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3 years ago

Which pairs of quadrilaterals can be shown to be congruent using rigid motions?

Mathematics

1 answer:

Elina [12.6K]3 years ago

3 0

Answer:

q1, q2, and q3 are all congruent.

Step-by-step explanation:

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If alpha and beta are the zeroes of the polynomial 6x2+x-2 find the value og alpha/beta + beta/alpha

castortr0y [4]

$6x^2+x-2=6x^2+4x-3x-2=2x(3x+2)-1(3x+2)\\\\=(3x+2)(2x-1)\\\\3x+2=0\to x=-\frac{2}{3}\\\\2x-1=0\to x=\frac{1}{2}\\\\\alpha=-\frac{2}{3};\ \beta=\frac{1}{2}\\\\\frac{\alpha}{\beta}+\frac{\beta}{\alpha}=\frac{-\frac{2}{3}}{\frac{1}{2}}+\frac{\frac{1}{2}}{-\frac{2}{3}}=-\frac{2}{3}\cdot\frac{2}{1}-\frac{1}{2}\cdot\frac{3}{2}=-\frac{4}{3}-\frac{3}{4}\\\\=-\frac{16}{12}-\frac{9}{12}=-\frac{25}{12}=-2\frac{1}{12}$

$use\ Vieta's\ formula:\\\\\frac{\alpha}{\beta}+\frac{\beta}{\alpha}=\frac{\alpha^2+\beta^2}{\alpha\beta}=\frac{\alpha^2+2\alpha\beta+\beta^2-2\alpha\beta}{\alpha\beta}=\frac{(\alpha+\beta)^2-2\alpha\beta}{\alpha\beta}=\frac{(\alpha+\beta)^2}{\alpha\beta}-2\\\\\alpha+\beta=\frac{-b}{a};\ \alpha\beta=\frac{c}{a}\\\\\frac{(\alpha+\beta)^2}{\alpha\beta}-2=\frac{\left(\frac{-b}{a}\right)^2}{\frac{c}{a}}-2=\frac{b^2}{a^2}\cdot\frac{a}{c}-2=\frac{b^2}{ac}-2$

$6x^2+x-2\\\\a=6;\ b=1;\ c=-2\\\\\frac{\alpha}{\beta}+\frac{\beta}{\alpha}=\frac{1^2}{6\cdot(-2)}-2=\frac{1}{-12}-2=-2\frac{1}{12}$

7 0

3 years ago

A company rents bicycles to customers. The company charges an initial fee

photoshop1234 [79]

The hourly rate is $3 a hour with a $2 initial fee.

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2 years ago

Solve using the quadratic formula x^2-4x+1=0

sergiy2304 [10]

Answer:

x=2+ or - the square root of 3

Step-by-step explanation:

solve the equation for x by finding a, b, and c of the quadratic then applying the quadratic formula.

4 0

3 years ago

Read 2 more answers

A grocery store clerk has 16 oranges ,20 apples and 24 pears the clerk needs to put an equal number of apples , oranges and pear

anyanavicka [17]

A.) The clerk has - 16 oranges 20 apples 24 pears

he needs to put all three fruits into baskets without any leftover fruits

each basket should have equal amounts of each fruit

so to find the largest number of baskets he can make we have to find the highest common factor for 16,20 and 24

so lets find the factors for each of these

16 - 1,2,4,8,16

20 - 1,2,4,5,10,20

24 - 1,2,3,4,6,8,12,24

from the given factors the common factors for all three are 1,2 and 4

from these the highest factor is 4

therefore the largest number of baskets he can make are 4

in each basket there will be

4 oranges 5 apples 8 pears

answer is 4 baskets

4 0

2 years ago

Evaluate 12: (2+2) 67 4 3 111 Help me and I will give u 20 points

Oxana [17]

Answer:

it is 27/16 or 1 11/16

Step-by-step explanation:

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2 years ago