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4 years ago

use symbols to compare the numbers 512 and 521. write the comparison to ways. then explain your thinking

Mathematics

1 answer:

Morgarella [4.7K]4 years ago

8 0

Solution:- Given numbers to compare are 512 and 521 .

As they are 3 digit numbers

So, we have to compare hundreds place.

But hundreds are equal in both the numbers with digit 5.

Next we have to compare tens place.

Case 1 :- 1 ten is smaller in 512 than 2 tens in 521 .

So we get the result that,

512 is smaller than 521

or 512 < 521

Case 2:-2 tens is greater in 521 than 1 ten in 512 .

So we get the result that,

521 is greater than 512

or  521 > 512

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Jon is in a raft 100m from the base of a 54m cliff. What is the angle of depression from the he top of the cliff to the raft? Le

kvv77 [185]

Answer:

28.4 degrees

Step-by-step explanation:

In the diagram attached

Height of the cliff, AB=54 m

Distance of the raft to the base of the cliff, AC=100m

We want to determine the angle of depression from the top of the cliff to the raft. This is angle OBA.

$\angle OBA = \angle BAC $ (Alternate Angles)\\Therefore, in the right triangle ABC\\\tan A =\dfrac{BC}{AC}\\ \tan A =\dfrac{54}{100}\\\tan A =0.54\\A=\arctan 0.54\\A=28.4^\circ$ (to the nearest tenth)$

The angle of depression from the top of the cliff to the raft is 28.4 degrees correct to the nearest tenth.

5 0

3 years ago

Triangle E G F is cut by line H J. Line H J goes from side E G through side G F. Lines E F and H J are parallel. Using the side-

goldenfox [79]

Answer:

Step-by-step explanation:

The "Side Splitter" Theorem says that if a line intersects two sides of a triangle and is parallel to the third side of the triangle, it divides those two sides proportionally.

In this case, lines EF and HJ are parallel, H is on side EG and J is on side GF; then using the side-splitter theorem:

$\frac{GH}{HE} = \frac{GJ}{JF}$

3 0

3 years ago

Read 2 more answers

Evaluate x square2 +12,when x=3

GarryVolchara [31]

Answer:

Step-by-step explanation:

3^2=9

9+12=21

Keep it up

6 0

3 years ago

My son is trying to figure out how to decompose 8/12 and what he has to work with is x/2 + x/2 =8/12

vekshin1

X/2 + x/2 = 2x / 2 or just x. So x = 8/12 which can be simplified by their greatest common factor of 4. Divide both top and bottom by 4. This gives you x = 2/3.

Your answer for that equation is x = 2/3

Not sure what you mean by "decompose" though.

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4 years ago

In the diagram below, points A, E, and F lie on the same line. If ABCDE is a regular pentagon, and \angle EFD=90^\circ, then how

mash [69]

The measure of ∠FDE = 18°

Explanation:

A Pentagon has 5 sides and is made of 3 triangles

So, sum of the interior angles of the triangle = 180°

Therefore, the total interior angle of a regular pentagon = 3 X 180° = 540°

A regular pentagon will have all its angle equal

All the five angles would make 540°

Let the measure of one angle = x

So,

5x = 540°

x = 108°

Therefore, the measure of each angle of a pentagon is 108°

From the diagram,

∠AED + ∠FED = 180°

∠AED = 108° as it is one of the sides of the pentagon

So,

108° + ∠FED = 180°

∠FED = 72°

In ΔEFD,

∠FED + ∠EFD + ∠FDE = 180°

72° + 90° + ∠FDE = 180°

∠FDE = 18°

Therefore, the measure of ∠FDE = 18°

8 0

3 years ago