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Andrej [43]
3 years ago
8

3/4 x - 2/3 less than or equal to 5/6

Mathematics
1 answer:
creativ13 [48]3 years ago
8 0

Answer:

The solution is:

\frac{3}{4}x-\frac{2}{3}\le \frac{5}{6}\quad :\quad \begin{bmatrix}\mathrm{Solution:}\:&\:x\le \:2\:\\ \:\mathrm{Interval\:Notation:}&\:(-\infty \:,\:2]\end{bmatrix}

The solution graph is also attached.

Step-by-step explanation:

Given the expression

' 3/4 x - 2/3 less than or equal to 5/6 '.

In inequality, the phrase 'less than or equal' is represented as ' ≤ ''.

Thus, the expression is

\frac{3}{4}\:x\:-\:\frac{2}{3}\:\:\le \frac{5}{6}\:

Add 2/3 to both sides

\frac{3}{4}x-\frac{2}{3}+\frac{2}{3}\le \frac{5}{6}+\frac{2}{3}

Simplify

\frac{3}{4}x\le \frac{3}{2}

Multiply both sides by 4

4\cdot \frac{3}{4}x\le \frac{3\cdot \:4}{2}

3x\le \:6

divide both sides by 3

\frac{3x}{3}\le \frac{6}{3}

Simplify

x\le \:2

Therefore, the solution is:

\frac{3}{4}x-\frac{2}{3}\le \frac{5}{6}\quad :\quad \begin{bmatrix}\mathrm{Solution:}\:&\:x\le \:2\:\\ \:\mathrm{Interval\:Notation:}&\:(-\infty \:,\:2]\end{bmatrix}

The solution graph is also attached.

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Aleksandr-060686 [28]

Answer:

Katie is not cheating. From the question, it sounds like Katie's spinner is 1-12. James has two dice so he has two sets of each number 1-6. This means that Katie can roll two numbers greater than six but James can only roll up to six. Using probability, I think there is a 50% chance that Katie's number will be bigger than James every time she spins. A fairer way would be for them both to play with the same dice or spinner.

Step-by-step explanation:

3 0
2 years ago
Given: KL ║ NM , LM = 45, m∠M = 50° KN ⊥ NM , NL ⊥ LM Find: KN and KL
Mice21 [21]

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

Find: KN and KL

1. Consider triangle NLM. This is a right triangle, because NL ⊥ LM. In this triangle,

LM = 45

m∠M = 50°

So,

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

Also

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

2. Consider triangle NKL. This is a right triangle, because KN ⊥ NM . In 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).

So,

\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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3 years ago
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Answer
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Use signed numbers to solve. A helicopter descended 1200 feet, rose 800 feet, and then descended 450 feet. What was the net gain
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B. Lost 850 ft
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