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olchik [2.2K]
2 years ago
12

Find a ⋅ b. a = 8i + 6j, b = 4i + 5j

Mathematics
2 answers:
frutty [35]2 years ago
7 0
You could rewrite this as double brackets, as you are multiplying together two sets of two terms. It would then look like:
(8i + 6j)(4i + 5j)
and you can expand by multiplying together all of the terms

8i × 4i = 32i²
8i × 5j = 40ij
6j × 4i = 24ij
6j × 5j = 30j²

To get your final answer, you then just need to add together all of the like terms, and get 32i² + 30j² + 64ij

I hope this helps!
dybincka [34]2 years ago
6 0
32i+30j should be correct(hopfully)

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The local orchestra has been invited to play at a festival. There are 111 members of the orchestra and 6 are licensed to drive l
Nezavi [6.7K]

- Make an equation representing the number of vehicles needed.

We have six drivers so

x + y ≤ 6

That's not really an equation; it's an inequality.  We want to use all our drivers so we can use the small vans, so

x + y = 6

- Make an equation representing the total number of seats in vehicles for the orchestra members.

s = 25x + 12y

That's how many seats total; it has to be at least 111 so again an inequality,

25x + 12y ≥ 111

We solve it like a system of equations.  

x + y = 6

y = 6 - x

111 = 25x + 12y = 25x + 12(6-x)

111 = 25x + 72 - 12x

111 - 72 = 13 x

39 = 13 x

x = 3

Look at that,  it worked out exactly.  It didn't have to.

y = 6 - x = 3

Answer: 3 buses, 3 vans

8 0
1 year ago
The total cost of a shirt and a tie was $75.62. if the price of the shirt was $4.02 less than the tie, what was the price of the
kifflom [539]
--------------------------------------------
Define x:
--------------------------------------------
Let the tie be x
Tie = x
Shirt = x - 4.02

--------------------------------------------
Construct equation :
 --------------------------------------------
The sum of the shirt and tie is $75.62
x + x -4.02 = 75.62
2x - 4.02 = 75.62
2x = 79.64
x = $39.82

--------------------------------------------
Find the cost of tie and shirt :
--------------------------------------------
Tie = x = $39.82
Shirt = x - $4.02 = $39.82 - $4.02 = $35.80

----------------------------------------------------------------------------------------
Answer: The price of the short is $35.80
----------------------------------------------------------------------------------------
5 0
1 year ago
A jar contains 27 marbles. There are 4 blue marbles and the rest are red. If a marble is chosen at random, what is the likelihoo
ikadub [295]

Answer:

23/27

Step-by-step explanation:

27-4=23

8 0
2 years ago
What is the quotient (x3 – 3x2 + 3x – 2) ÷ (x2 – x + 1)?
timofeeve [1]

We need to find the quotient of the given division problem.

\frac{x^{3}-3x^{2}+3x-2}{x^{2}-x+1}

In order to find its quotient, we will use long division.

x^{2}-x+1)x^{3}-3x^{2}+3x-2

First of all, we put x in the quotient as x^{2} goes into x^{3}, x times.

So, we get:

x^{2}-x+1)x^{3}-3x^{2}+3x-2(x

\text{ ..................}x^{3}-x^{2}+x

Upon subtracting, we get:

\text{....................}-2x^{2}+2x-2

We can see that x^{2} goes into -2x^{2}, -2 times, therefore, the next term in the quotient will be -2. This makes our quotient as (x-2).


5 0
2 years ago
Read 2 more answers
The flathead rail tunnel in Montana is about 7 3/4 miles long. A train travels at a speed of 3/4 mile per mile minute.how long w
kogti [31]
7 3/4 × 3/4 = So u add 3×3=9
Then add 4×4=16 Give you 9/16
Then you add that 7 you left out with 9/16
But just the 9 not the 16
7 × 9 = 63 And your answer is 63/16
Hope i help :-)
5 0
2 years ago
Read 2 more answers
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