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Oxana [17]
3 years ago
7

What are the coordinates of the shadow cast on the xy plane by a small object placed at the point (10,7,20) assuming that the su

n's rays are parallel to the vector (5,3,-2)?
Mathematics
1 answer:
BigorU [14]3 years ago
3 0
We are given with two coordinates
(10, 7, 20) and
(5, 3, -2)
Which can be used to create a linear equation represented by vectors
<x, y, z> = <x0, y0, z0> + t<mx, my, mz>
We can get the slope by
<mx, my, mz> = <10, 7, 20> - <5, 3, -2> = <5, 4, 22>

 <x, y, z> = <x0, y0, z0> + t<5, 4, 22>
At z = 0, and using the coordinates of either of the two points, the coordinates o the shadow of the point can be determined.
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you are riding a train. your carry-on bag can weigh no more than 50 pounds. Your bag weighs 38 pounds. How much more can you add
Strike441 [17]

Let the additional weight that can be added be = x

Current weight of the bag = 38 pounds

Total weight can be = 50 pounds

The equation becomes:

38+x\leq50

x\leq50-38=12

Hence, a weight of 12 pounds cab be added to the current wight.

8 0
3 years ago
BIOLOGY
kozerog [31]

Answer:

Step-by-step explanation:

Types of Angle Pairs

Adjacent angles: two angles with a common vertex, sharing a common side and no overlap.

Adjacent Angles

Angles ∠1 and ∠2 are adjacent.

Complementary angles: two angles, the sum of whose measures is 90°.

Complementary Angles

Angles ∠1 and ∠2 are complementary.

Complementary are these angles too(their sum is 90°):

Complementary Angles

Supplementary angles: two angles, the sum of whose measures is 180°.

Supplementary Angles

Angles ∠1 and ∠2 are supplementary.

 

Angle pairs formed by parallel lines cut by a transversal

When two parallel lines are given in a figure, there are two main areas: the interior and the exterior.  

When two parallel lines are cut by a third line, the third line is called the transversal. In the example below, eight angles are formed when parallel lines m and n are cut by a transversal line, t.  

There are several special pairs of angles formed from this figure. Some pairs have already been reviewed:  

Vertical pairs:

∠1 and ∠4  

∠2 and ∠3  

∠5 and ∠8  

∠6 and ∠7  

Recall that all pairs of vertical angles are congruent.  

Supplementary pairs:

∠1 and ∠2  

∠2 and ∠4  

∠3 and ∠4  

∠1 and ∠3  

∠5 and ∠6  

∠6 and ∠8  

∠7 and ∠8  

∠5 and ∠7  

Recall that supplementary angles are angles whose angle measure adds up to 180°. All of these supplementary pairs are linear pairs. There are other supplementary pairs described in the shortcut later in this section. There are three other special pairs of angles. These pairs are congruent pairs.

Alternate interior angles two angles in the interior of the parallel lines, and on opposite (alternate) sides of the transversal. Alternate interior angles are non-adjacent and congruent.  

 

Alternate exterior angles two angles in the exterior of the parallel lines, and on opposite (alternate) sides of the transversal. Alternate exterior angles are non-adjacent and congruent.  

 

Corresponding angles two angles, one in the interior and one in the exterior, that are on the same side of the transversal. Corresponding angles are non-adjacent and congruent.  

 

Use the following diagram of parallel lines cut by a transversal to answer the example problems.  

 

Example:  

What is the measure of ∠8?  

The angle marked with measure 53° and ∠8 are alternate exterior angles. They are in the exterior, on opposite sides of the transversal. Because they are congruent, the measure of ∠8 = 53°.  

Example:  

What is the measure of ∠7?  

∠8 and ∠7 are a linear pair; they are supplementary. Their measures add up to 180°. Therefore, ∠7 = 180° – 53° = 127°.

1. When a transversal cuts parallel lines, all of the acute angles formed are congruent, and all of the obtuse angles formed are congruent.  

 

In the figure above ∠1, ∠4, ∠5, and ∠7 are all acute angles. They are all congruent to each other. ∠1 ≅ ∠4 are vertical angles. ∠4 ≅ ∠5 are alternate interior angles, and ∠5 ≅ ∠7 are vertical angles. The same reasoning applies to the obtuse angles in the figure: ∠2, ∠3, ∠6, and ∠8 are all congruent to each other.

2. When parallel lines are cut by a transversal line, any one acute angle formed and any one obtuse angle formed are supplementary.  

 

From the figure, you can see that ∠3 and ∠4 are supplementary because they are a linear pair.

Notice also that ∠3 ≅ ∠7, since they are corresponding angles. Therefore, you can substitute ∠7 for ∠3 and know that ∠7 and ∠4 are supplementary.

Example:  

In the following figure, there are two parallel lines cut by a transversal. Which marked angle is supplementary to ∠1?  

 

The angle supplementary to ∠1 is ∠6. ∠1 is an obtuse angle, and any one acute angle, paired with any obtuse angle are supplementary angles. This is the only angle marked that is acute.

4 0
3 years ago
110 is between blank and blank so 110 divided by 8 is between 13 and 14
mixas84 [53]
The 2 numbers required are 13*8 and 14  * 8
that is  104 and 117
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Evie read an article that said 6\%6%6, percent of teenagers were vegetarians, but she thinks it's higher for students at her lar
11111nata11111 [884]

Answer:

p-value~ 0.075

Step-by-step explanation:

( Choice D on Khan Academy)

8 0
3 years ago
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Alexus [3.1K]
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2 years ago
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