12. 4(2x - 8) = 3(2 – 3x) Need help to solve it in steps

Wendy is standing 60 feet away from a tree. Her eyes are 5 feet above the ground. She sees a bird hovering above a tree. The ang

Gennadij [26K]

The bird is 17 feet above the tree.

Explanation:

We need to think of this in terms of right triangles. If Wendy is 60 feet from a tree, the base of the right triangle is 60 feet. The height of the tree is the height of the right triangle. The angle of elevation is the one from the ground at her feet to the top of the tree and then to the bird. Let's start with the top of the tree first.

She's 60 feet away, we have the angle of elevation as 25 degrees, and we are looking for the height of the tree. In regards to the angle, the base of 60 is adjacent, and the height of the tree is opposite. The tangent ratio is height / base.

Let x be the height of the tree.

So,

$tan (25) = \frac{x}{60}$

$60 tan(25) = x\\\\x = 27.9 feet$

x is approximately 28 feet

Since, Wendy's eyes are 5 feet above the ground, the height of the tree becomes

28 + 5 = 33 feet

For bird

Let y be the height of the bird in the air

$tan(37) = \frac{y}{60} \\\\60 tan(37) = y\\\\y = 45.2 feet$

y is approximately 45 feet

Since, Wendy's eyes are 5 feet above the ground, the height of the tree becomes

45 + 5 = 50 feet

To know how far above the tree that bird is

50 - 33 = 17 feet

Therefore, the bird is 17 feet above the tree.

3 0

3 years ago

In a calculus class, Jack Hartig scored 4 on a quiz for which the class mean and standard deviation were 2.9 and 2.1, respecti

nataly862011 [7]

Answer: Norm Alpina did better with z-score 0.79

Step-by-step explanation:

Z score formula = (raw score - mean) / standard deviation

For Jack Hartig,

score = 4; mean = 2.9; standard deviation = 2.1

Hence, Z score = (4 - 2.9) /2.1

= 1.1/2.1

= 0.52

For Norm Alpina,

score = 8; mean = 6.5; standard deviation = 1.9

Hence, Z score = (8 - 6.5) /1.9

= 1.5/1.9

= 0.79

Relatively, Norm Alpina did better for having Z score 0.79

6 0

3 years ago

Accidents on highways are one of the main causes of death or injury in developing countries and the weather conditions have an i

pashok25 [27]

Answer:

0.105 = 10.5% probability that an accident results in a death.

Step-by-step explanation:

What is the probability that an accident results in a death?

5% of 60%(sunny)

25% of 20%(foggy)

12.5% of 20%(rainy)

So

$p = 0.05*0.6 + 0.25*0.2 + 0.125*0.2 = 0.105$

0.105 = 10.5% probability that an accident results in a death.

6 0

2 years ago

While performing a piece of music, Tommy strikes the cymbals every 7 beats and the triangle is every 12 beats. If he just struck

Semmy [17]

Answer:

84

Step-by-step explanation:

In interval questions we use LCM

LCM of 7, 12=84

Therefore, the number of beats will pass before he again strikes them at the same time is 84

5 0

2 years ago

If the cost of a dress is $75.00 and

11Alexandr11 [23.1K]

Answer:

80%

Step-by-step explanation:

Original price =$75.00

Sale price =$60.00

The percentage discount can be calculated by dividing the sale price by the original price multiplied by 100%.

So % discount = $60.00/$75.00 x 100%

0.8 x 100%

80%

Janelle got the dress on a discount of 80%.

This is so because she got the dress for a price less than the original price

6 0

2 years ago