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lapo4ka [179]
3 years ago
14

The area A of a triangle with base b and height h is given by A = = bh. Find the area when b = 18 m (meters) and h = 30 m.

Mathematics
1 answer:
Pie3 years ago
6 0

Answer:

Area = 270m^2

Step-by-step explanation:

Given

A = \frac{1}{2}bh

b = 18m

h = 30m

Required

Solve for A

Simply substitute 18 for b and 30 for h

A = \frac{1}{2}bh

A = \frac{1}{2} * 18 * 30

A = 270

Hence:

The area is

Area = 270m^2

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50 POINTS!
Furkat [3]

Answer:

1.

a) 357 inches³ of water more would be required to fill the tank

b) Riley is not correct, the volume of the larger aquarium is 27

   times larger than the volume of the smaller on

c) Riley is not correct, the surface area of the larger aquarium is 9

   times the surface area of the smaller one

2.

a) There are 8 boxes of office supplies can be packed into

   the larger box for shipping

b) The surface area of the shipping box is 567 inches²

Step-by-step explanation:

1.

a) * Lets study the first aquarium:

- The formula for volume is V = l × w × h

∴ It is a rectangular box of dimensions 16 in , 8.5 in , 10.5 in

∴ Its volume = 16 × 8.5 × 10.5 = 1428 inches³

* The full capacity of this aquarium is 1428 inches³

- Riley noticed that it 3/4 full of water, then still can fill with

 1/4 to be full

- Why 1/4 because 1 - 3/4 = 1/4

∴ The volume of 1/4 the aquarium = 1/4 × 1428 = 357 inches³

* There are 357 inches³ of water more would be required to fill the tank

b) * Lets talk about the larger aquarium

- Each dimension will be triple to construct the larger aquarium

- That means we will multiply each dimension of the small aquarium by 3

- That means the ratio between each dimension in the larger

  aquarium to the smaller aquarium is 3 : 1

∴ The ratio between their volumes will be (3 : 1)³

- Because we will multiply each dimension by 3 and they

  are 3 dimensions, that means 3 × 3 × 3 ⇒ 3³

∴ The ratio between their volumes = 27 : 1

∴ Riley is not correct because the volume of the larger aquarium is 27

   times larger than the volume of the smaller aquarium

c) * Similar for the surface area of the larger aquarium

- Each dimension will be triple to construct the larger aquarium

- That means we will multiply each dimension of the small aquarium by 3

- That means the ratio between each dimension in the larger

  aquarium to the smaller aquarium is 3 : 1

∴ The ratio between their surface area will be (3 : 1)²

- Because we will multiply each dimension by 3 and to get the

 surface area we multiply each two dimensions for the six faces

 and then add them

∴ The ratio between their surface area = 9 : 1

∴ Riley is not correct because the surface area of the larger aquarium

  is 9 times larger than the surface area of the smaller aquarium

2.

a) * Lets think about this situation

- We want to fill some office supplies boxes of side length

 4.5 inches inside the shipping box of dimensions 18 in , 9 in , 4.5 in

- That means the volume of the shipping box is how many times

 the volume of the office supplies box

∴ The number of office supplies boxes = the volume of shipping box ÷ the volume of the office supplies box

∵ the volume of shipping box = 18 × 9 × 4.5 = 729 inches³

∵ the volume of the office supplies box = 4.5 × 4.5 × 4.5 = 91.125 inches³

∴ The number of office supplies boxes = 729 ÷ 91.125 = 8 boxes

* There are 8 boxes of office supplies can be packed into

   the larger box for shipping

b) Look to the Net of the shipping box

- The net has 6 faces shaped rectangles

- Each two faces are congruent

- To find the surface area we will add all the areas of the 6 faces

- Two faces with dimensions 18 in and 9 in

∴ Their areas = 2 (18 × 9) = 324 inches²

- Two faces with dimensions 18 in and 4.5 in

∴ Their areas = 2 (18 × 4.5) = 162 inches²

- Two faces with dimensions 4.5 in and 9 in

∴ Their areas = 2 (4.5 × 9) = 81 inches²

∴ The total surface area = 324 + 162 + 81 = 567 inches²

* The surface area of the shipping box is 567 inches²

3 0
3 years ago
Find the measure of the are or angle indicated. Assume that lines which appear tanget are tangents. ​
Brilliant_brown [7]

9514 1404 393

Answer:

  1. 85°
  2. 60°

Step-by-step explanation:

1. Angle JKL is half the measure of the intercepted arc JK.

  (1/2)JK = 1/2(360° -190°) = (1/2)(170°) = 85°

  angle JKL is 85°

__

2. The angle between tangents is the supplement of the intercepted arc.

  angle JKL = 180° -(360° -240°)

  angle JKL = 60°

8 0
2 years ago
Lori needs at least 12 liters of water to fill a water cooler. She has a container with 4.55 liters of
Stels [109]

Answer:

<u></u>

  • <u>Yes, she has enough water.</u>

Explanation:

To <em>estimate</em> the value, you can work with friendly numbers: numbers closed to the given numbers and with which you can perform easy mental calculations.

For example 4.55 may be rouned to 5, 4.85 may be rounded to 5, and 3.25 may be rounded to 3. That yields 5 + 5 + 3 = 13

Then, it seems you have about 13 liters. Is the final number equal or greater than 12 for sure?

To round 4.55 to 5 you increased the amount in 0.45, to round 4.85 to 5 you increased the amount by 0.15, and to round 3.25 to 3 you decreased the amount in 0.25.

What was the net change in your values: 0.45 + 0.15 - 0.25 = 0.60 - 0.25 = 0.35. Those are easy calculations that you can perform in your mind.

That means that you increased your total in less than 1 liter. Meaning that the final total is overestimated by 0.35, and that if you used the real amounts to make the calculations, the total will be still more than 12.

4 0
2 years ago
PLEASE HURRY!!! TIMED!!!! WILL GIVE BRAINLIEST!!!
fgiga [73]

Answer:

3.

7.608

Step-by-step explanation:

An irrational number is any number which can't be written as a fraction this way. For example, pi and the square root of two cannot be expressed as a fraction of two whole numbers, so they are both irrational.

if we make the respective accounts in the first and second problem we will see that they are irrational numbers

the fourth is a periodic number, which falls within the irrational

the only rational is the third

7 0
2 years ago
Read 2 more answers
Turn the sentence into an expression please
Hatshy [7]

Answer:

x + 5x

Step-by-step explanation:

X is the variable in this case, or 'a number.' This number x is added to the product of 5 and the number, or 5x. Therefore the expression is x+5x. It can also be simplified to 6x.

7 0
2 years ago
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