ΔABC ≅ ΔDEF

Mathematics

1 answer:

Varvara68 [4.7K]3 years ago

7 0

You match by order. A= D, C= F

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HIJK is a rectangle. HJ=x and IK=2x-7 Find the length of each diagonal

laila [671]

The diagonals of a rectangle are congruent so set them equal to each other to get x = 2x - 7. isolate the variable (0 = x - 7 — x = 7) to get x = 7. the diagonals are seven.

3 0

3 years ago

1. Simplify -7 + {12 - 3[50 - 4(2+3)] }

Komok [63]

1. Simplify $-7 + (12 - 3[50 - 4(2+3)])$ this expression step by step:

$2+3=5;$
$4\cdot (2+3)=4\cdot 5=20;$
$50-4\cdot (2+3)=50-20=30;$
$3\cdot [50-4(2+3)]=3\cdot 30=90;$
$12-3\cdot[50-4(2+3)]=12-90=-78;$
$-7 + (12 - 3[50 - 4(2+3)])=-7+(-78)=-7-78=-85.$

2. Simplify the expression $\dfrac{1}{3} + 6\left(\dfrac{2}{3} - \dfrac{1}{6}\right)^2$ in the same way:

$\dfrac{2}{3}-\dfrac{1}{6}=\dfrac{2\cdot 2-1}{6}=\dfrac{3}{6}=\dfrac{1}{2}$
$\left(\dfrac{2}{3} - \dfrac{1}{6}\right)^2=\left(\dfrac{1}{2} \right)^2=\dfrac{1}{4}$
$\dfrac{1}{3} + 6\left(\dfrac{2}{3} - \dfrac{1}{6}\right)^2=\dfrac{1}{3} + 6\cdot \dfrac{1}{4}=\dfrac{1}{3}+\dfrac{3}{2}=\dfrac{1\cdot 2+3\cdot 3}{6}=\dfrac{11}{6}$