function is a Mathematical function in the form f (x) = aˣ, where “x” is a variable and “a” is a constant which is called the base of the function and it should be greater than 0.

So, here given a fill in the blank statement, we need to find the words to be filled in the blanks,

So, the whole statement is =

The function is called an exponential function became the exponent is a variable.

The function y = 3ˣ is an exponential function because it is having a power which is a variable.

The graph of the same is attached to the solution.

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Answer:

11 17/20t

Step-by-step explanation:

add the whole numbers first then add the numbers in fraction then there you get your answer.

Answer:

25

Step-by-step explanation:

x+115=180 (straight angle)

x= 65

y= 180-90-65

=25

Answer:

32.59 (nearest hundredth)

Step-by-step explanation:

Geometric sequence

General form of a geometric sequence: [tex]a_n=ar^{n-1}[/tex]

(where a is the first term and r is the common ratio)

Given:

[tex]\displaystyle \sum^{20}_{n=1} 4 \left(\dfrac{8}{9}\right)^{n-1}[/tex]

Therefore:

Sum of the first n terms of a geometric series:

[tex]S_n=\dfrac{a(1-r^n)}{1-r}[/tex]

To find the sum of the first 20 terms, substitute the found values of a and r, together with n = 20, into the formula:

[tex]\implies S_{20}=\dfrac{4\left(1-\left(\frac{8}{9}\right)^{20}\right)}{1-\left(\frac{8}{9}\right)}[/tex]

[tex]\implies S_{20}=32.58609013...[/tex]

[tex]\implies S_{20}=32.59\:\: \sf (nearest\:hundredth)[/tex]                    

General form of geometric progression

On comparing to the summation

Apply Sum formula

[tex]\boxed{\sf S_n=\dfrac{a(1-r^n)}{1-r}}[/tex]

[tex]\\ \implies \sf S_{20}=\dfrac{4\left(1-\left(\frac{8}{9}\right)^{20}\right)}{1-\left(\frac{8}{9}\right)}[/tex]

[tex]\\ \implies\sf S_{20}=32.586[/tex]

[tex]\\ \sf\mplies S_{20}=32.59[/tex]

The meal cost spent by Jack at the restaurant if he spent $15 including tip and bill is $11.79.

An equation is an expression that shows the relationship between two or more variables and numbers.

Let x represent the meal cost, hence:

Total cost = x + 0.2x + 0.0725x

15 = 1.2725x

x = 11.79

The meal cost spent by Jack at the restaurant if he spent $15 including tip and bill is $11.79.

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The equation √(x – 1) – 5 = x – 8 has the solution 2 and 5. But the valid solution for x will be 5.

The complete question is attached below.

The solution of the equation means the value of the unknown or variable.

The equation is given below.

√(x – 1) – 5 = x – 8

Add 5 on both sides, then we have

√(x – 1) = x – 3

Square on both sides, then

            x – 1 = (x – 3)²

           x – 1 = x² – 6x + 9

x² – 7x + 10 = 0

Then the factor of the equation will be

        x² – 7x + 10 = 0

x² – 5x – 2x + 10 = 0

      (x – 5)(x – 2) = 0

                         x = 5, 2

Then the valid solution will be 5.

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First let's define bisected

To bisect an angle means to split an angle exactly in half. Both sides of a bisected angle are equal to each other

The original angle (48 degrees) is bisected so we must divide 48 by 2 to find a degree of each angle

48 ÷ 2 = 24

The measure of each new angle is 24 degrees

Answer:

t=4+6n

Step-by-step explanation:

a = 10

d=6

in general

tn = a + (n-1)*d

tn = 10 + (n-1)*6

tn = 10 + 6n - 6

tn = 4 + 6n

So if n = 5 then

t5= 4+6*5

t5= 4 + 30

t5 = 34 which agrees with your givens.