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gulaghasi [49]
3 years ago
11

For what value of "a" will the product shown below have a purely imaginary value? (Show work please)

Mathematics
1 answer:
MakcuM [25]3 years ago
5 0
If you expand out the brackets you get this,

(4+5i)(a+2i) = 4a + (5a)i + 8i - 10

The -10 comes from 5i * 2i.
Squaring i becomes -1.

Let's group the real stuff together,
and imaginary separately,

(4a - 10) + (5a + 8)i

For this to be purely imaginary,
the real part needs to be zero.

Therefore 4a - 10 = 0

Solve for a.
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Susanna walked 2/7 of a mile in two over five of an hour what is a unit rate in miles per hour
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Answer:

speed = distance/ time so:

(2/7) / (2/5) = (2/7) x (5/2) = 10/14 = 5/7 mph

5/7 = 0.71 miles per hour if you need decimal formatStep-by-step explanation:

8 0
2 years ago
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A hydro company is laying down power lines in the ground. They have two sections of cable so far that are 325.0 m and 430.0 m lo
Hoochie [10]

The length of extra cable that is required to connect the two pieces of existing cable is equal to 182 meters.

<h3>How to determine the length of extra cable?</h3>

In order to determine the length of extra cable that is required to connect the two pieces of existing cable, we would apply the law of cosine as follows:

B² = A² + C² - 2(A)(C)cosB

Substituting the given parameters into the formula, we have;

B² = 325.0² + 430.0² - 2(325.0)(430.0)cos23

B² = 105,625 + 184,900 - 279,500(0.9205)

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B = √33,245.25

B = 182.33 ≈ 182 meters.

Read more on cosine law here: brainly.com/question/11000638

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3 0
2 years ago
Solve: the sum of two numbers is 70. one number is 4 times the other. what are the two numbers?
Thepotemich [5.8K]
Lets say two numbers are x and y

x+y=70-----------------------eq1

x=4y--------------------eq2

4y+y=70
5y=70
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then x=4*14

x=56


8 0
3 years ago
2. Solve each equation. Check your solutions.<br> b. 5 +<br> - 16
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Step-by-step explanation:

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Rita makes and sells necklaces. The materials to make each necklace cost $2.75. Last week she made 8 necklaces and wants to make
Lisa [10]

9514 1404 393

Answer:

  The equation should be 8 (x minus 2.75) = 78, and she needs to sell each necklace for $12.50.

Step-by-step explanation:

The contribution margin of each necklace is the difference between its selling price (x) and its cost (2.75). Then the total profit from 8 necklaces would be ...

  8(x -2.75)

If Rita wants that profit to be $78, then she needs to solve the equation ...

  8(x -2.75) = 78 . . . . correct equation

The solution is ...

  x -2.75 = 9.75 . . . . divide by 8

  x = 12.50 . . . . . . . . add 2.75

She needs to sell each necklace for $12.50.

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3 years ago
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