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2 years ago

If a 5 foot post casts an 8 foot shadow at the same time that a nearby tree casts a 48 foot shadow how tall is the tree

1 answer:

3 0

The first thing we are going to assume for this case is that the tree and the post are located in the same place.
From that place, both cast a shadow in the same direction.
We then have two similar triangles.
Therefore, we have the following relationship:
$\frac{x}{48} = \frac{5}{8}$
From here, we clear the value of x.
We have then:
$x = \frac{5}{8} *48$
Rewriting:
$x=30$
Answer:
the tree is 30 feet tall

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1. What is the extraneous solution of √x−3 + x = 9?

Sunny_sXe [5.5K]

Answer:

1. x = 12

2. 3∛4 feet.

Step-by-step explanation:

1. We are given the equation of x as $\sqrt{x - 3} + x = 9$ and we have to find the extraneous solution of the equation.

Now, $\sqrt{x - 3} + x = 9$ ............. (1)

⇒ $\sqrt{x - 3} = 9 - x$

Squaring both sides we get,

⇒ x - 3 = 81 - 18x + x²

⇒ x² - 19x + 84 = 0

⇒ x² - 12x - 7x + 84 = 0

⇒ (x - 12)(x - 7) = 0

⇒ x = 12 or 7.

Now, putting x = 12 in the equation (1) we get,

$\sqrt{12 - 3} + 12 \neq 9$

Again, putting x = 7 in the equation (1) we get,

$\sqrt{7 - 3} + 7 = 9$

Therefore, x = 12 is an extraneous solution of this equation. (Answer)

2. The volume of a cube with side lengths a ft. is given to be 108 ft³.

So, a³ = 108

⇒ a = 3∛4 feet.

Therefore, the length of the sides of the cube are each 3∛4 feet. (Answer)

3 0

2 years ago

Customers at the Palace Pro Shop receive a 10% discount if they are members. All customers must pay 7% in sales tax. The functio

11111nata11111 [884]

Answer:

The total amount a member pays for an item with a regular price of x dollars is T (x) = 0.963x.

Step-by-step explanation:

Key points:

Discount is subtracted from the regular price of an item.
Sales tax is added to the regular price of an item.

It is provided that the customers receive a 10% discount if they are members and all customers must pay 7% in sales tax.

Two functions are provided are:

f (x) = 0.90x ; the price of an item after the 10% member discount

g (x) = 1.07x ; the total amount customers pay for a purchase after sales tax is applied.

Compute the total amount a member pays for an item with a regular price of x dollars as follows:

T (x) = Discount × Sales Tax

= 0.90 × 1.07 × x

= 0.963x.

Thus, the total amount a member pays for an item with a regular price of x dollars is T (x) = 0.963x.

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2 years ago

Hich correctly describes how the graph of the inequality 4x − 2y > 20 is shaded?

joja [24]

Answer:

First we need to express y in this inequality:

-2y > -4x + 20

-y > -2x + 10

y < 2x - 10

The line isn't solid because the "less" sign doesn't include equal in it.

Because the sign is "less than" the shaded part is Below the line.

Merging these 2 conclusion we get the answer:

below the dashed line.

Step-by-step explanation:

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2 years ago

Help pleaseee? i will give you brainliest answer

Leokris [45]

All i know is that both of them are parallel

i think for the first one its 6

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7 0

3 years ago

Given that a 12 foot long piece of steel pipe weighs 5 pounds per foot, how much does it weigh in kilograms per meter? 1 pound =

sdas [7]

Answer:

1 foot = 0.305 meters.

Convert 1 meter to feet:

1 meter = 1/0.305 = 3.28 feet

Find the weight in pounds per meter:

5 pounds x 3.28 feet = 16.4 pounds per meter.

Convert pounds per meter to kilograms per meter:

16.4 pounds x 0.454 kilograms per pound = 7.44 kg/m

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2 years ago