Marco's equation is correct. Cosine is an even function, which means that for every x, f(-x) = f(x). In other words, you get the same answer for a negative value that you would for its corresponding positive value.
It shoukd be A if im not mistaken
Answer:
<em>a) 3<x<8</em>
<em>b) -4<x<-2</em>
<em>c) -6<x<5</em>
<em>d) -21/4 < x-8/3</em>
<em>e) 0<x<7</em>
Step-by-step explanation:
Given the following inequalities
a) x > 3, 2x - 3 < 15
Solve 2x - 3 < 15
2x < 15+3
2x<18
x<18/2
x<8
Combine x>3 and x<8
If x>3, then 3<x
On combining, we have:
3<x<8
b) For the inequalities 25 > 1 - 6x, 1 > 3x + 7
25 > 1 - 6x
25-1>-6x
24>-6x
Divide through by -6:
24/-6 > -6x/-6
-4 <x
For the inequality 1 > 3x + 7
1-7>3x
-6>3x
-6/3 > 3x/3
-2 > x
x < -2
Combining both results i.e -4 <x and x < -2, we will have:
-4<x<-2
c) For the inequalities 2x - 7<3< 27 + 4x
On splitting:
2x - 7<3 and 3< 27 + 4x
2x < 3+7
2x<10
x<5
Also for 3< 27 + 4x
3-27<4x
-24<4x
-24/4 < 4x/4
-6<x
Combining both solutions i.e x<5 and -6<x will give;
<em>-6<x<5</em>
d) For the inequalities 3x + 8 <0 < 21 + 4x
3x + 8 <0
3x < -8
x < -8/3
Also for 0 < 21 + 4x
0-21<4x
-21<4x
-21/4 < 4x/4
-21/4 < x
Combining -21/4 < x and x < -8/3 will give;
<em>-21/4 < x-8/3</em>
<em></em>
e) For the inequalities 5x - 36 < -1 < 2x – 1
Split:
5x - 36 < -1
5x < -1+36
5x<35
5x/5 < 35/5
x < 7
For the expression -1 < 2x – 1
-1+1 < 2x
0 < 2x
0<x
Combining both inequalities 0<x and x < 7 will give:
<em>0<x<7</em>
Answer:
Part A) The statement is True
Part B) The statement is False
Part C) The statement is True
Part D) The statement is True
part E) The statement is False
Step-by-step explanation:
Part A) we have

The statement Is True
Convert the repeating decimal 1.66.. to an equivalent fraction
Let

Convert to mixed number

therefore

Part B) we have

The statement is false
Because

so
substitute
-----> is not true
Part C) we have

The statement is True
Because

substitute
----> is true
Part D) we have

The statement is True
Because

substitute
----> is true
Part E) we have

The statement is false
Because
Convert mixed number to an improper fraction

Convert decimal number to an improper fraction

substitute
-----> is not true
2.0076* 10^4
move the decimal 4 places to the right
20076.
20076 < 26970