the window of a building 65m above the street level from this window ,a person looks across the street at a building and finds that the Angle of elevation of the top of the building is 72°and the angle of depression if the bottom of the building is 28° .if the street level is horizontal and the ground distance between the building is 80m.find to the nearest m the vertical heights of the building
​

Answer:

(3, 3) (1, -1)

Step-by-step explanation:

Answer:

(1, - 1) , (3, 3 )

Step-by-step explanation:

Given the 2 equations

3 + y - 2x = 0 → (1)

3x² + 2y² - 4xy = 9 → (2)

In (1) subtract 3 - 2x from both sides

y = 2x - 3 → (3)

Substitute y = 2x - 3 into (2)

3x² + 2(2x - 3)² - 4x(2x - 3) = 9 ← distribute and simplify left side

3x² + 2(4x² - 12x + 9) - 8x² + 12x = 9

3x² + 8x² - 24x + 18 - 8x² + 12x = 0

3x² - 12x + 18 = 9 ( subtract 9 from both sides )

3x² - 12x + 9 = 0 ( divide through by 3 )

x² - 4x + 3 = 0 ← in standard form

(x - 1)(x - 3) = 0 ← in factored form

Equate each factor to zero and solve for x

x - 1 = 0 ⇒ x = 1

x - 3 = 0 ⇒ x = 3

Substitute these values into (3) for corresponding values of y

x = 1 : y = 2(1) - 3 = 2 - 3 = - 1 ⇒ (1, - 1 )

x = 3 : y = 2(3) - 3 = 6 - 3 = 3 ⇒ (3, 3 )

Answer:

a) 20 km away fro the starting point.

b) The bearing from P to R is 80°.

c) Q is 60 km North P.

d) Q is - 60 km west of P

Step-by-step explanation:

Stating Facts in the Question:

P to Q is 80 km and bearing 330°

It turned around, Q to R is 60 km and bearing 250°.

a) Picture a number line (Look at the first image)

You go 80 to the right. You turn around and go 60 to the left.

80 - 60 = 20

20 km away fro the starting point

b) Picture a number line (Look at the second image)

P to Q is bearing 330°

Q to R is 60 km is bearing 250°

P to Q is red

Q to R is blue

330° - 250° = 80°

The bearing from P to R is 80°

c) P to Q is 60 km

The plane went forward or North so the answer is 60 km.

Q is 60 km North P.

d) Q to P is 60 km

Q is not to the west of P

Q is - 60 km west of P

Answer:

x=±√7

Step-by-step explanation:

Hi there!

We're given the quadratic equation 6x²-42=0 and we need to find the roots of the equation (the values of x that make the equation true).

So we need to isolate x onto one side.

We can start by adding 42 to both sides

6x²=42

divide both sides by 6

x²=7

Now, take the square root of both sides (remember that when we take the square root, we get both POSITIVE and NEGATIVE answers).

x=√7 and x=-√7 (can be rewritten as x=±√7)

Hope this helps! :)

Answer:

Step-by-step explanation:

6x the ''2'' is supposed to be a exponent  all the time -42=0

6x2 -42 + 42=0 +42 {add 42 to both sides}

6x2=42

6x2                                    42

------fraction brackets =  ------- {divide by 6}

6                                           6

x2 =7

6576 cm2

See the image encrypted above.

Answer:

AB = 8 inches

Step-by-step explanation:

given :

AD = 10 inches

BD = 6 inches

AB = ?

using pythagoras theorem

a^2 + b^2 = c^2

BD^2 + AB^2 = AD^2

6^2 + AB^2 = 10^2

36 + AB^2 = 100

AB^2 = 100 - 36

AB^2 = 64

AB = [tex]\sqrt{64[/tex]

AB = 8

The length of the AB in the given triangle ADC such that A-B-C and DB ⊥ AC  is equal to 8 inches.

In the figure of triangle ADC ,

DB is perpendicular to AC such that A- B- C.

Measure of angle CBD = 90 degrees

This implies,

As angle ABD and CBD are linear pair

⇒ Measure of angle CBD + Measure of ABD = 180°

⇒ 90° + Measure of ABD = 180°

⇒  Measure of ABD = 180° - 90°

⇒  Measure of ABD = 90°

Now triangle ABD is right angle triangle,

AD = 10 inches

BD = 6 inches

By applying Pythagoras theorem we have,

AB² + BD²  = AD²

⇒ AB² = AD² - BD²

⇒ AB² = 10² - 6²

⇒ AB² = 100 -36

⇒ AB² = 64

⇒ AB = √64

⇒ AB = 8 inches

Therefore, the length of the AB is equal to 8 inches.

