True or False? In an isosceles trapezoid the diagonals are congruent.

1 answer:

3 0

It is true, they are congruent by doing a proof. You have to divide the trapezoid into 2 equal triangles. Then you can prove it. They are congruent since corresponding parts of congruent triangles are congruent.

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When the sum of 5 and three times a positive number is subtracted from the square of the number, 0 results. Find the number.

Juliette [100K]

$x-the\ number\\\\x^2-(5+3x)=0\\\\x^2-5-3x=0\\\\x^2-3x-5=0$

$Use\ the\ quadratic\ formula:\\a^2x+bx+c=0\\\\\Delta=b^2-4ac\\\\if\ \Delta > 0\ then\ x_1=\dfrac{-b-\sqrt\Delta}{2a}\ and\ x_2=\dfrac{-b+\sqrt\Delta}{2a}\\\\if\ \Delta=0\ then\ x_0=\dfrac{-b}{2a}\\\\if\ \Delta < 0\ then\ no\ solution$

$x^2-3x-5=0\\\\a=1;\ b=-3;\ c=-5\\\\\Delta=(-3)^2-4\cdot1\cdot(-5)+3+20=29 \ \textgreater \ 0\\\\\sqrt\Delta=\sqrt{29}\\\\x_1=\dfrac{3-\sqrt{29}}{2\cdot1}=\dfrac{3-\sqrt{29}}{2} \ \textless \ 0\\\\x_2=\dfrac{3+\sqrt{29}}{2\cdot1}=\dfrac{3+\sqrt{29}}{2} \ \textgreater \ 0$

$Answer:\ \boxed{x=\dfrac{3+\sqrt{29}}{2}}$

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2 years ago

Find the domain of the following relation. <br> R={(19,96),(20,101),(21,106),(22,111)}

mafiozo [28]

(x, y)

The domain are all the x-values, the range are all the y-values.

R={(19,96),(20,101),(21,106),(22,111)}

The domain is: 19, 20, 21, and 22
The range is: 96, 101, 106, and 111

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2 years ago

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Answer:

1. 35 degrees

2. 44 degrees

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2 years ago

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A dance school has 63 ballet dancers. If 42% of the total number of dancers in the school are ballet dancers, what is the total

maria [59]

The total number of dancers in the school is 150.

7 0

3 years ago

Can someone help me please

goldenfox [79]

Answer:

$1. \quad\dfrac{1}{k^{\frac{2}{3}}}\\\\2. \quad\sqrt[7]{x^5}\\\\3. \quad\dfrac{1}{\sqrt[5]{y^2}}$

Step-by-step explanation:

The applicable rule is ...

$x^{\frac{m}{n}}=\sqrt[n]{x^m}$

It works both ways, going from radicals to frational exponents and vice versa.

The particular power or root involved can be in either the numerator or the denominator. The transformation applies to the portion of the expression that is the power or root.

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3 years ago