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natta225 [31]
3 years ago
15

A man is standing next to a tree. The shadow cast by the tree is four times longer than the man’s shadow. If the man is 2 meters

tall, how tall is the tree?
Mathematics
1 answer:
gogolik [260]3 years ago
3 0

Answer:

I think the tall of the tree is eight meters

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4TH TIME ASKING THIS!!! Please help me! Someone pleaseeee. I need the correct answers. I don’t want to fail
Alexeev081 [22]

Answer:

The functions are inverses; f(g(x)) = x ⇒ answer D

h^{-1}(x)=\sqrt{\frac{x+1}{3}} ⇒ answer D

Step-by-step explanation:

* <em>Lets explain how to find the inverse of a function</em>

- Let f(x) = y

- Exchange x and y

- Solve to find the new y

- The new y = f^{-1}(x)

* <em>Lets use these steps to solve the problems</em>

∵ f(x)=\sqrt{x-3}

∵ f(x) = y

∴ y=\sqrt{x-3}

- Exchange x and y

∴ x=\sqrt{y-3}

- Square the two sides

∴ x² = y - 3

- Add 3 to both sides

∴ x² + 3 = y

- Change y by f^{-1}(x)

∴ f^{-1}(x)=x^{2}+3

∵ g(x) = x² + 3

∴ f^{-1}(x)=g(x)

∴ <u><em>The functions are inverses to each other</em></u>

* <em>Now lets find f(g(x))</em>

- To find f(g(x)) substitute x in f(x) by g(x)

∵ f(x)=\sqrt{x-3}

∵ g(x) = x² + 3

∴ f(g(x))=\sqrt{(x^{2}+3)-3}=\sqrt{x^{2}+3-3}=\sqrt{x^{2}}=x

∴ <u><em>f(g(x)) = x</em></u>

∴ The functions are inverses; f(g(x)) = x

* <em>Lets find the inverse of h(x)</em>

∵ h(x) = 3x² - 1 where x ≥ 0

- Let h(x) = y

∴ y = 3x² - 1

- Exchange x and y

∴ x = 3y² - 1

- Add 1 to both sides

∴ x + 1 = 3y²

- Divide both sides by 3

∴ \frac{x + 1}{3}=y^{2}

- Take √ for both sides

∴ ± \sqrt{\frac{x+1}{3}}=y

∵ x ≥ 0

∴ We will chose the positive value of the square root

∴ \sqrt{\frac{x+1}{3}}=y

- replace y by h^{-1}(x)

∴ h^{-1}(x)=\sqrt{\frac{x+1}{3}}

4 0
3 years ago
Angle C is 60 degrees and angle CAB is 78 we need to find angle DAB
ioda

Answer:

∠ DAB = 48°

Step-by-step explanation:

The sum of the 3 angles in Δ ACD = 180° , then

∠ CAD + 60° + 90° = 180° , that is

∠ CAD + 150° = 180° ( subtract 150° from both sides )

∠ CAD = 30°

Then

∠ DAB + ∠ CAD = ∠ CAB

∠ DAB + 30° = 78° ( subtract 30° from both sides )

∠ DAB = 48°

5 0
2 years ago
A past survey of students taking a standardized test revealed that ​% of the students were planning on studying engineering in c
Angelina_Jolie [31]

Complete Question

The  complete question is shown on the first uploaded image  

Answer:

The  95% confidence interval is  -0.00870

Step-by-step explanation:

From the question we are told that

     The first sample  size  is  n_1  =  1068000

     The first proportion  \r p_1 = 0.084

     The second  sample size is  n_2  =  1476000

     The  second  proportion is  \r p_2 =  0.092

Given that the confidence level is  95%  then the level of significance is mathematically represented as

      \alpha =  (100 - 95)\%

     \alpha =  0.05

From the normal distribution table  we obtain the critical value of  \frac{ \alpha }{2}  the value is  

      Z_{\frac{\alpha }{2} } =z_c=  1.96

Now using the formula from the question to construct the 95% confidence interval we have  

  (\r p_1 - \r p_2  )- z_c \sqrt{ \frac{\r p_1 \r q_1 }{n_1} + \frac{\r p_2 \r q_2 }{n_2} }

Here \r q_1 =  1 - \r p_1

  =>   \r q_1 =  1 - 0.084

 =>    \r q =  0.916

and  

   \r q_2 =  1 - \r p_2

 =>   \r q_2 =  1 - 0.092

=>   \r q_2 = 0.908

So  

 (0.084 - 0.092 )- (1.96)*  \sqrt{ \frac{0.092* 0.916 }{1068000} + \frac{0.084* 0.908 }{1476000} }

  -0.00870

 

3 0
3 years ago
The solutions to the equation 2x^2 + x - 1 = 2 are x = -3/2 or x = _______.
garik1379 [7]

Answer:

The remaining solution to the equation is x = 1

Step-by-step explanation:

2x^2 + x - 1 = 2

First set the equation to zero by subtracting 2 from each side:

2x^2 + x - 1 - 2 = 2 - 2

2x^2 + x - 3 = 0

Factor the left side of the equation:

2x^2 + x - 3 = 0

(2x + 3)(x - 1) = 0

Now set each factor to zero and solve:

2x+ 3 = 0

2x+ 3 - 3  = 0 - 3

2x= -3

2x/2= -3/2

x= -3/2 (The given expression)

x - 1 = 0

x - 1 + 1 = 0 + 1

x = 1

Since we already knew x = -3/2, the missing solution is x = 1.

4 0
3 years ago
2×__=9+9 <br> Complete the equation
Elenna [48]

Answer:

2×9=9+9

Step-by-step explanation:

5 0
3 years ago
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