Learn more about length here

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Answer:

You would need to add the picture in order to get an answer

Answer:

9x^2 + 27x + 18

Step-by-step explanation:

(9x + 9)(x + 2)

=9x(x + 2) +9(x + 2)

=9x^2 + 18x + 9x + 18

=9x^2 + 27x + 18

Answer:

it's got unlimited solutions

Step-by-step explanation:

9514 1404 393

Answer:

  x = -1/3

Step-by-step explanation:

Maybe you mean ...

  (1/49)^(x +2) = 7^(x -3)

Taking logarithms base 7, we have ...

  -2(x +2) = x -3

  -2x -4 = x -3 . . . . . eliminate parentheses

  -1 = 3x . . . . . . . . . . add 3+2x

  x = -1/3 . . . . . . . . . divide by the coefficient of x

This is confirmed by a calculator in the first attachment.

_____

As written, the equation is ...

  ((1/49)^x) +2 = (7^x) -3

Multiplying both sides by 7^(2x) gives us ...

  1 + 2·7^(2x) = 7^(3x) -3·7^(2x)

Subtracting the left side gives us the cubic equation in 7^x:

  (7^x)^3 -5·(7^x)^2  -1 = 0

This has one irrational real root (found using a graphing calculator). The solution is ...

  x ≈ 0.83111881051

This answer is confirmed in the second attachment. (10^-16 is essentially zero for this purpose.)

__

Additional comment

Part of the reason for going to the trouble to solve the "as written" equation is to show you that it is possible, though messy. What we'd like to emphasize here is that grouping symbols are needed when exponents contain math operations.

In typeset text, the superscript font indicates the grouping of parts of an exponent. In plain text, we cannot tell if 7^x-3 means (7^x)-3 or 7^(x-3). The Order of Operations tells us to interpret it the first way: (7^x) -3, because exponentiation is done before addition. That leads to trouble in this problem.

Answer:

x + 5 = 3x -1

7x + 21 = 5x + 35

5x + 5 = 6x - 5

Step-by-step explanation:

7x+21=5x+35

-5x -5x

2x+21=35

-21 -21

2x=14

÷2 ÷2

x=7

x+5=3x-1

-x -x

5=2x-1

+1 +1

6=2x

÷2 ÷2

x=3

5x+5=6x-5

-5x -5x

5=x-5

+5 +5

x=10

Hope this helps! :)

Answer:

4.9 hours

Step-by-step explanation:

3185/650 = 4.9

Answer:

x = 4 , y = 0

Step-by-step explanation:

x -    y = 4 --------- ( 1 )  

x + 2y = 4 -------- ( 2 )

( 1 ) x - 1 => - x + y = - 4  -------------( 3 )

( 2 )      =>    x + 2y = 4  ----------- ( 2 )

( 2 ) + ( 3 ) => 0 x  + 3y = 0

               => y = 0

Substitute y = 0 in ( 1 ) => x - y = 4

                                  => x - 0 = 4

                                        x = 4

Step-by-step explanation:

r=21cm

a=135

perimeter=2r+ar

=2×21+135×21

=42+2835

=2877cm

Answer:

x = 2

Step-by-step explanation:

Given

2.5(6x - 4) = 10 + 4(1.5 + 0.5x) ← distribute parenthesis on both sides

15x - 10 = 10 + 6 + 2x , that is

15x - 10 = 16 + 2x ( subtract 2x from both sides )

13x - 10 = 16 ( add 10 to both sides )

13x = 26 ( divide both sides by 13 )

x = 2

Answer:

2

Step-by-step explanation:

15x-10=10+6+2x

15x-2x=10+10+6

13x=26

divide 13 both sides

x=2

Answer:

hello the function graph is turned 90 degree like clock way.

All the plotted graphs represent functions whose inverse is also a function.

A function is a relation between a dependent and independent variable. We can write the examples of functions as -

y = f(x) = ax + b

y = f(x, y, z) = ax + by + cz

Given is to find the function whose inverse is also a function.

A one to one function is a type of function whose inverse is also a function. The linear equations are one to one functions. They are of the form {y} = ax + b. This means that all of the graphs plotted represent a  function whose inverse is also a function. So, we can conclude that all the plotted graphs represent the straight line, and all of them represent functions whose inverse is also a function.

Therefore, all the plotted graphs represent functions whose inverse is also a function.

To solve more questions on functions, visit the link below-

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Answer:

Exponent

Step-by-step explanation:

^ means raised to the power of

The number being raised is known as the exponent

In this case it's the exponent is 4

Answer:  Choice B

MN, NO, OM

Refer to the diagram below

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

Explanation:

M = 57 and N = 75 are the two given angles.

