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4 years ago

The question is below:

Mathematics

1 answer:

SSSSS [86.1K]4 years ago

5 0

Answer:

Triangles ABE and CDE are congruent by AAS.

Step-by-step explanation:

AB ≅ DC (Opposite sides of a parallelogram are congruent.

m < AEB = m < DEC (Vertical angles).

m < ABE = m < EDC ( Alternate Interior angles).

So triangles ABE and CDE are congruent by AAS.

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Factor the expression completely over the complex numbers.

nekit [7.7K]

Answer:

The factor form of given expression is (x-4)(x-2i)(x+2i).

Step-by-step explanation:

The given expression is

$x^3-4x^2+4x-16$

It can be written as

$f(x)=x^3-4x^2+4x-16$

According to the rational root theorem, all possible rational roots are in the form of

$\frac{a_0}{a_n}$

Where, a₀ is constant term and $a_n$ is leading coefficient.

$f(4)=4^3-4(4)^2+4(4)-16=0$

Since the value of f(x) is 0 at x=4, therefore 4 is a root of the function and (x-4) is a factor of given expression.

Use synthetic method to find the remaining factors.

$(x^3-4x^2+4x-16)=(x-4)(x^2+4)$

$(x^3-4x^2+4x-16)=(x-4)(x^2-(2i)^2)$

$(x^3-4x^2+4x-16)=(x-4)(x-2i)(x+2i)$

Therefore the factor form of given expression is (x-4)(x-2i)(x+2i).

8 0

4 years ago

Read 2 more answers

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prohojiy [21]

Y=x-1
The slope is 1 and it is going through the x axis at -1

4 0

3 years ago

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12,20,28,36 are all multiples of 1, 2 and what?

liberstina [14]

1) one is multiple of all positive integers. So, yes it is multiple of all that numbers.

2) Two is multiple for all those number which has even digit in unit place. So, yes they all are multiple of 2 too.

4 0

4 years ago

Read 2 more answers

Given square ABCD, with point P on side AB , point Q on side BC, point R on side CD, and point S on side DA as shown. Additional

sveta [45]

The ratio of the area of square PQRS to the area of square ABCD is 5/9

<h3>Area of square ABCD</h3>

Assume the measure of the side lengths of the square ABCD is 1, then the area of the square ABCD is:

$A_1 = 1 \times 1$

$A_1 = 1$

See attachment for the diagram that represents the relationship between both squares.

<h3 /><h3>Pythagoras theorem</h3>

The measure of length PQ is then calculated using the following Pythagoras theorem:

$PQ^2 = (\frac 13)^2 + (\frac 23)^2$

Evaluate the squares

$PQ^2 =\frac 19 + \frac 49$

Add the fractions

$PQ^2 =\frac 59$

<h3>Area of square PQRS</h3>

The above represents the area of the square PQRS.

i.e.

$A_2 =\frac 59$

So, the ratio of the area of PQRS to ABCD is:

$Ratio = \frac{A_2}{A_1}$

This gives

$Ratio = \frac{5/9}{1}$

$Ratio = \frac{5}{9}$

Hence, the ratio of the area of square PQRS to the area of square ABCD is 5/9