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Alona [7]
3 years ago
14

Write the expression as a complex number in standard form.

Mathematics
1 answer:
ValentinkaMS [17]3 years ago
3 0

Answer:

15+2i

Step-by-step explanation:

Hi there!

We are given the following expression:

(7-4i) + (8+6i)

And we want to write it as a complex number in standard form

Standard form is <u>a+bi</u>, where a is the real part of the number and bi is the imaginary part of the number.

We can open up the parentheses on the expression

7-4i+8+6i

Now combine the like terms (add 8 and 7 together, then add -4i and 6i together)

<u>15+2i </u>

The complex number is now in standard form

Hope this helps!

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LA plane is trying to travel 250 miles at a bearing of 20° E of S, however, it ends 230 miles away from the
Semmy [17]

Answer:

The wind pushed the plane 65.01 miles in the direction of 45.56 ^{\circ} East of North  with respect to the destination point.

Step-by-step explanation:

Let origin, O, br the starting point and point D be the destination at 250 miles at a bearing of 20° E of S, but due to wind let D' be the actual position of the plane at 230 miles away from the  starting point in the direction of 35° E of South as shown in the figure.

So, we have |OD|=250 miles and |OD'|=230 miles.

Vector \overrightarrow{DD'} is the displacement vector of the plane pushed by the wind.

From figure, the magnitude of the required displacement vector is

|DD'|=\sqrt{|AB|^2+|PQ|^2}\;\cdots(i)

and the direction is \alpha east of north as shown in the figure,

\tan \alpha=\frac{|PQ|}{|AB|}\;\cdots(ii)

From the figure,

|AB|=|OA-OB|

\Rightarrow |AB|=|OD\cos 20 ^{\circ}-OD'\cos 35 ^{\circ}|

\Rightarrow |AB|=|250\cos 20 ^{\circ}-230\cos 35 ^{\circ}|

\Rightarrow |AB|=45.52 miles

Again, |PQ|=|OP-OQ|

\Rightarrow |PQ|=|OD\sin 20 ^{\circ}-OD'\sin 35 ^{\circ}|

\Rightarrow |PQ|=|250\sin 20 ^{\circ}-230\sin 35 ^{\circ}|

\Rightarrow |PQ|=46.42 miles

Now, from equations (i) and (ii), we have

|DD'|=\sqrt{|45.52|^2+|46.42|^2}=65.01 miles, and

\tan \alpha=\frac{|46.42|}{|45.52|}

\alpha=\tan^{-1}\left(\frac{|46.42|}{|45.52|}\right)=45.56 ^{\circ}

Hence, the wind pushed the plane 65.01 miles in the direction of 45.56 ^{\circ} E astof North  with respect to the destination point.

5 0
2 years ago
270 is 75% of what number?
Solnce55 [7]
First, you have to divide 270 by 3, so you get 25%. This comes out to be 90. So, 90 is 25%. Now, multiply this by four to get 100%. This comes out to be 360. So, 270 is 75% of 360, which answers the question '270 is 75% of what number?'
5 0
3 years ago
Simplify the expression 7+3(1-2x)
Levart [38]

Answer:

-6x + 10

Step-by-step explanation:

7 + 3( 1 − 2x)

Distribute:

=7 + (3) (1) + (3) (−2x)

=7 + 3 + −6x

Combine Like Terms:

=7 + 3 + −6x

=(−6x) + (7 + 3)

= −6x + 10

Answer:

= −6x + 10

hope this helps and is right :)

p.s. i rlly need brainliest

7 0
3 years ago
Read 2 more answers
A square piece of tissue paper has a perimeter of 164 centimeters. How long is each side of the tissue paper?​
soldier1979 [14.2K]

Answer:

s = 41 cm

Step-by-step explanation:

Since all the sides on a square are equal, we can use this formula for perimeter:  P = 4s

Plugging in 164 gives us 164 = 4s, where solving for s gives us s = 41

4 0
2 years ago
Help me please!! I am so confused!!
Gwar [14]

Answer:

(4,1), (-4,1), (4,6), (-4,6)

Step-by-step explanation:

Here can be identified two points with the same 'y' value: (4,1), (-4,1)

it means that there is a line passing by y=1

Same for (4,6), (-4,6): it means that there is a line passing by y=6

Now find the distance between two points in both cases


7 0
3 years ago
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