All categories

3 years ago

Simplify (5+11i) - (16-4i) +9i.

Mathematics

2 answers:

Sunny_sXe [5.5K]3 years ago

7 0

Answer:

5 + 11i -16 + 4i + 9i

collecting like terms

5-16 + 11i + 4i + 9i

24i - 11

lisabon 2012 [21]3 years ago

6 0

Answer:

5+11i-16-4i+9i

5-16+11i-4i+9i

-11+7i+9i

-11+16i

Step-by-step explanation:

First, get the like terms together. Then add or subtract until its simplified. Simplified is -11+16i.

You might be interested in

Which two operations are needed to write the expression that represents "five less than the quotient of a number and

RUDIKE [14]

Answer:

Division and subtraction.

Step-by-step explanation:

The quotient is the result of a division and 'less than is a subtraction.

4 0

3 years ago

Read 2 more answers

Help asap marking as BRAINLIST ace only

Soloha48 [4]

Answer:

O: The circle's name is "O"

Step-by-step explanation:

A circle is ALWAYS named for the center point. The point in the center of this circle is "O" so the circle is named "O"

8 0

3 years ago

Evaluate the expression for the given value of the variable(so).

Ksju [112]

The answer is -30-25 which in turn becomes -55

4 0

3 years ago

The managers of 21 supermarkets counted the number of cars in their parking lots on the same day. The results are shown in the l

mixer [17]

The IQR is 42.5

Step-by-step explanation:

Interquartile range is the difference of third and first quartile.

First of all we have to find the median for that purpose the data has to be arranged in ascending order. The data is already in ascending order.

As the number of values are odd

n=21

The median will be: $(\frac{n+1}{2}) th\ term$

Putting n=21

$(\frac{21+1}{2})th\ term\\=(\frac{22}{2})th\ term\\= 11th\ term$

The 11th term is 133

So median = 133

Now the data is divided into two halves

One is: 98, 100, 101, 102, 108, 109, 111,118, 129, 132

2nd is: 135, 135, 145, 146, 146, 156, 170 176, 180, 180

Q1 will be the median of first half and Q3 will be the median of 2nd half.

As now the halves contain even number of values, the medians will be the average of middle two values

For First Half:

98, 100, 101, 102, 108, 109, 111,118, 129, 132

$Q_1 = \frac{108+109}{2}\\Q_1 = \frac{217}{2}\\Q_1 = 108.5$

For Second Half:

135, 135, 145, 146, 146, 156, 170 176, 180, 180

$Q_2 = \frac{146+156}{2}\\Q_2 = \frac{302}{2}\\Q_2 = 151$

Now

Interquartile Range:

$IQR = Q_3-Q_1\\= 151-108.5\\=42.5$

Hence,

The IQR is 42.5

Keywords: Median, IQR

Learn more about median at:

#LearnwithBrianly

7 0

3 years ago

A jumping spider's movement is modeled by a parabola. The spider makes a single jump from the origin and reaches a maximum heigh

aleksklad [387]

The spider's movement is an illustration of a parabola.

The equation of a parabola is: $\mathbf{y = -\frac{1}{160}(x - 40) + 10}$
The focus of a parabola is: (40,-30)
The axis of symmetry is: $\mathbf{x = 40}$
The directrix is: $\mathbf{y = 50}$

(a) The equation

The spider passes through the origin.

So, we have:

$\mathbf{(x,y) = (0,0)}$

The spider jumps to a maximum height of 10mm, midway 80mm.

So, the vertex is:

$\mathbf{(h,k) = (40,10)}$

The equation of a parabola is:

$\mathbf{y = a(x - h)^2 + k}$

So, we have:

$\mathbf{0 = a(0 - 40)^2 + 10}$

Subtract 10 from both sides

$\mathbf{a(0 - 40)^2 =- 10}$

$\mathbf{1600a =- 10}$

Solve for a

$\mathbf{a =- \frac{1}{160}}$

Substitute $\mathbf{a =- \frac{1}{160}}$ and $\mathbf{(h,k) = (40,10)}$ in $\mathbf{(h,k) = (40,10)}$

$\mathbf{y = -\frac{1}{160}(x - 40) + 10}$

(b) The focus, directrix and the axis of symmetry

The focus of a parabola is:

$\mathbf{Focus= (h, k + p)}$

Where:

$\mathbf{p = \frac{1}{4a}}$

So, we have:

$\mathbf{p = \frac{1}{4 \times -1/160}}$

$\mathbf{p = -\frac{160}{4}}$

$\mathbf{p = -40}$

So, we have:

$\mathbf{Focus = (40,10-40)}$

$\mathbf{Focus = (40,-30)}$

The axis of symmetry is:

$\mathbf{x = h}$

So, we have:

$\mathbf{x = 40}$

The directrix is:

$\mathbf{y = k - p}$

$\mathbf{y = 10 + 40}$

$\mathbf{y = 50}$