All categories

3 years ago

Which is the best interpretation of the solution set for the compound inequality?

Mathematics

1 answer:

saw5 [17]3 years ago

8 0

For this case we must find the solution set of the given inequalities:

Inequality 1:

$3 (2x + 1)> 21$

Applying distributive property on the left side of inequality:

$6x + 3> 21$

Subtracting 3 from both sides of the inequality:

$6x> 21-3\\6x> 18$

Dividing by 6 on both sides of the inequality:

$x> \frac {18} {6}\\x> 3$

Thus, the solution is given by all the values of "x" greater than 3.

Inequality 2:

$4x + 3$

Subtracting 3x from both sides of the inequality:

$4x-3x + 3$

Subtracting 3 from both sides of the inequality:

$x$

Thus, the solution is given by all values of x less than 4.

The solution set is given by the union of the two solutions, that is, all real numbers.

Answer:

All real numbers

You might be interested in

A shorter style of cup is stacked tall. The graph displays the height of the stack in centimeters for different numbers of cups.

Strike441 [17]

Answer:

0.5

Step-by-step explanation:

We are looking for how much height is gained per cup added.

Height per cup added can be calculated by finding the slope of the line that runs through the two given points on the graph, (3, 5.5) and (8, 8).

Formula for slope =

Let,

3 0

3 years ago

Read 2 more answers

The graph shows the height of a hiker above sea level.

dimaraw [331]

The <u>correct answer</u> is:

B) The variables are height and time. For the first part of the graph, the height is increasing slowly, which means the hiker is walking up a gentle slope. Flat parts of the graph show where the elevation does not change, which means the trail is flat here. The steep part at the end of the graph shows that the hiker is descending a steep incline.

Explanation:

The variables are marked on the graph. Time is marked along the x-axis, which means it is the independent variable. Height is marked along the y-axis, which means it is the dependent variable.

The first part of the graph rises slowly. This means the elevation does not change much over the time; this would be consistent with a gentle slope being climbed.

The flat areas are where the elevation does not change. This would be consistent with the hiker resting.

The steep decrease at the end shows that the elevation goes down quickly. This is consistent with the hiker climbing down a steep slope.

3 0

3 years ago

Read 2 more answers

Mathematical connection A lighthouse casts a revolving beam of light as far as the pier

Alexandra [31]

The light's coverage area is given mathematically as i.e. Area= $\pi d^{2}$

Given that a lighthouse casts a revolving beam of light as far as they peir and asked the area is covered.

The revolving beam of light covers the whole space i.e entirely 360°

I.e. it forms a circle-like region

Area of circle = $\pi r^{2}$ { where r is the radius of circle}

Let's assume the distance traveled by light as "d"

as it forms a circular region, it forms a circle of radius "d"

Mathematical connection i.e. area of the region

⇒area of circular region= $\pi d^{2}$ {where d is the radius of region}

Learn more about area here:

brainly.com/question/27683633

#SPJ9

4 0

2 years ago

Solve the absolute value inequality: 1x + 12 + 5 < 27

san4es73 [151]

Answer:10

Step-by-step explanation:

Dont know how to explain on here but I know for sure its 10 :)

5 0

3 years ago

If possible help me in this. I need to find the two odd numbers...

Lelechka [254]

Part (a)

Consecutive odd integers are integers that odd and they follow one right after another. If x is odd, then x+2 is the next odd integer

For example, if x = 7, then x+2 = 9 is right after.

<h3>Answer: x+2</h3>

========================================================

Part (b)

The consecutive odd integers we're dealing with are x and x+2.

Their squares are x^2 and (x+2)^2, and these squares add to 394.

<h3>Answer: x^2 + (x+2)^2 = 394</h3>

========================================================

Part (c)

We'll solve the equation we just set up.

x^2 + (x+2)^2 = 394

x^2 + x^2 + 4x + 4 = 394

2x^2+4x+4-394 = 0

2x^2+4x-390 = 0

2(x^2 + 2x - 195) = 0

x^2 + 2x - 195 = 0

You could factor this, but the quadratic formula avoids trial and error.

Use a = 1, b = 2, c = -195 in the quadratic formula.

$x = \frac{-b\pm\sqrt{b^2-4ac}}{2a}\\\\x = \frac{-(2)\pm\sqrt{(2)^2-4(1)(-195)}}{2(1)}\\\\x = \frac{-2\pm\sqrt{784}}{2}\\\\x = \frac{-2\pm28}{2}\\\\x = \frac{-2+28}{2} \ \text{ or } \ x = \frac{-2-28}{2}\\\\x = \frac{26}{2} \ \text{ or } \ x = \frac{-30}{2}\\\\x = 13 \ \text{ or } \ x = -15\\\\$

If x = 13, then x+2 = 13+2 = 15

Then note how x^2 + (x+2)^2 = 13^2 + 15^2 = 169 + 225 = 394

Or we could have x = -15 which leads to x+2 = -15+2 = -13

So, x^2 + (x+2)^2 = (-15)^2 + (-13)^2 = 225 + 169 = 394

We get the same thing either way.

<h3>Answer: Either 13, 15 or -15, -13</h3>

4 0

3 years ago