Simplify the following expression. (3x + 4)(x − 7)
2 answers:
<h2>Answer:</h2>
The given problem is in algebra, this is because it has both variable and constant.
From question, we need to find the simplified form of the given expression. The simplified form denotes the form which is more understandable form.
Now, we need to multiply the brackets,
On solving,
Which cannot be solved further.
This expression has ‘x’ to the power 2 which will form second order equation when equated to zero.
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Answer:
a) 1,440 ways
b) 59,280 or 64,000
Step-by-step explanation:
a) Aircraft boarding.
8 people, 2 in first class, boarding first, then 8 economy class.
The 2 people in first class board first, but they can board as AB or BA... so 2 ways here.
For the 6 economy class passengers, we have a permutation of 6 out of 6, so 720, as follows:
Since the two are independent, we multiply them to have a global number of ways: 2 * 720 = 1,440 different ways for the 8 passengers to board that plane.
b) combination lock.
Here we do have a little problem... the question doesn't specify if the 3 numbers are different numbers of not. So, we'll calculate both:
Numbers go from 1 to 40 inclusively... so 40 possibilities.
Normally, in a combination lock, the numbers are different, so let's start with that one:
First number: 40 options available
Second number: 39 options available (cannot take the first one again)
Third number: 38 different options (can't take First or Second number again)
Overall, we then have 40 * 39 * 38 = 59,280 different lock combinations.
If we can pick pick the same number twice:
First number: 40 options available
Second number: 40 options available
Third number: 40 options available
Overall 40 * 40 * 40 = 64,000 different lock combinations
The volume of a rectangular prism is represented by the following equation:
Where the variables are for volume, width, height, and length, respectively.
We are given that the area of one end is 16 cm² (units have to be correct when solving these problems, so it's 16 cm², not 16 cm as described in the problem). We know that
Using this knowledge, we can change the volume equation to our needs.
Note: We know that A is 16 since it's given
The volume is 208 cm³ (once again, incorrect units given). Insert this into the equation.
Divide both sides of the equation by 16.
The length is 13 cm.
Let me know if you need any clarifications, thanks!