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1 year ago

If | 8x -2 | < 4, Which of the following is true of x? Explain as well.

Mathematics

1 answer:

wariber [46]1 year ago

3 0

The true expression of the variable x in the inequality expression given as |8x - 2| < 4 is -0.25 < x < 0.75

<h3>What are inequality expressions?</h3>

Inequality expressions are mathematical statements that are represented by variables, coefficients and operators where the opposite sides are not equal

<h3>How to determine the true expression of the variable x?</h3>

The inequality expression is given as

|8x - 2| < 4

Divide through the above equations by 2

So, we have the following inequality expression

|4x - 1| < 2

Remove the absolute value sign from the inequality expression

So, we have

-2 < 4x - 1 < 2

Add 1 to all sides of the above inequality expression

So, we have

-1 < 4x < 3

Divide through the above inequality expression by 4

So, we have

-0.25 < x < 0.75

Hence, the true expression of the variable x in the inequality expression given as |8x - 2| < 4 is -0.25 < x < 0.75

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A man is standing at a radar base and observes an unidentified plane at an altitude 6000m flying towards the radar base at an an

liubo4ka [24]

Answer:

The speed in of the plane is 115.47 m/sec

Step-by-step explanation:

Given:

Height at which the plane is flying = 6000 m

Angle of elevation at the radar base = 30 Degrees

Angle of elevation at the radar base after one minute = 60 Degrees

To Find:

The Speed of the plane in meter per second = ?

Solution:

Let us use the tangent of the angle to find the distance (d) to a point directly below plane:

when the angle is 30 degrees

$tan(30) = \frac{6000}{d1}$

$d1 = \frac{6000}{tan(30)}$

$d1 = \frac{6000}{0.577}$

d1 = 10392.3 meters

when the angle is 60 degrees

$tan(60) = \frac{6000}{d2}$

$d2 = \frac{6000}{tan(60)}$

$d2 = \frac{6000}{1.732}\\$

d2 = 3464.1 meters

distance travelled by aircraft in 1 min is

=>d1 - d2

=>0392.3 - 3464.1

= 6928.2 m/min

Now converting to m/sec

=> $\frac{6928.2}{60}$

=>115.47 m/sec

4 0

3 years ago

How do you find the cube root

zvonat [6]

Use a calculator to find the cube root of positive or negative numbers. Given a number x, the cube root of x is a number a such that a3 = x. If x positive a will be positive, if x is negative a will be negative. Cube roots is a specialized form of our common radicals calculator.

Example Cube Roots:The 3rd root of 64, or 64 radical 3, or the cube root of 64 is written as $ \sqrt[3]{64} = 4 $.The 3rd root of -64, or -64 radical 3, or the cube root of -64 is written as $ \sqrt[3]{-64} = -4 $.The cube root of 8 is written as $ \sqrt[3]{8} = 2 $.The cube root of 10 is written as $ \sqrt[3]{10} = 2.154435 $.

The cube root of x is the same as x raised to the 1/3 power. Written as $ \sqrt[3]{x} = x^{\frac{1}{3}} $. The common definition of the cube root of a negative number is that 
(-x)1/3 = -(x1/3).[1] For example:

The cube root of -27 is written as $ \sqrt[3]{-27} = -3 $.The cube root of -8 is written as $ \sqrt[3]{-8} = -2 $.The cube root of -64 is written as $ \sqrt[3]{-64} = -4 $.

This was not copied from a website or someone else. This was from my last year report.


f -64, or -64 radical 3, or the cube root of -64 is written as $ \sqrt[3]{-64} = -4 $.The cube root of 8 is written as $ \sqrt[3]{8} = 2 $.The cube root of 10 is written as $ \sqrt[3]{10} = 2.154435 $.

The cube root of -27 is written as $ \sqrt[3]{-27} = -3 $.The cube root of -8 is written as $ \sqrt[3]{-8} = -2 $.The cube root of -64 is written as $ \sqrt[3]{-64} = -4 $.

6 0

3 years ago

Find an equation of the line that passes through the pair of points(1,-6) and (-4,9)

AlexFokin [52]

Answer:

The equation of the line that passes through the points

(1,-6) and (-4,9)

y=-3x-3

6 0

3 years ago

In which direction must the graph of f(x) = |x| be shifted to produce the graph of g(x) = |x − 3|?

ElenaW [278]