What is the value of m? O 10 O 30 O 70 O 150

The right side of the orchestra section of the Nederlander Theater in New York City has 19 rows, and the last row has 27 seats.

STALIN [3.7K]

27+26+25+24+23+22+21+20+19+18+17+16+15+14+13+12+11+10+9=342
A.342 seats.

7 0

3 years ago

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A businessman buys 1,440 dozen pens at $2.50 a dozen and then sells them at a price of 25¢ apiece. What is his total proﬁt on th

LekaFEV [45]

He spend: 1440*2.5=3600
he earn: 0.25*1440*12=4320
[because he sells 0.25/each and buy 1440 dozen so 1440*12]

4320-3600=720

5 0

2 years ago

Perform the indicated operations. Write the answer in standard form, a+bi. 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

2 years ago

Which statement explains how the lines x + y = 2 and y = x + 4 are related?

zysi [14]

Answer: X = -1 and Y = 3
—————————————
X + Y = 2
X = 2 - Y
————————
Y = x + 4
Y = 2 - Y + 4
2Y = 2 + 4
2Y = 6
Y = 3
————————
X + Y = 2
X + 3 = 2
X = -1

8 0

2 years ago

List all the factors of 36

OLEGan [10]

The factors of 36 are:
1,2,3,4,6,9,12,18,36.

4 0

2 years ago

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