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inysia [295]
3 years ago
10

Find the intersection between thelines 2x + 3y = 5 and 3x + 4y = 6

Mathematics
1 answer:
Archy [21]3 years ago
4 0
An intersection point, is a shared coordinate. If the equations share a coordinate we can say they are "equal". There are two ways (algebraically) to find this point. Substitution or linear combination. Because the coefficients are different, let's use linear combination

First stack the equations on top of each other.

2x + 3y = 5
3x + 4y = 6

Next let's manipulate one or both of the equations to get coefficients that are equal, but opposite. For this I'm going to turn the coefficient of x into 6 and -6 respectively by multiplying the first equation by 3 and the second by -2 to get 

6x + 9y = 15
-6x -8y = -12

Now we can combine the equations with addition and the x's will cancel leaving a single variable (which we can solve)

y = 3

Now plug this back into either original equation to find the x coordinate.

2x + 3(3) = 5

2x + 9 = 5

2x = -4

x = -2.

So your intersection point is (-2,3)
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Step-by-step explanation:

We know this because it follows the rule of perfect squares in which the ends are both squares and the middle term is -2 times each term.

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2 years ago
What is the volume of corn held in this cone-shaped grain silo? Use 3.14 for π and round to the nearest cubic foot. Enter your a
babymother [125]

Answer:

V = 301 ft^3

Step-by-step explanation:

The volume of a cone is given by

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We know pi = 3.14 r =6 and

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We can find h from the Pythagorean theorem where 6 is a leg and 10 is the hypotenuse

h^2 +6^2 = 10^2

h^2 +36 = 100

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h = 8

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Rounding to the nearest cubic foot

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7 0
3 years ago
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if i supposedly got 2 cats and trained them to bring me quarters and they did and supposedly everyday i got 10 quarters how much
ivanzaharov [21]

Answer:

After a year you would have $1,825

Step-by-step explanation:

Amount for one cat a day in cents

10x25=250

Amount for one cat for a year in cents

250x365=91,250

Amount for both cats for a year in cents

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8 0
1 year ago
Help easy math question!!!
bogdanovich [222]

Answer:

The length of the third side of the triangle is 30.

Step-by-step explanation:

Here is the formula for the Pythagorean Theorem:

a^{2} + b^{2} = c^{2}

The hypotenuse, based on the problem, is 50. Anyways, let's get back to calculating!

We need to multiply 40 times 40 and 50 times 50.

40 times 40, or 40 squared, equals to 1600.

50 times 50, or 50 squared, equals to 2500.

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Now, let's subtract. 2500 - 1600 = 900. We need to find the square root of 900--which is 30, because 30 times 30, or 30 squared, equals to 900.

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3 years ago
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