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aalyn
16 hours ago
13

Which cost category in the table shows an example of direct variation?

Mathematics
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A rectangle on a coordinate plane has vertices at (7,5), (-7,5), (-7,-2), and (7,-2). What is the perimeter of the rectangle?
lawyer [12517]
For a rectangle, the perimeter can be calculated as P=2l+2w. Assuming the length is horizontal and the width is vertical, the span between the x coordinates will give the length, while the span between the y coordinates will determine the width. Once these measurements are obtained, you can apply them to the perimeter formula. |7 -(-7)| = 14 gives l = 14, |5-(-2)| = 7 gives w=7. Therefore, P=2(14)+2(7), which results in P= 28+14, thus, P= 42.
7 0
2 months ago
Read 2 more answers
Given: KL ║ NM , LM = 45, m∠M = 50° KN ⊥ NM , NL ⊥ LM Find: KN and KL
Leona [12618]

Answer:

KL=45\tan 50^{\circ}\sin 50^{\circ}\approx 41.08\\ \\KN=45\sin 50^{\circ}\approx 34.47

Step-by-step explanation:

Given:

KL ║ NM,

LM = 45

m∠M = 50°

KN ⊥ NM  

NL ⊥ LM

To determine: KN and KL

1. Analyzing triangle NLM, we see it is a right triangle due to NL ⊥ LM. In this context,

LM = 45

m∠M = 50°

Consequently,

\tan \angle M=\dfrac{\text{opposite leg}}{\text{adjacent leg}}=\dfrac{NL}{LM}=\dfrac{NL}{45}\\ \\NL=45\tan 50^{\circ}

It is also true that

(angles LNM and M are complementary).m\angle LNM=90^{\circ}-50^{\circ}=40^{\circ}

2. Now considering triangle NKL, it also forms a right triangle as KN ⊥ NM. Within this triangle,

NL=45\tan 50^{\circ}

m\angle KLN=m\angle LNM=40^{\circ} (alternate interior angles)

m\angle KNL=90^{\circ}-40^{\circ}=50^{\circ} (angles KNL and KLN are complementary).

Thus,

\sin \angle KNL=\dfrac{\text{opposite leg}}{\text{hypotenuse}}=\dfrac{KL}{LN}=\dfrac{KL}{45\tan 50^{\circ}}\\ \\KL=45\tan 50^{\circ}\sin 50^{\circ}\approx 41.08

and

\cos \angle KNL=\dfrac{\text{adjacent leg}}{\text{hypotenuse}}=\dfrac{KN}{LN}=\dfrac{KN}{45\tan 50^{\circ}}\\ \\KN=45\tan 50^{\circ}\cos 50^{\circ}=45\sin 50^{\circ}\approx 34.47

3 0
3 months ago
Read 2 more answers
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