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Rufina [12.5K]
3 years ago
9

Pete is standing 4 feet away from a mirror on the ground. Pete is 6 feet tall and can just see the top of the tree in the mirror

from where he is standing. The two triangles formed in the picture above are similar.
If the mirror is 16 feet away from the base of the tree, how tall is the tree?

a. 18 ft
b. 10 ft
c. 24 ft
d. 15 ft
Mathematics
2 answers:
Murljashka [212]3 years ago
5 0
It’s option c, 24ft.
Sedaia [141]3 years ago
3 0

Answer:

24ft

Step-by-step explanation:

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Erik and Caleb were trying to solve the equation: 0=(3x+2)(x-4) Erik said, "The right-hand side is factored, so I'll use the zer
Mumz [18]

Answer:

C) Both

Step-by-step explanation:

The given equation is:

0=(3x+2)(x-4)

To solve the given equation, we can use the Zero Product Property according to which if the product <em>A.B = 0</em>, then either A = 0 OR B = 0.

Using this property:

(3x+2) = 0 \Rightarrow \bold{x = -\frac{2}{3}}\\(x-4) = 0 \Rightarrow \bold{x = 4}

So, Erik's solution strategy would work.

Now, let us discuss about Caleb's solution strategy:

Multiply (3x+2)(x-4) i.e. 3x^2-12x+2x-8 = 3x^2-10x-8

So, the equation becomes:

0=3x^2-10x-8

Comparing this equation to standard quadratic equation:

ax^2+bx+c=0

a = 3, b = -10, c = -8

So, this can be solved using the quadratic formula.

x=\dfrac{-b\pm\sqrt{b^2-4ac}}{2a}

x=\dfrac{-(-10)\pm\sqrt{(-10)^2-4\times3 \times (-8)}}{2\times 3}\\x=\dfrac{-(-10)\pm\sqrt{196}}{6}\\x=\dfrac{10\pm14}{6} \\\Rightarrow x= 4, -\dfrac{2}{3}

The answer is same from both the approaches.

So, the correct answer is:

C) Both

3 0
3 years ago
Old faithful in Yellowstone National Park shoots water 60 feet into the air that casts a shadow of 42 feet. What is the height o
Serhud [2]

Answer:

The height of near by tree will be 90 feet.

Step-by-step explanation:

Considering the water triangle as shown in figure a.

As the old faithful shoots water 60 feet into the air that casts a shadow of 42 feet.

Considering the tree triangle as shown in figure a. The tree triangle has a shadow 63 feet long.

Let x be the height of near by tree that cost a shadow 63 feet long.

Assuming that the triangles are similar

So,

the ratios of similar triangles will be related as:

\frac{63}{42}=\frac{x}{60}

\mathrm{Switch\:sides}

\frac{x}{60}=\frac{63}{42}

{x}=60.\frac{63}{42}

x=90 feet

Therefore, the height of near by tree will be 90 feet.

Keywords: ratio, similar triangle

Learn more about similar triangle from brainly.com/question/10161974

#learnwithBrainly

7 0
3 years ago
12/18 ATB - Review question -<br> Evaluate 18x + 75 when x= 8.
boyakko [2]

Answer:

solution

x=8

so,

18 .8 +75

144 +75

219

7 0
3 years ago
This is a picture of a cube and the net for the cube.
morpeh [17]

Answer:

150cm2

Step-by-step explanation:

A=6a2, where a is the side of one face of the cube. Given a=5cm

A=6(5cm)^2

=6×25cm^2

=150cm^2 or 150cm2

3 0
3 years ago
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3x(×-4)-5(x+2)=2-(x+24)
just olya [345]
The zeros to the problem are:
x = .90283246
x = 4.4305009
4 0
3 years ago
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