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2 years ago

Madeline is standing 2x- 4 feet from the base of a tree. The height of the tree is 5x + 6 feet. Find the equation that shows

Mathematics

2 answers:

galben [10]2 years ago

6 0

Answer:

Madeline is standing 2x - 4 feet from the base of a tree, and the height of the tree is 5x + 6

Now we want to know the distance from Madeline's feet to the top of the tree.

You could picture it as a triangle rectangle, where the cathetus is the distance between Madeline and the tree and the distance between the floor and the top of the tree, in this case the distance between Madeline's feet and the top of the tree is the hypotenuse of such triangle rectangle, and can be obtained using the Pythagorean theorem: "the square of the hypotenuse is equal to the sum of the square cathetus"

then:

$H^2 = (2x - 4)^2 + (5x + 6)^2$

$H^2 = (4x^2 -16x + 16) + (25x^2 + 60x +36)$

$H^2 = (29x^2 + 44x + 52)$

$H = \sqrt{ (29x^2 + 44x + 52)}$

this is the distance from Madeline's feet to the top of the tree in terms of x.

kumpel [21]2 years ago

5 0

Answer:

c = sqrt( 29x^2 + 44x + 52)

Step-by-step explanation:

This is an application of the Pythagorean theorem

c = sqrt(a^2 + b^2)

a = 2x - 4

b = 5x + 6

c = sqrt( (2x - 4)^2 + (5x + 6)^2 ) Substitute and expand

c = sqrt( 4x^2 - 16x + 16 + 25x^2 + 60x + 36) Collect like terms

c = sqrt( 4x^2 + 25x^2 - 16x + 60x + 16+36) Combine the like term pairs.

c = sqrt( 29x^2 + 44x + 52)

This does not factor into anything very nice.

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. A triangle has side lengths of 8, 7, and 14. To the nearest tenth of a degree find the measure of the angle opposite the side

4vir4ik [10]

Given:

The measure of three sides of a triangle are 8, 7 and 14.

To find:

The measure of the angle opposite the side of length 8.

Solution:

According to the Law of Cosine:

$\cos A=\dfrac{b^2+c^2-a^2}{2bc}$

Let a=8, b=7 and c=14, then by using Law of Cosine, we get

$\cos A=\dfrac{7^2+14^2-8^2}{2(7)(14)}$

$\cos A=\dfrac{49+196-64}{196}$

$\cos A=\dfrac{181}{196}$

Taking cos inverse on both sides.

$A=\cos^{-1}\dfrac{181}{196}$

$A=22.561328$

$A\approx 22.6$

Therefore, the measure of the angle opposite the side of length 8 is 22.6 degrees.

7 0

2 years ago

Which expressions are equal to 105?

Tamiku [17]

Answer:

103 and 102

Step-by-step explanation:

u add them together

6 0

2 years ago

In a company, 80% of the workers are women. If 480 men work for the company, how many workers are there in all? Use pencil

nekit [7.7K]

Answer:

The total workers are 2400.

Step-by-step explanation:

Given:

In company 80% of the workers are women.

480 workers are men.

Now, to find the total workers in all.

In first way:

If women are 80%, then men would be 100-80 = 20%.

Let the total workers be $x$ .

According to question:

$20\%\ of \ x=480$

⇒ $\frac{20}{100} \times x=480$

⇒ $0.20\times x=480$

⇒ $0.20x=480$

Dividing both sides by 0.20 we get:

⇒ $x=2400$ .

Total workers = 2400.

Now, in second way.

Again, let the total workers be $x$ .

According to question:

$x-80\%\ of\ x=480$

⇒ $x-\frac{80}{100}\times x=480$

On solving:

⇒ $x-0.80x=480$

⇒ $0.20x=480$

Dividing both sides by 0.20 we get:

⇒ $x=2400$ .

Total workers = 2400.

Therefore, the total workers are 2400.

7 0

2 years ago

Write an equation for each problem. The square of a number is 8 more than twice the number.

avanturin [10]

Answer:

The equation is equal to

$x^{2}=2x+8$

Step-by-step explanation:

Let

x -----> the number

we know that

The equation that represented the problem is equal to

$x^{2}=2x+8$

$x^{2}-2x-8=0$

Solve the quadratic equation by graphing

The solution are x=-2 and x=4

see the attached figure

therefore

The number can be -2 or 4

3 0

2 years ago

Express the ratio as a fraction in it's lowest terms.3kg to 800g

MA_775_DIABLO [31]

Answer:

15 / 4

Step-by-step explanation:

1 kg = 1000 g

3 kg

= 3 x 1000

= 3000 g

3kg to 800g

= 3kg : 800g

= 3000 : 800

= 30 : 8

= 30 / 8

= 15 / 4

6 0

2 years ago

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