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2 years ago

How do we solve the three variable systems

Mathematics

1 answer:

zaharov [31]2 years ago

3 0

Answer:

Step-by-step explanation:

1. Pick any two pairs of equations from the system.

2. Eliminate the same variable from each pair using the Addition/Subtraction method.

3. Solve the system of the two new equations using the Addition/Subtraction method.

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Joey and Armando live on the same st as the park. The park is 9/10 mile from Joey's home. Joey leaves home and walks to Armando'

AleksandrR [38]

Let's start by assuming Armando's house is between Joey's and the park.

Let $x$ be the distance Joey walked to Armando's house.

The park is 9/10 mile from Joey's home. Joey leaves home and walks to Armando's home. Then Joey and Armando walk 3/5 mile to the park.

 $\dfrac{9}{10} = x + \dfrac{3}{5}$

$x = \dfrac{9}{10} - \dfrac{3}{5} = \dfrac{9}{10} -\dfrac{6}{10} = \dfrac{3}{10}$

That's probably the answer they're looking for. But what if the park is between Joey and Armando's houses or Joey is between the park and Armando? (The latter isn't really possible with the given distances.)

Let $a, b, c$ be the distances between three collinear points like we have here. Our equation is really a few equations in one, something like

$\pm a \pm b = \pm c$

Let's get rid of the plus/minuses. Squaring,

$a^2 + b^2\pm 2ab = c^2$

$\pm 2ab = c^2-a^2-b^2$

$4a^2b^2 = (c^2-a^2-b^2)^2$

For us, that's a quadratic equation for $c^2$

$4(9/10)^2(3/5)^2= (c^2-(9/10)^2 - (3/5)^2)^2$

I'll skip right to the solutions,

$c^2=\dfrac{9}{100} \textrm{ or } c^2=\dfrac{9}{4}$

$c=\dfrac{3}{10} \textrm{ or } c=\dfrac{3}{2}$

We could have gotten the 3/2 just by adding 9/10+3/5 but this was more fun.

6 0

4 years ago

Two factors of 18 add up to 12. What are they?

stepladder [879]

Answer:

3 and 9

Step-by-step explanation:

The factors of 18 can be listed as

1, 2, 3, 6, 9, 18

The two which sum to 12 are 3 and 9

7 0

3 years ago

A blueprint for a new house has a scale of 1:50. Here are the dimensions of two rooms. Calculate the dimensions of each room on

Lorico [155]

Answer:

a.) =30.72*50

b.)13.02*50

Step-by-step explanation:

you got to calculate the area of the two rooms by multipling the sides.

as we know that the scale is 1:50, this means for every 1meter it is 50 meters.

once we have calculated the area of the space used multply it by 50 to get the area dimensions occupied

8 0

3 years ago

Count back write the difference = 11 - 3

sergey [27]

Answer:

11-3=8

Step-by-step explanation:

so your answer is going to equal 8

4 0

3 years ago

Read 2 more answers

What is 13,931 round by 10

miv72 [106K]

Answer:

13,930

Step-by-step explanation:

hope this helps!

4 0

3 years ago