How many solutions does 2x + 3y = -6 and 3x - 4y = -12 have

Mathematics

1 answer:

Ostrovityanka [42]3 years ago

8 0

Answer:

As there are 2 equations and two unknowns there is 1 solution

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The inventory of a store 2 years ago was worth $45,000. This year it is worth $49,500. What is the percent increase?

UkoKoshka [18]

It is 0.4500% hope this helps

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3 years ago

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.

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3 years ago

Can anybody answer this??

Arturiano [62]

Answer:

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3 years ago

What is the measure of the largest angle on the triangle!

nalin [4]

Okay, so as you may know the inside angles of a triangle always add up to 180! so you must first find x, so that means add up all equations to find x. your answer is 41

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3 years ago

Read 2 more answers

In ΔEFG, the measure of ∠G=90°, the measure of ∠E=6°, and GE = 71 feet. Find the length of EF to the nearest tenth of a foot.

djyliett [7]

Answer:68.2

Step-by-step explanation:

cos6=71/EF

cos6= 0.960170286650366

0.960170286650366= 71/EF

0.960170286650366*71=EF

EF= 68.2