The solution to the system of inequality expression is 1 < x < 10
Inequality expressions are expressions not separated by an equal sign
Given the inequality expressions
- 4x – 2 < -6 and - 4x – 2 > -42
For the inequality - 4x – 2 < -6
- 4x – 2 + 2 < -6 + 2
-4x < -4
x > 1
For the inequality - 4x – 2 > -42
- 4x – 2 + 2> -42 +2
-4x > -40
x < 10
Combining both inequality solutions:
1 < x < 10
Hence the solution to the system of inequality expression is 1 < x < 10
Representing on the number line we have:
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The general solution of the pair of equations:
- 4x – 2 < -6 and - 4x – 2 > -42 is; 1 < x > 10
By solving the first inequality;
By dividing both sides by -4, we have;
x > 1
Subsequently, by solving the second inequality;
By dividing both sides by -4, we have;
x < 10
Therefore, the inequality that satisfies both equations is;
1 < x > 10
The image attached contains the solution on the number line.
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Answer:
Hector's kite is 61.84 feet from the ground.
Step-by-step explanation:
The angle of elevation of the kite is 42°15’30” when converted to decimals, it is ≅
Let the height of the kite to the horizontal of angle of elevation be represented as x. Applying the trigonometric function to the sketch of Hector's kite,
Sin θ =
Sin =
⇒ x = 86 x Sin
= 86 x 0.6725
= 57.835
x ≅ 57.84 feet
The height of Hector's kite from the ground = x + 4
= 57.84 + 4
= 61.84 feet
Answer:
see below
Step-by-step explanation:
Option 1: the two solution sets overlap at <em>x=1</em>.
Option 2: the two solution sets do not overlap; no solution.
Option 3: together, the two set describe <em>all real numbers</em>.
