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3 years ago

What is equivalent to (4+5i)(4-5i)

Mathematics

2 answers:

Luden [163]3 years ago

6 0

16-25i because you have to find like terms and since there are parenthesis you have to mutiply the like terms

Lemur [1.5K]3 years ago

5 0

(4+5i)(4-5i)=(4)²-(5i)²=16-25(i)²=16-25(-1)=16+25=41

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Lizzy wants to solve the equation 6(2x + 1) = 4x – 5. Which step would be an appropriate first step for Lizzy to take to solve f

e-lub [12.9K]

Answer:

distribute parenthesis

Step-by-step explanation:

6(2x + 1) = 4x - 5 ← distribute parenthesis on left side

12x + 6 = 4x - 5 ( subtract 4x from both sides )

8x + 6 = - 5 ( subtract 6 from both sides )

8x = - 11 ( divide both sides by 8 )

x = - $\frac{11}{8}$

7 0

3 years ago

The following graphs have a scale assigned to them: The area of each grid

dezoksy [38]

The graphs that are density curves for a continuous random variable are: Graph A, C, D and E.

<h3>How to determine the density curves?</h3>

In Geometry, the area of the density curves for a continuous random variable must always be equal to one (1). Thus, we would test this rule in each of the curves:

Area A = (1 × 5 + 1 × 3 + 1 × 2) × 0.1

Area A = 10 × 0.1

Area A = 1 sq. units (True).

For curve B, we have:

Area B = (3 × 3) × 0.1

Area B = 9 × 0.1

Area B = 0.9 sq. units (False).

For curve C, we have:

Area C = (3 × 4 - 2 × 1) × 0.1

Area C = 10 × 0.1

Area C = 1 sq. units (False).

For curve D, we have:

Area D = (1 × 4 + 1 × 3 + 1 × 2 + 1 × 1) × 0.1

Area D = 10 × 0.1

Area D = 1 sq. units (True).

For curve E, we have:

Area E = (1/2 × 4 × 5) × 0.1

Area E = 10 × 0.1

Area E = 1 sq. units (True).

Read more on density curves here: brainly.com/question/26559908

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6 0

2 years ago

A robot moving forward at a constant speed takes 2.5 hours to travel 1 kilometer. Moving forward at this same constant speed, it

makvit [3.9K]

Answer:

The length of the hallway is 10 m.

Step-by-step explanation:

Given:

Time taken to cover 1 km = 2.5 hours

Distance covered in 2.5 hours = 1 km

Therefore, speed of robot = $\frac{\textrm{Distance}}{\textrm{TIme}}=\frac{1}{2.5}=0.4\ km/h$

Now, speed is constant.

Now, time taken to cover the length of hallway = 90 s

Speed of the robot = 0.4 km/h

Converting 0.4 km/h to m/s, we multiply by the factor $\frac{5}{18}$ . This gives,

$0.4\times \frac{5}{18}=\frac{1}{9}\ m/s$

Now, distance of the hallway is equal to the product of speed and time. So,

Distance of hallway = Speed $\times$ Time

Distance of hallway = $\frac{1}{9}\times 90=\frac{90}{9}=10\ m$

Therefore, the length of the hallway is 10 m.

5 0

3 years ago

Two bonds are available on the market as follows: Bond 1: Face value $250, 5 years to maturity at a (simple) interest rate of 5%

tester [92]

The value of r is 5.95%

Step-by-step explanation:

The formula of the simple interest is I = P r t, where

P is the initial amount of money
r is the interest rate in decimal
t is the time

Bond 1:

∵ The face value is $250

∴ P = 250

∵ The value is in the bond for 5 years

∴ t = 5

∵ The simple interest rate is 5%

∴ r = 5% = 5 ÷ 100 = 0.05

∵ I = P r t

- Substitute the values of P, r and t in the rule

∴ I = (250)(0.05)(5) = 62.5

∴ The interest of Bond 1 is $62.5

Bond 2:

∵ The face value is $350

∴ P = 350

∵ The value is in the bond for 3 years

∴ t = 3

∵ The simple interest rate is r

∵ I = P r t

- Substitute the values of P and t in the rule

∴ I = (350)(r)(3) = 1050 r

∴ The interest of Bond 2 is 1050 r

∵ The both bonds yield the same interest to maturity

- Equate the interests of bonds 1 and 2

∵ 1050 r = 62.5

- Divide both sides by 1050

∴ r = 0.0595

- Multiply it by 100% to change it to percentage

∵ r = 0.0595 × 100% = 5.95%

∴ r = 5.95%

The value of r is 5.95%

Learn more:

You can learn more about interest in brainly.com/question/11149751

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3 0

3 years ago

Find the value of x in this figure.

AleksAgata [21]

Step-by-step explanation:

angle x is equal to 65

angles of triangle is equal to 180

3 0

3 years ago

Read 2 more answers