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blsea [12.9K]
2 years ago
6

Which number line represents the solution set for the inequality 3(8 – 4x) < 6(x – 5)?

Mathematics
1 answer:
MrMuchimi2 years ago
8 0

The solution to the inequality is x > 3

The number line that represent the solution set will be:

<em>A number line from negative 5 to 5 in increments of 1. An open circle is at 3 and a bold line starts at 3 and is pointing to the right</em>. The correct option is the second option

<h3>Linear Inequalities </h3>

From the question, we are to determine the number line that represents the solution set for the given inequality

The given inequality is

3(8 – 4x) < 6(x – 5)

First, we will solve the inequality

3(8 – 4x) < 6(x – 5)

Clear the brackets

24 - 12x < 6x - 30

Collect like terms

24 + 30 < 6x + 12x

54 < 18x

Divide both sides by 18

3 < x

∴ x > 3

Hence, the number line that represent the solution set will be:

<em>A number line from negative 5 to 5 in increments of 1. An open circle is at 3 and a bold line starts at 3 and is pointing to the right</em>. The correct option is the second option

Learn more on Linear inequalities here: brainly.com/question/28003708

#SPJ1

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Spiro travels 140km per week travelling to and from work. If Spiro works 5 days per week. What distance is his work from home?
Ber [7]

Answer:

14 km

Step-by-step explanation:

<u>1) look at the information you are given:</u>

140 km total (<em>to and from work</em>)

Note that this number includes both the distance to work and the distance from work.

He works 5 days a week.

<u>2)Figure out the distance he travels within one day</u>

This means that you should take the 140 km and divide it by 5 in order to find out the amount of km he travels each day.

<h2>140 km / 5 days = 28 km</h2>

28 km is the amount of KM he travels each DAY.

<u>3) Figure out the distance from work to home </u>

From this point, it is important to note the question is asking for <u>the distance his work is from home.</u>

Each day, he must travel 2 times: he must go to work and go from work to home, which are both the same distance.

This means that in order to get only the distance from work to home, you must divide by 2.

<h2>28 km / 2 = 14 km</h2>

4 0
3 years ago
Read 2 more answers
The point (Negative StartFraction StartRoot 2 EndRoot Over 2 EndFraction, StartFraction StartRoot 2 EndRoot Over 2 EndFraction)
sveticcg [70]

The values of cosine Ф and cotangent Ф are \frac{-\sqrt{2} }{2} and -1

Step-by-step explanation:

When a terminal side of an angle intersect the unit circle at

point (x , y), then:

  • The x-coordinate is equal to cosine the angle between the positive part of x-axis and the terminal side
  • The y-coordinate is equal to sine the angle between the positive part of x-axis and the terminal side
  • If x and y coordinates are positive, then the angle lies in the 1st quadrant
  • If x-coordinate is negative and y-coordinate is positive, then the angle lies in the 2nd quadrant
  • If x and y coordinates are negative, then the angle lies in the 3rd quadrant
  • If x-coordinate is positive and y-coordinate is negative, then the angle lies in the 4th quadrant

∵ The terminal ray of angle Ф intersects the unit circle at point (\frac{-\sqrt{2} }{2},\frac{\sqrt{2} }{2})

- According to the 1st and 2nd notes above

∴ cosФ = x-coordinate of the point

∴ sinФ = y-coordinate of the point

∵ The x-coordinate of the point is negative

∵ They-coordinate of the point is positive

- According the the 4th note above

∴ Angle Ф lies in the 2nd quadrant

∵ x-coordinate = \frac{-\sqrt{2} }{2}

∴ cosФ = \frac{-\sqrt{2} }{2}

∵ y-coordinate = \frac{\sqrt{2} }{2}

∴ sinФ = \frac{\sqrt{2} }{2}

- cotФ is the reciprocal of tanФ

∵ tanФ = sinФ ÷ cosФ

∴ cotФ = cosФ ÷ sinФ

∴ cotФ = \frac{-\sqrt{2} }{2} ÷ \frac{\sqrt{2} }{2}

∴ cotФ = -1

The values of cosine Ф and cotangent Ф are \frac{-\sqrt{2} }{2} and -1

Learn more:

You can learn more about the trigonometry function in brainly.com/question/4924817

#LearnwithBrainly

4 0
3 years ago
Read 2 more answers
Aidan is participating in an 8 mile walk for his favorite charity. The organizers used a coordinate grid to plot the course. The
Travka [436]

Answer:

Aidan is 2 miles far from the ending point when he reaches the water station.

Step-by-step explanation:

The locations of the starting point, water station and ending point are (3, 1), (3, 7) and (3, 9), all expressed in miles. First we determine the distances between starting and ending points and between starting point and water station by the Pythagorean Theorem:

From starting point to ending point:

D = \sqrt{(3-3)^{2}+(9-1)^{2}} (Eq. 1)

D = 8\,mi

From starting point to water station:

d = \sqrt{(3-3)^{2}+(7-1)^{2}} (Eq. 2)

d = 6\,mi

The distance between the water station and the ending point is:

s = D-d (Eq. 3)

s = 8\,mi-6\,mi

s = 2\,mi

Hence, Aidan is 2 miles far from the ending point when he reaches the water station.

3 0
3 years ago
What is the domain of y = log Subscript 4 Baseline (x + 3)?
LekaFEV [45]

Answer:

All real numbers greater than -3

Step-by-step explanation:

The domain of a log is the baseline is greater than 0.

Set x + 3 greater than zero and solve

x + 3 > 0

x > -3

3 0
1 year ago
5 2/3 divided by 3/2
Zinaida [17]

Answer: 34/9

Step-by-step explanation:

5  2/3  /   3/2

= 17/3  /   3/2

=17/3 x 2/3        [reciprocal]

=34/9

Hope it helped u,

pls mark as the brainliest

^_^

7 0
3 years ago
Read 2 more answers
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