Which rule describes the composition of transformations that maps figure ABCDE to figure A"B"C'D"E"?

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

2 months ago

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If Machine A makes a yo-yo every five minutes and Machine B takes ten minutes. How many hours would it take them to make 20yo−yo

zzz [12365]

Time required equals 66 2/3 minutes, which is equivalent to approximately 1.11 hours.

4 0

2 months ago

The parent function f(x) = log3x has been transformed by reflecting it over the x-axis, stretching it vertically by a factor of

babunello [11817]

The third option is correct. Step-by-step explanation: Various transformations apply to a function f(x). If a transformation is applied downward by 'k' units, the function shifts down; if upward, it rises 'k' units. Additionally, if scaled vertically by a factor of 'b', it will stretch; if reflected over the x-axis, the operation is indicated. Thus, since the parent function has undergone reflection over the x-axis, a vertical stretch by a factor of 2, and a downward shift of three units, we can derive that the transformed function is presented.

3 0

1 month ago

John is filling a bathtub that is 18 inches deep. He notices it takes 2 mins. To fill the tub 3 inches of water. He estimates it

Svet_ta [12734]

The bathtub's depth measures 18 inches

It takes 2 minutes to fill 3 inches of the bathtub

Subsequently

The remaining depth needed for filling with water = (18-3) inches

= 15 inches

The time needed to fill the remaining 15 inches of the bathtub = (15*2)/3 minutes

= 30/3 minutes

= 10 minutes

Therefore, John is right in believing that it will require an additional 10 minutes to fill the tub to the brim at the same rate.

Hope this clarifies things!

6 0

2 months ago

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Lindy works at a pizza restaurant and gets a 10% employee discount. She knows that if she orders d drinks and a medium pizza wit

PIT_PIT [12445]

Result: OPTION D.

Step-by-step reasoning:

The total cost for Lindy can be calculated employing the expression given in the task:

$0.90(2.25d + 1.40t + 6)$

Here, "d" signifies the drinks ordered and "t" represents the toppings on a medium pizza she selects.

Since she and her friends order 4 drinks alongside a medium pizza that includes 3 toppings, you can derive the total cost by substituting these values into the provided expression.

The values are:

$d=4\\\\t=3$

Upon substituting into the expression and performing the calculations, the result is:

$0.90(2.25d + 1.40t + 6)= 0.90(2.25(4) + 1.40(3) + 6)=\$17.28$

4 0

1 month ago

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