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3 years ago

5

A triangle with angle measures of two 33 degree angles and 114 degree angle. Is that a unique triangle more than one or no trian

gle?

1 answer:

Zarrin [17]3 years ago

6 0

Answer:

Step-by-step explanation:

we can have infinite similar triangles with different side lengths but if the base length is same then two triangles on the opposite side of base.

On one side of base only one triangle can be formed.

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Perform the indicated operations. Write the answer in standard form, a+bi.<br> 5-3i / -2-9i

Vsevolod [243]

$\huge \boxed{\mathfrak{Answer} \downarrow}$

$\large \bf\frac { 5 - 3 i } { - 2 - 9 i } \\$

Multiply both numerator and denominator of $\sf \frac{5-3i}{-2-9i} \\$ by the complex conjugate of the denominator, -2+9i.

$\large \bf \: Re(\frac{\left(5-3i\right)\left(-2+9i\right)}{\left(-2-9i\right)\left(-2+9i\right)}) \\$

Multiplication can be transformed into difference of squares using the rule: $\sf\left(a-b\right)\left(a+b\right)=a^{2}-b^{2}$ .

$\large \bf \: Re(\frac{\left(5-3i\right)\left(-2+9i\right)}{\left(-2\right)^{2}-9^{2}i^{2}}) \\$

By definition, i² is -1. Calculate the denominator.

$\large \bf \: Re(\frac{\left(5-3i\right)\left(-2+9i\right)}{85}) \\$

Multiply complex numbers 5-3i and -2+9i in the same way as you multiply binomials.

$\large \bf \: Re(\frac{5\left(-2\right)+5\times \left(9i\right)-3i\left(-2\right)-3\times 9i^{2}}{85}) \\$

Do the multiplications in $\sf5\left(-2\right)+5\times \left(9i\right)-3i\left(-2\right)-3\times 9\left(-1\right)$ .

$\large \bf \: Re(\frac{-10+45i+6i+27}{85}) \\$

Combine the real and imaginary parts in -10+45i+6i+27.

$\large \bf \: Re(\frac{-10+27+\left(45+6\right)i}{85}) \\$

Do the additions in $\sf-10+27+\left(45+6\right)i$ .

$\large \bf Re(\frac{17+51i}{85}) \\$

Divide 17+51i by 85 to get $\sf\frac{1}{5}+\frac{3}{5}i \\$ .

$\large \bf \: Re(\frac{1}{5}+\frac{3}{5}i) \\$

The real part of $\sf \frac{1}{5}+\frac{3}{5}i \\$ is $\sf \frac{1}{5} \\$ .

$\large \boxed{\bf\frac{1}{5} = 0.2} \\$

3 0

3 years ago

The drama club is selling tickets to the play to raise money for the shows expenses. Each student ticket sales for five dollars

djyliett [7]

Answer:

45 student tickets and 30 adult tickets

Step-by-step explanation:

You can check your work by plugging both answers into both of the original equations. :)

8 0

3 years ago

The question is attached

Bingel [31]

Answer:

We call the denominator rational.

Step-by-step explanation:

For example:

$\frac{1}{\sqrt{2}} = \frac{\sqrt2}{\sqrt2 \cdot \sqrt2} = \frac{\sqrt2}{2}$

It's clear that the denominator is now a rational number, not an irrational one anymore.

5 0

2 years ago

The polygon angle sum theorem states that the sum of the measures of the interior angles of an n-gon is

mafiozo [28]

Answer:

D.

Step-by-step explanation:

The formula is Sum(n) = (n -2) 180.

8 0

3 years ago

To compute the first four terms of the arithmetic sequence -6(n-1) + 22, what formula would be used in cell B3?

yulyashka [42]

= -6 * (A3 - 1) + 22 .

3 0

3 years ago