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4 years ago

A maple tree is 12 meters tall. A model of it was built with a scale of 1 cm:3 cm. How tall was the model?

Mathematics

1 answer:

ch4aika [34]4 years ago

8 0

Change 12 m to 120 cm

1cm=x
------------
3cm=120

120=3x. Cross mult.
120/3=x
40cm or 4m

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horrorfan [7]

Complete Question

The complete question is shown on the first uploaded image

Answer:

$g(h(x)) = \sqrt[4]{x^2 + x +5} + 3$

$h(g(x)) = \sqrt{x} + 7\sqrt[4]{x} + 17$

$h(h(x)) = [x^2 + x + 5 ]^2 + x^2 + x + 10$

Step-by-step explanation:

From the question we are told that

$h(x) = x^2 + x + 5$

and

$g(x) = \sqrt[4]{x} + 3$

Considering first question

Now we are told g(h(x))

i.e

$g(h(x)) = [x^2 + x + 5 ]^{\frac{1}{4} } + 3$

=> $g(h(x)) = \sqrt[4]{x^2 + x +5} + 3$

Considering second question

Now we are told h(g(x))

i.e

$h(g(x)) = [x^{\frac{1}{4} } + 3]^2 + x^{\frac{1}{4} } + 3 + 5$

=> $h(g(x)) = x^{\frac{1}{2} } + 6x^{\frac{1}{4} } + 9+ x^{\frac{1}{4}} + 8$

=> $h(g(x)) = x^{\frac{1}{2}} + 7x^{\frac{1}{4}} + 17$

=> $h(g(x)) = \sqrt{x} + 7\sqrt[4]{x} + 17$

Considering third question

$h(h(x))= [x^2 + x + 5]^2 + [x^2 + x + 5 ] + 5$

=> $h(h(x)) = [x^2 + x + 5 ]^2 + x^2 + x + 10$

8 0

4 years ago

The perimeter of a standard basketball court is 288 feet. The length is 44 feet longer than the width. What are the dimensions o

Nuetrik [128]

Answer:

Perimeter = 2l + 2w //l=length, w=width

l = 44 + w

Now substitute 44 + w in place of l in the above equation and you have

2(44 + w) + 2w = 288

=> 88 + 2w + 2w = 288

=> 88 + 4w = 288

=> 4w = 200

=> w = 50 and l = 44 + 50 = 94

2*94 + 2*50=288

Step-by-step explanation:

5 0

3 years ago

simplify the expression write your answer as a complex number. three square root of 16 plus square root of - 9

german

Answer:

$\large\boxed{3\sqrt{16}+\sqrt{-9}=12+3i}$

Step-by-step explanation:

$3\sqrt{16}+\sqrt{-9}\\\\\sqrt{16}=4\ \text{because}\ 4^2=16\\\\\sqrt{-9}=\sqrt{(9)(-1)}\qquad\text{use}\ \sqrt{ab}=\sqrt{a}\cdot\sqrt{b}\\=\sqrt9\cdot\sqrt{-1}=(**)\\\sqrt9=3\ \text{because}\ 3^2=9\\\sqrt{-1}=i\\(**)=3i\\\\3\sqrt{16}+\sqrt{-9}=(3)(4)+3i=12+3i$

5 0

4 years ago

Which algebraic expression is a polynomial with a degree of 5?

Eddi Din [679]

The degree of a polynomial is the highest exponent or sum of exponents of the variables in the individual terms of a polynomial.

Looking at each the polynomial:

3x5 + 8x4y2 – 9x3y3 – 6y5: Degree is 6 (look at the 2nd and 3rd term)

2xy4 + 4x2y3 – 6x3y2 – 7x4: Degree is 5 (look at 1st, 2nd, and 3rd term)

8y6 + y5 – 5xy3 + 7x2y2 – x3y – 6x4: Degree is 6 (look at 1st term)

–6xy5 + 5x2y3 – x3y2 + 2x2y3 – 3xy5: Degree is 6 (look at 1st and last term)

Therefore, the answer is the second option:
2xy4 + 4x2y3 – 6x3y2 – 7x4

6 0

3 years ago

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What does the numerator of a fraction tell you about where to place it on a number line?

bixtya [17]

Is there a fraction or a number line to explain you question?☺

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3 years ago