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3 years ago

Solve the system of equations using substitution or elimination by addition.

Mathematics

2 answers:

Anvisha [2.4K]3 years ago

8 0

Answer: A. The unique solution to the system is $(0.1,0.4)$

Step-by-step explanation:

You can follow these steps to solve the system of equation by the Elimination Method:

- Multiply the first equation by -0.7, then add both equations and solve for "y":

$\left \{ {-0.7(x + y) =-0.7(0.5)} \atop {0.7x + 0.6y = 0.31}} \right.\\\\\left \{ {-0.7x-0.7y =-0.35} \atop {0.7x + 0.6y = 0.31}} \right.\\............................\\-0.1y=-0.04\\\\y=0.4$

- Substitute the value of "y" into any original equation to find the value of "x". Then:

$x + (0.4) = 0.5\\\\x=0.5-0.4\\\\x=0.1$

Therefore, the unique solution to the system is $(0.1,0.4)$

irakobra [83]3 years ago

4 0

Answer:

a. (0.1,0.4)

Step-by-step explanation:

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The general form of a circle is given as x^2+y^2+4x - 12y + 4 = 0. A) What are the coordinates of the center of the circle? B) W

Alex_Xolod [135]

Answer:

center = (-2, 6)

radius = 6

Step-by-step explanation:

Equation of a circle

$(x-a)^2+(y-b)^2=r^2$

(where (a, b) is the center and r is the radius)

Therefore, we need to rewrite the given equation into the standard form of an equation of a circle.

Given equation:

$x^2+y^2+4x-12y+4=0$

Collect like terms and subtract 4 from both sides:

$\implies x^2+4x+y^2-12y=-4$

Complete the square for both variables by adding the square of half of the coefficient of $x$ and $y$ to both sides:

$\implies x^2+4x+\left(\dfrac{4}{2}\right)^2+y^2-12y+\left(\dfrac{-12}{2}\right)^2=-4+\left(\dfrac{4}{2}\right)^2+\left(\dfrac{-12}{2}\right)^2$

$\implies x^2+4x+4+y^2-12y+36=-4+4+36$

Factor both variables:

$\implies (x+2)^2+(y-6)^2=36$

Therefore:

center = (-2, 6)
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leonid [27]

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About 28cm

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3.14÷circumference of the circle (88cm)=28.04.

About 28cm.

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