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3 years ago

What is the product of ( 4 + 3 i ) and ( 12 − 2 i )

Mathematics

1 answer:

Morgarella [4.7K]3 years ago

3 0

Answer:

Step-by-step explanation:

(4+3i)(12-2i)

48 - 8i + 36i - 6i^2

48 + 28i +6

54 + 28i

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The roof of a high rise is in the shape of an isosceles triangle with a base of 89 feet. The perimeter of the roof is 281 feet.

inysia [295]

Answer:

96 ft

Step-by-step explanation:

Perimeter= a (base)+b (side)+c (side)

281 = 89 +b + c

281 -89 = b + c

192 = b+ c ( however in an iscoceles triangle, 2 sides aree equal therefore b and c will be equal)

So: 192/2 = 96

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3 years ago

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How many ways can a person with five nickels, three dimes, and two quarters make a 75-cent purchase from the machine?

DIA [1.3K]

2 quarters, 2 dimes, and 1 nickel

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3 years ago

Your dinner bill was $37.90 with 8% tax and 19% tip.

Tpy6a [65]

Tip would be the best answer choice

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3 years ago

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Simplify : 3p+2p+8-3=15

Ann [662]

Answer:

3p+2p+8-3=15

5p+5=15

5p=15-5

5p=10

p=10/5

p=2

have a great dayy.

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3 years ago

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Point p(a,b) is in the first quadrant on the graph of the line x+y=4. A triangular region is shown on the diagram. What is the m

Gala2k [10]

Answer:

The maximum area of the triangular region is 2 square units

Step-by-step explanation:

we know that

The area of the triangular region is equal to

$A=\frac{1}{2}(x)(y)$ -----> equation A

where

x is the x-coordinate of point P

y is the y-coordinate of point P

we have

The equation of the graph of the line is

$x+y=4$

$y=-x+4$ -----> equation B

substitute equation B in equation A

$A=\frac{1}{2}(x)(-x+4)$

$A=-\frac{1}{2}x^2+2x$

This is a vertical parabola open downward (the leading coefficient is negative)

The vertex represent a maximum

The y-coordinate of the vertex represent the maximum area of the triangular region

Find the vertex

Convert the quadratic equation in vertex form

Factor -1/2

$A=-\frac{1}{2}(x^2-4x)$

Complete the square

$A=-\frac{1}{2}(x^2-4x+4)+2$

Rewrite as perfect squares

$A=-\frac{1}{2}(x-2)^2+2$

The vertex is the point (2,2)

The maximum area is the y-coordinate of the vertex

The maximum area of the triangular region is 2 square units

Find the coordinates of point P for the maximum area

x=2 (x-coordinate of the vertex)

Find the y-coordinate of point P

substitute in equation B

y=-2+4=2

The coordinates of point P for the maximum area is P(2,2)

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4 years ago