Answer:
inconsistent
Step-by-step explanation:
The two lines are parallel which means they will never intersect. This means they have no solution. When there is no solution they are inconsistent.
Coincident- same line - infinite solutions
Inconsistent - parallel lines - no solutions
Consistent and independent - 1 solutions
Answer:
(20-3x)/2 GB
Explanation:
Total amount of data on my computer = 10GB
Total amount of data occupied by movies = x GB
If pictures take up half the amount of space that movies do, then;
Total amount of data occupied by pictures = 1/2 of space occupied by movies = 1/2 x
If the remaining are music, the amount of space occupied by music will be expressed as shown;
Total space -(space occupied by movies + space occupied by pictures)
= 10 - (x+1/2 x)
Total amount of data occupied by music = 10 - (x+1/2 x) GB
On simplification;
= 10 - (x+1/2 x)
= 10-{(2x+x)/2}
= 10 - {3x/2}
= (20-3x)/2 GB
Hence, amount of gigabytes of music stored on my computer is expressed as (20-3x)/2 GB.
Answer: 103, 104, 105, and 106
Step-by-step explanation: This problem states that the sum of 4 consecutive integers is 418 and it asks us to find the integers.
First represent your 4 consecutive integers as follows.
X ⇒ first integer
X + 1 ⇒ second integer
X + 2 ⇒ third integer
X + 3 ⇒ fourth integer
Since their sum is 418, our equation reads
x + (x + 1) + (x + 2) + (x + 3) = 418.
Simplifying on the left side we get 4x + 6 = 418.
Now we can subtract 6 from both sides of the equation and we have
4x = 412.
Now just divide both sides by 4 and we find that <em>x = 103</em>.
Finally, make sure you list all your answers.
If <em>x</em> is 103, then <em>x </em>+ 1 is 104, <em>x</em> + 2 is 105, and <em>x</em> + 3 is 106
Therefore, our 3 consecutive integers are 103, 104, 105, and 106.
Answer:
√7 ≈ 2.646
Step-by-step explanation:
The law of cosines is applicable. It tells you ...
c² = a² + b² - 2ab·cos(C) . . . . . where a, b, c are triangle side lengths, and angle C is opposite side c.
Filling in the given information, you have ...
c² = 2² + 3² - 2·2·3·cos(60°) = 4 + 9 - 12·(1/2) = 7
c = √7 ≈ 2.646
The length of the third side is √7, about 2.646 units.
