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Luda [366]
2 years ago
15

Solve the absolute value inequality. |2x - 3| > 7

Mathematics
1 answer:
s344n2d4d5 [400]2 years ago
6 0

Hi!

<u><em>NOTE: When solving absolute value inequalities, > or ≥ means OR, and < and ≤ means AND.</em></u>

<u><em /></u>

|2x - 3| > 7

Since the absolute value is isolated, we can now solve.

First, remove absolute value signs, then solve for x.

2x - 3 > 7

2x > 10

x > 5

Now, we have to solve again, but this time we flip the inequality sign and switch positive 7 to a negative 7, like so:

2x - 3 < -7

2x < -4

x < -2

Now, as stated above, since it's a greater than symbol it means OR.

<u><em>x > 5 OR x < -2</em></u>

<u><em></em></u>

<u><em>For more information on solving absolute value inequalities:</em></u>

brainly.com/question/14473339

<em />

<em />

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A hemisphere fake stone made of clay has a diameter of 16 inches. The density of clay is 0.0035 pounds per cubic inch. The clay
Rufina [12.5K]

Answer:

$137.82

Step-by-step explanation:

The volume of a hemisphere stone is given by the volume of a half-sphere:

Volume = (2/3) * pi * radius^3

If the diameter is 16 inches, the radius is 16/2 = 8 inches, so the volume is:

Volume = (2/3) * pi * 8^3 = 1072.33 in3

We need a total of 8 stones, so the total volume is:

Total Volume = 8 * 1072.33 = 8578.64 in3

The density of clay is 0.0035 pounds per cubic inch, so the total weight of the 8 stones is:

Weight = Total Volume * density = 8578.63 * 0.0035 = 30.0252 pounds

Finally, if the price of each pound of clay if $4,59, the final price is:

Price = 30.0252 * 4.59 = $137.82

8 0
3 years ago
Write the following as an inequality 6 is greater than or equal to x and -2 is less than or equal to x
kipiarov [429]

Answer:

  -2 ≤ x ≤ 6

Step-by-step explanation:

The first is ...

  6 ≥ x

and it can also be written as ...

  x ≤ 6

The second is

  -2 ≤ x

The two inequalities can be combined into one compound inequality:

  -2 ≤ x ≤ 6

_____

<em>Comment on this answer</em>

I prefer the answer in this form because it puts the parts of the expression in the same order that they appear on a number line. It can also be written as ...

  6 ≥ x ≥ -2

7 0
3 years ago
Determine the x- and y-intercepts of the graph of y=1/4x−2 .
KATRIN_1 [288]
To find the x-intercept, put in 0 for the y.

0=1/4x-2
2=1/4x
8=x

The x-intercept is 8. The point is (8, 0).

To find the y-intercept, put in 0 for the x.

y=1/4(0)-2
y=0-2
y=-2

The y-intercept is -2. The point is (0, -2).

To graph, find the points on a coordinate plane and draw a straight line through them.

Hope this helps!
5 0
3 years ago
Explain why 2/3 ×12 can be written as 2 × 12 ÷3
nalin [4]

Answer:

violates the rules or bedmas

Step-by-step explanation:

When doing questions like these, bedmas comes into play. althought multiplication and division are the same in terms of priority, you should do the one that comes first when reading the equation/formula left to right.

this would mean you would do 2 ÷ 3 and the answer would be multiplied by 12.

8 0
3 years ago
If i have a 83.5 as my grade and let's just say i would get a 70/100 what would be my grade?
daser333 [38]

Answer:

76.75

Step-by-step explanation:

83.5 + 70=  153.5

153.5 / 2 = 76.75

Your grade would be 76.75.

HOPE THIS HELPED

6 0
3 years ago
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