Multiply the following complex numbers (7 + 2i)(2+3i) O A. 20-25i B. 8-25i O C. 8+ 25i O D. 20-25i​

Answer:

(a) The time to complete 1 cycle and return is 16/3

(b) The minimum height is 30 inches and the maximum is 54 inches

Step-by-step explanation:

Given

[tex]f(t) = 12\sin(\frac{3\pi}{8}t) + 42[/tex]

Solving (a): Time to complete 1 cycle and return

This implies that we calculate the period.  This is calculated using:

[tex]T = \frac{2\pi}{w}[/tex]

Where:

[tex]w =\frac{3\pi}{8}[/tex]

So, we have:

[tex]T = \frac{2\pi}{\frac{3\pi}{8}}[/tex]

[tex]T = \frac{2}{\frac{3}{8}}[/tex]

[tex]T = \frac{2*8}{3}[/tex]

[tex]T = \frac{16}{3}[/tex]

Solving (b): The maximum and the minimum height

To do this, we have:

[tex]-1 \le \sin(\theta) \le 1[/tex]

Which means:

[tex]-1 \le \sin(\frac{3\pi}{8}) \le 1[/tex]

So, the minimum is:

[tex]\sin(\frac{3\pi}{8}) =- 1[/tex]

And the maximum is:

[tex]\sin(\frac{3\pi}{8}) =1[/tex]

Recall that the height is:

[tex]f(t) = 12\sin(\frac{3\pi}{8}t) + 42[/tex]

So, the maximum and the minimum of  are:

[tex]h_{min} =12 * -1 + 42[/tex]

[tex]h_{min} =30[/tex]

and

[tex]h_{max} =12*1+42[/tex]

[tex]h_{max} =54[/tex]

Answer:

(2,1)

Step-by-step explanation:

-3x + 7 = -2x + 5

x = 2

y = -6 + 7

y = 1

Answer:

(2,1)

Step-by-step explanation:

Remark

One thing you need to remind yourself of: The y value in both equations must be the same.

That means that the two right hand values are

-3x + 7 = - 2x + 5         Subtract 5 from both sides.

      -5              -5

-3x + 2 = - 2x               Add 3x to both sides

+3x          +3x

       2 = x

Now use one of the equations to solve for y

y = -2x + 5

y = -2(2) + 5

y = - 4 + 5

y = 1

We should check this by graphing it. Notice the two graphs do cross at (2,1) just as predicted.

Answer:

Scalene.

Step-by-step explanation:

It's scalene because non of the triangle's sides are congruent.

Answer:

Proved

Step-by-step explanation:

Given

[tex]n = 6[/tex] --- sides of hexagon

[tex]l = 1[/tex] --- side length

Required

Prove that for 7 points picked from the interior, 2 points are at most 1 unit apart

1. Draw a hexagon  (see attachment)

2. Divide the hexagon into 6 triangles

3. Select 7 points on the hexagon

You will notice that at least 2 points will be in one of the triangle.

The maximum distance between these two points is 1 unit. This is because

1. The triangle is equilateral (all sides equal)

2. The length of each is 1 unit (in other words, the distance between points, cannot exceed the side length)

Answer:

The width of the rectangle lies between 12 and 20.

Step-by-step explanation:

Let the width of the rectangle is w.

length of the rectangle,

L = 8 w + 20

116 < L < 180

So,

116 < 8 w + 20 < 180

96 < 8 w < 160

12 < w < 20

So, the width of the rectangle lies between 12 and 20.

Answer:

Step-by-step explanation:

Split it into two:

Y<3x

Y<5

X = 1

Y = 3

(1,3)

X = 2

Y = 6

(2, 6)

Plot the line up to y = 4.999999999999999999999 and not higher.

Answer:

Plot the line up to y = 4.999999999999999999999 and not higher

Answer:

Sum of 2 interior angles =180

1 angle+70=180

Another angle=110

Step-by-step explanation:

Answer:

The bulding is 381,623 meters high.

Step-by-step explanation:

To dertermine the height of the bulding I would use tanα = rectangulair side / closest rectangulair side.

19,08 = the height/ 20m.

<=> 19,08.20m= the height = 381,623 m

Answer:

87 gallons

Step-by-step explanation:

5 gallons: 3 weeks = x gallons: 52 weeks

5/3 = x/52

3x = 260

x= 86.6, about 87 gallons

Answer:

B. Identity

Step-by-step explanation:

Now,

1 million = 10 lakhs

4 millions = 10 * 4

= 40 lakhs

There are 40 lakhs in 4 millions.

I hope it's help you...

Mark me as brainliest...

Answer: There are 40 lakhs in 4 million.

Step-by-step explanation:

A lakh is 1,00,000. We can divide 4 million by 1,00,000 to get our answer.

