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8 days ago

12. The traffic warning sign below has a triangle shape with base of 18 inches,

Mathematics

1 answer:

Inessa [12.1K]8 days ago

8 0

Answer:

Step-by-step explanation:

The area of the triangle is

$\text{Area}=\dfrac{1}{2}\cdot \text{Base}\cdot \text{Height}$

It’s known that

Area - irrational number

$\dfrac{1}{2}$ - rational number (rational numbers can be expressed as fractions)

Base = 18 inches - rational number (in fact, 18 is a natural number, and all natural numbers are rational)

Height - unknown

You may rewrite the earlier formula as

$\text{Area}=\dfrac{1}{2}\cdot 18\cdot \text{Height}\\ \\\text{Area}=9\cdot \text{Height}$

Analyzing all options:

A. If the height is a whole number, then the area will also be a whole number due to multiplying two whole numbers. Incorrect

B. If the height is a rational number, the area becomes rational since it's a product of rational numbers. Incorrect

C. If the height is irrational, the area is also irrational because of the product of rational and irrational numbers. Correct

D. If height is a non-real complex number, then area is non-real complex as it comes from a product of rational and non-real complex numbers. Incorrect

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To determine the future value of an initial amount of $845 at an interest rate of 11.3% over 7 years, we will utilize the compound interest formula, which is expressed as:
A=p(1+r/100)^n
where:
A=future value
r=rate=11.3%=0.113
time=7 years
Hence, the future value of the capital will be:
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25 days ago

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Given: KL ║ NM , LM = 45, m∠M = 50° KN ⊥ NM , NL ⊥ LM Find: KN and KL

Leona [12066]

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

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

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18 days ago

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If m∠7 = 55°, which of the following statements are true? Select all that apply. There are two horizontal parallel lines are cut

Leona [12066]

Answer:

The accurate assertions include:

A. m∠6 = 55°

C. m∠1 + m∠4 = 250°

D. m∠1 + m∠6 = m∠7 + m∠4

Step-by-step clarification:

The provided information is as follows:

m∠7 = 55°

The angles formed by the transversal and the upper horizontal parallel line are (starting from the top left and moving in clockwise direction) 1, 2, 4, 3

Likewise, the angles from the transversal and the lower horizontal parallel line are (starting from the top left and going clockwise) 5, 6, 8, 7

Consequently, we have;

m∠7 ≅ m∠6 (Vertically opposite angles are equal)

Thus, m∠6 = m∠7 = 55°

m∠6 = 55°, which aligns with option A.

m∠5 + m∠6 = 180° (The sum of angles on a straight line)

So, m∠5 = 180° - m∠6 = 180° - 55° = 125°

m∠5 = 125°

m∠1 ≅ m∠5 (Corresponding angles)

Thus, m∠1 = m∠5 = 125°

m∠1 ≅ m∠4 (Vertically opposite angles)

Therefore, m∠1 = m∠4 = 125°

Thus, m∠1 + m∠4 = 125° + 125° = 250°

m∠1 + m∠4 = 250°, which corresponds to option C.

m∠1 ≅ m∠4 (Vertically opposite angles)

m∠6 ≅ m∠7 (Vertically opposite angles)

Thus, m∠1 + m∠6 = m∠7 + m∠4 (Transitive property), which matches option D.

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24 days ago

2. Peter drew two rays, AC and AP with A as a common endpoint. Which of the following statements

PIT_PIT [11868]

The complete question reads:

Peter created two rays, AC and AP, sharing a common vertex at point A. Which of the following statements

might accurately describe Peter's drawing?

I. AC and AP are parallel.

II. PAC represents an angle.

III. AC and AP are at right angles.

A. I and II

B. II and III

C. I and III

D. I, II, and III

Answer:

Option B: II & III

Step-by-step explanation:

We know Peter has drawn rays AC and AP.

Since the point A is shared as the endpoint, it indicates an angular relationship at this common point.

This angle could potentially be 90°, suggesting that rays AC and AP may be perpendicular.

Thus, the valid statements that characterize his drawing are: II & III.

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1 month ago

Which figure represents the image of parallelogram LMNP after a reflection across the line y=x?

Zina [11949]

Answer:c

Step-by-step explanation:

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