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vodka [1.7K]
3 years ago
10

Simultaneous equations 2x+3y=13 4x-y=-2

Mathematics
1 answer:
Rufina [12.5K]3 years ago
3 0

Answer:

(0.5, 4 )

Step-by-step explanation:

Given the 2 equations

2x + 3y = 13 → (1)

4x - y = - 2 → (2)

Multiplying (2) by 3 and adding to (1) will eliminate the term in y

12x - 3y = - 6 → (3)

Add (1) and (3) term by term to eliminate y

14x = 7 ( divide both sides by 14 )

x = 0.5

Substitute x = 0.5 into either of the 2 equations and evaluate for y

Substituting into (1)

2(0.5) + 3y = 13

1 + 3y = 13 ( subtract 1 from both sides )

3y = 12 ( divide both sides by 3 )

y = 4

Solution is (0.5, 4 )

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Jesse's mother needs 24 feet of fabric to make curtains for all of her windows. The fabric is sold by the yard. How many yards o
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Answer:

B: 8 yards

Step-by-step explanation:

  3: feet in one yard

3/24=8

4 0
2 years ago
You're ordering a sandwich at the local deli, below is a tree diagram of the possible orders. What is the probability that your
dusya [7]

Answer:

Step-by-step explanation:

1. So there is two bread options but let's ignore that due every option being the same for both bread options.

2. So if you look there are three meat options meaning there is a one in three chance logical chance someone picks turkey (note when I say logical I mean that doesn't mean that this will be true in real life) and there is a one in two logical chance someone picks Swiss cheese.

3. So with a one in three chance logical meat option and a one two chance cheese option and.

4. Now knowing this it is simple math at this point as simple as \frac{1}{3} x \frac{1}{2}

5. 1 x 1 = 1 and 3 x 2 = 6

6. leading to \frac{1}{6}

4 0
2 years ago
A swimming pool had 2.5 liters of water in it. Some water evaporated, and then the pool only had 2 million liters of water in it
djyliett [7]
Hi!

If I have done this correctly, then the answer is:

2 million is 80% of 2.5

That means that 20% of the water evaported.
5 0
3 years ago
How many elements does A contains if it has 64 subsets​
Amanda [17]
<h3>Answer:  6</h3>

===========================================================

Explanation:

Rule: If a set has n elements in it, then it will have 2^n subsets.

For example, there are n = 3 elements in the set {a,b,c}. This means there are 2^n = 2^3 = 8 subsets. The eight subsets are listed below.

  1. {a,b,c} .... any set is a subset of itself
  2. {a,b}
  3. {a,c}
  4. {b,c}
  5. {a}
  6. {b}
  7. {c}
  8. { } ..... the empty set

Subsets 2 through 4 are subsets with exactly 2 elements.  Subsets 5 through 7 are singletons (aka sets with 1 element). The last subset is the empty set which is a subset of any set. You could use the special symbol \varnothing to indicate the empty set.

For more information, check out concepts relating to the power set.

-------------------

The problem is asking what value of n will make 2^n = 64 true.

You could guess-and-check your way to see that 2^n = 64 has the solution n = 6.

Another approach is to follow these steps.

2^n = 64\\\\2^n = 2^6\\\\n = 6

Which is fairly trivial.

Or you can use logarithms to solve for the exponent.

2^n = 64\\\\\text{Log}\left(2^n\right)=\text{Log}\left(64\right)\\\\n*\text{Log}\left(2\right)=\text{Log}\left(64\right)\\\\n=\frac{\text{Log}\left(64\right)}{\text{Log}\left(2\right)}\\\\n\approx\frac{1.80617997398389} {0.30102999566399} \ \text{ ... using base 10 logs}\\\\n\approx5.99999999999983\\\\

Due to rounding error, we don't land exactly on 6 even though we should.

5 0
2 years ago
Jada and Noah wanted to find the total volume of a cube and a rectangular prism. They know the prism's volume is 20 cubic units,
jeyben [28]

Answer:

Volume of the cube = 10^3 = 1000 units.

Total volume of the cube + the prism = 1000 + 2

= 1020 cubic units.

Step-by-step explanation:

sorry if i get it wrong

5 0
3 years ago
Read 2 more answers
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