[tex]\frac{4,000,000}{1,00,000}[/tex]

The 5 zeros on the 4 million and on 1,00.000 cancel each other out giving us

[tex]\frac{40}{1} \\40[/tex]

Answer:

Shelter from a tornado should be sought:

in any of the above

in a room in the center of the first floor

in a basement

under a staircase in the center of the house

Shelter from a tornado should be sought:

in any of the above

in a room in the center of the first floor

in a basement

under a staircase in the center of the house

Answer:

1)  2/20 x 200 = 1/10 x 200 = 20

2) 3/20 x 200 = 30

3) 4/20 x 200 = 1/5 x 200 = 40

4) 5/20 x 200 = 1/4 x 200 = 50

5) 18/20 = 9/10 x 200 = 180

Answer:

80%

Step-by-step explanation:

Because Shirly spelled 12 out 15 correctly, she got a 12/15, which is equal to 4/5 or 80%

Answer:

17.

Step-by-step explanation:

The differences form an arithmetic sequence 3, 5, 7, 9,,11.

The missing number  is 10 + 7 = 17.

This is a quadratic sequence.

The nth term = n^2 + 1.

Thus the 4th term = 4^2 + 1 = 17.

Answer:

See Explanation

Step-by-step explanation:

The question is incomplete, as the right trianglea are not given. The general explanation is as follows.

Using Pythagoras Theorem, we have:

a² = b² + c²

Where:

a => hypotenuse

Assume that the opposite and the adjacent sides are given as 3 and 4, respectively.

The hypotension becomes

a² = 3² + 4²

a² = 9 + 16.

a² = 25

Take square roots.

a = 5

If any of the other side lengths is missing; you make that side the subject and then solve.

Answer:

m = 0

General Formulas and Concepts

Pre-Algebra

Order of Operations: BPEMDAS

Algebra I

Step-by-step explanation:

Step 1: Define

Identify points

Point (-6, 8)

Point (-1, 8)

Step 2: Find slope m

Simply plug in the 2 coordinates into the slope formula to find slope m

Answer:

3.24%

Step-by-step explanation:

Percentage error =[ (|calculated value  - actual value) / actual value] x 100

calculated area = length x width

6.5 x 7.8 = 50.7

[(|50.7 - 52.4|] / 52.4] x 100 = 3,24

Answer:

E) π/9

Step-by-step explanation:

The angles are complementary meaning they add up to 90°.

Convert radians to degrees:

7π/18 · 180/π = 70°

Now we know that we need the radian equivalent of 20°.

Convert degrees to radians:

70 · π/180 = π/9

Therefore, the measure of the missing degree is π/9.

the answer is b. insurance

Answer and Step-by-step explanation:

Solve for x.

First, we divide both sides of the equation by 2.

2(8 - 2x) = 7 - x

Distribute the 2.

16 - 4x = 7 - x

Add 4x to and subtract 7 from both sides of the equation.

9 = 3x

Divide by 3 to both sides of the equation.

x = 3 <-- This is the answer.

#teamtrees #PAW (Plant And Water)

Answer:

x = 3

General Formulas and Concepts:

Pre-Algebra

Order of Operations: BPEMDAS

Distributive Property

Equality Properties

Algebra I

Step-by-step explanation:

Step 1: Define

Identify

4(8 - 2x) = 2(7 - x)

Step 2: Solve for x

Answer:

Buses - 43 people

Vans - 12 people

Answer:

0.8X = Final cost

Step-by-step explanation:

Given that jeans are on sale for 20% off the regular price, to determine which function would give you the total cost for purchasing a pair of jeans that costs X dollars, the following calculation must be performed:

1X = Initial cost of the jeans

20% = 0.2

1 - 0.2 = 0.8

0.8X = Final cost

Given:

The table and the relative frequency histogram show the distribution of the number of tails and three coins are tossed.

To find:

The probability [tex]P(T=3)[/tex].

Solution:

In the given table T represents the number of tails.

From the given table it is clear that the value of probability is [tex]\dfrac{1}{8}[/tex] and [tex]T=3[/tex]. So,

[tex]P(T=3)=\dfrac{1}{8}[/tex]

Therefore, the probability [tex]P(T=3)[/tex] is equal to [tex]\dfrac{1}{8}[/tex].

Answer:

-8/32 or -1/4(if simplified)

Step-by-step explanation:

-15+7 = -8

-8/32 or -1/4

9514 1404 393

Answer:

  C.  -2.00 m/sec

Step-by-step explanation:

The average velocity on the interval [a, b] is found by ...

  m = (s(b) -s(a))/(b -a)

One end of the interval remains constant here, so we can define 'd' so that the interval is [4, 4+d]. Then the average velocity is ...

  m = (s(4 +d) -s(4))/((4 +d) -4)

  m = (s(4+d) -s(4))/d

The attached table shows the average velocity values on the intervals required by the problem statement. Respectively, they are ...

  -1.5 m/s, -1.7 m/s, -1.9 m/s, -1.99 m/s, 2.01 m/s, 2.1 m/s, 2.3 m/s, 2.5 m/s

We expect the instantaneous velocity at d=0 to be the average of the values at d=-0.01 and d=+0.01. We estimate the instantaneous velocity at t=4 seconds to be -2.00 m/s.

Answer:

153.86.

Step-by-step explanation:

Use the formula pi times radius squared.