Angle O is the missing angle of the triangle.

Recall that for any triangle, the three inside angles always add to 180

M+N+O = 180

57+75+O = 180

132+O = 180

O = 180-132

O = 48

Angle O is 48 degrees.

Note: be sure not to mix up the letter 'oh' with the number zero. Unfortunately, they look very similar.

-------------------------

We know the following three angles of this triangle

As a rule, the smallest side is always opposite the smallest angle. The smallest angle is O = 48, and the side opposite that is MN.

Also, the largest side is always opposite the largest angle. The largest angle is N = 75, and the side opposite that is OM

-------------------------

In short, we found that MN is the smallest side and OM is the longest side.

That must mean side NO is placed in the middle of MN and OM

So that's how we get get the answer of MN, NO, OM which is choice B.

Refer to the diagram below.

Answer:

28cm^2

Step-by-step explanation:

By splitting the shape into 2 separate rectangles, you can find that they would be  6cm by 3cm and 5cm by 2cm. doing length x width on both and adding them gives 28cm.

Answer:

Assuming you want to know there was for UK it was [tex]\frac{3}{8}[/tex]

Step-by-step explanation:

Let's add the fractions together

[tex]\frac{1}{3} +\frac{1}{6}+\frac{1}{8\\}\\\frac{8}{24} +\frac{4}{24} +\frac{3}{24} =\frac{15}{24}[/tex]

The remainder is the amount in UK so

[tex]\frac{24}{24} -\frac{15}{24} =\frac{9}{24} \\[/tex]

Simplified it's [tex]\frac{3}{8}[/tex]

Answer:

11.16

Step-by-step explanation:

4sf=four numbers

if 0 is first number, leave it out because 0 is a significant figure

Answer:

11•16

u won't add zero because its less than 5.

Answer:

Sorry icant help

Step-by-step explanation:

i never did this before

Answer:

367.5

Step-by-step explanation:

5x7x10.5

Answer:

367.5

Step-by-step explanation:

5 x 7 = 35

35 x 10.5 = 367.5

Answer:

1/9

Step-by-step explanation:

You combine the fractions finding the least common denominator. Once you do that, you get your answer of 1/9.

I hope this information was of any use to you.

Answer:

i don't know ha ha ha ha sorry

Answer:

232

Step-by-step explanation:

In picture

Brainliest please

9514 1404 393

Explanation:

Given:

Prove:

Proof:

∠BOA +∠BOC +∠AOC = 360° . . . . . sum of arcs of a circle is 360°

2α +∠BOA = 180°, 2β +∠AOC = 180° . . . . . sum of triangle angles is 180°

∠BOA = 180° -2α, ∠AOC = 180° -2β . . . . solve statement 2 for central angles

(180° -2α) +∠BOC +(180° -2β) = 360° . . . . . substitute into statement 1

∠BOC = 2(α +β) . . . . . add 2α+2β-360° to both sides

∠BOC = 2×∠BAC . . . . . substitute given for α+β; the desired conclusion

Answer:

D is correct answer to the question

Answer:

The height of the triangle is [tex]6[/tex] cm.

Step-by-step explanation:

----------------------------------------

The formula for solving the area of a triangle is  [tex]A=\frac{1}{2}bh[/tex] where [tex]b[/tex] stands for base and [tex]h[/tex] stands for height.

Let's substitute 30 [tex]cm^2[/tex] for the area and 10 for the base.

[tex]30=\frac{1}{2} (10)h[/tex]

-------------------->>>>

Now, let's solve to find the height.

[tex]30=\frac{1}{2}(10)h[/tex]

Multiply [tex]\frac{1}{2}[/tex] times [tex]10[/tex]

[tex]30=5h[/tex]

Divide both sides by 5.

[tex]6=h[/tex]

-----------------------------------------

Hope this is helpful.

Answer:

6 cm

Step-by-step explanation:

thanks for the pts

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Answer:

Answer is 670000 If you can please give me brainliest

Answer:

$90

Step-by-step explanation:

Answer:

The original price is $93.75 if it is 20% off you will pay $75.

Step-by-step explanation:

1st.) We know the original price is considered 100%

So...Subtract the discount from the original percent.

100% (original percent)

20% (discount percent)

----

80%

2nd.) Make equation. We need the percent to be in decimal form so move the decimal point to the left two places. (80% will now equal 0.8)

0.8x=$75

0.8x/0.8=$75/0.8

x=$93.75

----------------------------

The original price is $93.75 if it is 20% off you will pay $75.