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3 years ago

56 is 140% of what number

Mathematics

2 answers:

motikmotik3 years ago

8 0

To find the answer, you convert the percentage to a decimal. 140% = 1.4

Then you divide 56 by 1.4

56/1.4 = 40

Margarita [4]3 years ago

3 0

Write an equation: "is" means =, and "of" means multiply
56 = 1.4 N

Divide both sides by 1.4:
N = 56 ÷ 1.4

N = 40

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Let the coordinates of the circumcentre O of the triangle DEF be (x, y). Circumcentre of a triangle is equidistant from each of the vertices.

1. Distance OD=distance OE, then:

$(x-1)^2+(y-3)^2=(x-8)^2+(y-3)^2$ .

2. Distance OD=distance OE, then:

$(x-1)^2+(y-3)^2=(x-1)^2+(y+5)^2$ .

Solve the system:

$\left\{\begin{array}{l} (x-1)^2+(y-3)^2=(x-8)^2+(y-3)^2 \\ (x-1)^2+(y-3)^2=(x-1)^2+(y+5)^2 \end{array}\right.$ ,

$\left\{\begin{array}{l} x^2-2x+1+y^2-6y+9=x^2-16x+64+y^2-6y+9 \\ x^2-2x+1+y^2-6y+9=x^2-2x+1+y^2+10y+25 \end{array}\right.$ ,

$\left\{\begin{array}{l} 14x=63 \\ -16y=16 \end{array}\right.$ .

Then

$x=\dfrac{63}{14} =\dfrac{9}{2} =4.5,\\ \\ y=-1$ .

Answer: the coordinates of the circumcenter for ∆DEF are x=4.5, y=-1.

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