b) The height of the control tower. a) The shortest distance between the pilot and the base of the control tower. From a horizontal distance of 10.5km, a pilot observes that the angles of depression of the top and base of a control tower are 36° and 41 degrees respectively. Calculate he following:

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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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:

Step-by-step explanation:

A geometric series is the collection of an unlimited number of terms with a fixed ratio between them. The value of a₅ is -729.

A geometric series is the collection of an unlimited number of terms with a fixed ratio between them.

Given the value of a₁=9 and the value of [tex]a_n=-3a_{(n-1)}[/tex]. Therefore, the value of a₅ can be written as,

a₂ = -3(a₁) = -3(9) = -27

a₃ = -3(a₂) = -3(-27) = 81

a₄ = -3(a₃) = -3(81) = -243

a₅ = -3(a₄) = -3(-243) = -729

Hence, the value of a₅ is -729.

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Answer:

1.5

Step-by-step explanation:

The average rate of change is 1.5

when x=0 , the value of y =1

when x=2 the value of y = 4

average rate of change formula = [tex]\frac{f(b)-f(a)}{b-a}[/tex]

a= 0 , f(a)=1

b=2, f(b)= 4

4 - 1 / 2 - 0 = 3/2 = 1.5

Answer:

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

Step-by-step explanation:

Answer:

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

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.

Answer:

a. 2.25 km

Step-by-step explanation:

the scale on a map means how many units in the mapp corresponds to how many units in reality.

in this case

1 cm on the map = 75000 cm in reality =

= 75000/100 m = 750 m =

= 750/1000 km = 0.75 km

3 cm = 3×1 cm = 3 × 0.75 km = 2.25 km

Answer:3/20

Step-by-step explanation:

Fraction of total area mowed = (3/5) + (1/4) = 17/20

Therefore fraction of total area left = 1 - (17/20) = (20/20) - (17/20) = 3/20

I don't understand your question

Sorry!!! :)

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.

Answer:

The third graph

Step-by-step explanation:

The third graph depicts the function f(x) = -1/2x because for every 1 unit decrease along the y-axis, you travel 2 units on the x-axis.

Also, the two points on the third graph can satisfy the equation.

Point 1: (-2,1)

f(-2) = (-1/2)(-2)

f(-2) = 1

Point 2: (0,0)

f(0) = (-1/2)(0)

f(0) = 0

Considering the formulas for the area and the perimeter of the rectangle, the one with the desired measures is given as follows:

a length of 3 units and a width of 4 units.

Considering a rectangle of length l and width w, we have that:

For a rectangle with a length of 3 units and a width of 4 units, we have that:

Hence it is the correct option.

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It is possible that a small sample size contributed to the 82% (±24%) estimate at a 95% confidence level.

A proportional confidence interval is provided by

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

Where π is the sample proportion, z is the critical value and n is the sample size.

The margin of error is represented by

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

As a result, smaller sample sizes result in wider margins of error. Option A has the greater margin of error in this scenario, so it most likely employed the smallest sample size.

Therefore we can conclude It is possible that a small sample size contributed to the 82% (±24%) estimate at a 95% confidence level. Option A is correct.

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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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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.

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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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

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:

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:

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

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:

Side b is approximately 4.00064cm or since the question asked for the answer to be up to one decimal point, your answer should be 4 cm

Step-by-step explanation:

First of all, this triangle isn't a right triangle. This can be proven if we assume that the triangle is a right triangle. If it is a right triangle, since, one of its angle is 30 degrees, we can find the last unknown angle to = 60 degrees. Therefore, using the side ratios of a 30-60-90 triangle, and since side b is the smallest side (because it has the smallest angle facing it), its length is one half the length of the hypotenuse, therefore making its length 4. However, the 30-60-90 ration also states that, in this case, side b * sqrt(3) should be equal to the side tha measure 7cm, which is clearly not true. Therefore, proving that this triangle isn't a rigt tirangle.

So now, let's get to solving the question. Since we found out that this isn't a right triangle, we have to use the law of cosines which states

a^2 = b^2 + c^2 - 2bc*cos(A) where A is the angle facing side a

If we do this, it comes to the solution that a is approximately 4.00064cm.

Therefore, side b measures to 4.00064cm.

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.

[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]

Answer:

25

Step-by-step explanation:

x+115=180 (straight angle)

x= 65

y= 180-90-65

=25