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3 years ago

Solve the following equations mentally 1. 5 – x = 8 2. -1 = x – 2 3. -3x = 9 4. -10 = -5x

Mathematics

2 answers:

Ghella [55]3 years ago

3 0

Answer:

1. 5 – x = 8 , x = -3

2. -1 = x – 2 , x = 1

3. -3x = 9 , x = -3

4. -10 = -5x , x= 2

Step-by-step explanation:

Lapatulllka [165]3 years ago

3 0

Answer:

1. x= -3 ,2. x=1 , 3.x= -3 ,4.x=2

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Type the correct answer in each box. A circle is centered at the point (5, -4) and passes through the point (-3, 2). The equatio

Galina-37 [17]

Answer:

$(x+ \boxed{-5})^2+(y+\boxed4)^2=\boxed{100}$

Step-by-step explanation:

Given:

Center of circle is at (5, -4).

A point on the circle is $(x_1,y_1)=(-3, 2)$

Equation of a circle with center $(h,k)$ and radius 'r' is given as:

$(x-h)^2+(y-k)^2=r^2$

Here, $(h,k)=(5,-4)$

Radius of a circle is equal to the distance of point on the circle from the center of the circle and is given using the distance formula for square of the distance as:

$r^2=(h-x_1)^2+(k-y_1)^2$

Using distance formula for the points (5, -4) and (-3, 2), we get

$r^2=(5-(-3))^2+(-4-2)^2\\r^2=(5+3)^2+(-6)^2\\r^2=8^2+6^2\\r^2=64+36=100$

Therefore, the equation of the circle is:

$(x-5)^2+(y-(-4))^2=100\\(x-5)^2+(y+4)^2=100$

Now, rewriting it in the form asked in the question, we get

$(x+ \boxed{-5})^2+(y+\boxed4)^2=\boxed{100}$

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3 years ago