If the complex number x = 3 + bi and |x|2 = 13, which is a possible value of b?
2
4
9
10

Answer:

Step-by-step explanation:

Substitute a = -3 and b = -8 to the expression 10a²b⁰:

10(-3)²(-8)⁰ = 10(9)(1) = 90

a⁰ = 1 for any real number

Answer:

90

Step-by-step explanation:

10a^2b^0

Let a=–3, b=–8

10 (-3)^2 ( -8)^0

10 * 9 *1

90

The correct equation to representing the temperature y, in degrees Fahrenheit, at x hours after sunset will be;

⇒ y = - 4°x + 0°

What is an expression?

Mathematical expression is defined as the collection of the numbers variables and functions by using operations like addition, subtraction, multiplication, and division.

Given that;

At 2 hours before sunset, the temperature is 0°F.

And,  At 2 hours after sunset, the temperature is −4°F.

Now,

Let the temperature in degrees Fahrenheit = y

So, We can formulate;

⇒ y = - 4°x + 0°

Thus, The correct equation to representing the temperature y, in degrees Fahrenheit, at x hours after sunset will be;

⇒ y = - 4°x + 0°

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The equivalent expression to  4√3 is  √48 or 6.928.

An equivalent expression is an expression that has equal value to the original given expression.

From the given expression, we can determine its equivalent expression as follows;

The given expression = 4√3

We can square 4 and multiply it by 3 and enclose all with the square root.

4√3 = √(4² x 3 )

= √ ( 16 x 3 )

= √ ( 48 )

= 6.928

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Answer:

1,300

Step-by-step explanation:

1256, if something is more than 5 then it goes up but if it's 4 or lower it goes down so 1256 rounded up to the nearest hundredth is 1300.

Answer: 1300

1256, if something is more than 5 then it goes up but if it's 4 or lower it goes down so 1256 rounded up to the nearest hundredth is 1300

Step-by-step explanation:

Answer:

Step-by-step explanation:

3x  +  5  +  x  -  25  =  180

4x  -  20  =  180

4x  =  200

x  =  50

The option that describes h(x) is B. The function h(x) is increasing on the interval (5, ∞).

In mathematics, a function simply means a relation between the inputs and the outputs.

In this case, the information given is that h(x) is 2 times the square root x minus 5. The square root of the negative number cannot be taken, therefore, the domain of the function is restricted.

Since the domain is restricted, the function is increasing. Therefore, the function h(x) is increasing on the interval (5, ∞).

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Answer:

The function h(x) is increasing on the interval (5, ∞).

Step-by-step explanation:

I got it right on the test.

Ordering the side lengths of the triangle, we have FG < FH < GH

From the question, we have the following parameters that can be used in our computation:

The triangle

The general rule is that

The length opposite the gretaest angle is the greatest length

The length opposite the least angle is the least length

Using the above as a guide, we have

<G = 180 - 43 - 77

<G = 60

So, we have

43 < 60 < 77

For the side lengths, we have

FG < FH < GH

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Answer:

N12.8

Assume the money in the box Is M.

therefore, 3/4 of M=N4.80.

Recall N1=100k..... where k 'kobo'

N4.80=X

X=4.80x100. this gives us 480k.

this implies that 3/4 X M= 480k

therefore by cross multiplication, and dividing by 3; 3M=480 X 4

M = (480 X 4) ÷3

M=1280k

converting from kobo' to Naira. the rate of conversion is;

100k = N1

1280k=?

M in naira= 1280/100

M is N12.8

Answer:

Yes, the equations are equivalent by the Distributive Property.

Explanation:

Given the equation:

Opening the bracket on the left-hand side, we have::

Therefore, we conclude that the equation 3(2x-4)= -18 equivalent to 6x-12=-18 by the Distributive Property.

Recall: By the distributive property:

1.1. Accumulated depreciation:

The accumulated depreciation for the machine bought on 1 July 2013 would be R150,000 as of 31 March 2016.

1.2. Machine realization:

The machine bought in 2013 was sold for R120,000 on 30 June 2015, resulting in a profit/loss on the sale of R10,000.

1.1. Accumulated Depreciation:

To calculate the accumulated depreciation, we need to determine the annual depreciation expense for each machine and then accumulate it over the years.

Machine bought on 1 July 2013:

Cost: R250,000

Depreciation rate: 20% per annum on cost

Depreciation expense for the year ended 31 March 2014: 20% of R250,000 = R50,000

Depreciation expense for the year ended 31 March 2015: 20% of R250,000 = R50,000

Depreciation expense for the year ended 31 March 2016: 20% of R250,000 = R50,000

Accumulated depreciation for the machine bought on 1 July 2013:

As of 31 March 2014: R50,000

As of 31 March 2015: R100,000

As of 31 March 2016: R150,000

1.2. Machine Realisation:

To record the sale of the machine bought in 2013, we need to adjust the machine's value and the accumulated depreciation.

Machine's original cost: R250,000

Accumulated depreciation as of 30 June 2015: R100,000

Net book value as of 30 June 2015:  

R250,000 - R100,000 = R150,000.

On 30 June 2015, the machine was sold for R120,000.

Realisation amount: R120,000

To record the sale:

Debit Cash: R120,000

Debit Accumulated Depreciation: R100,000

Credit Machine: R250,000

Credit Machine Realisation: R120,000

Credit Profit/Loss on Sale of Machine: R10,000 (difference between net book value and realisation amount).

These entries will reflect the appropriate balances in the ledger accounts and properly close off the accounts for the years ended 31 March 2016.

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Answer:

There are a total of 20 presents, and 3 of them contain gems. Therefore, there are 20 - 3 = 17 presents that do not contain gems.

The probability of randomly selecting a present that does not contain a gem is 17/20 = 0.85 or 85%.

hope it helps you...

Answer:

a}\(P_1= 0.3\)

b)\(P_2 =0.45\)

c) NOT INDEPENDENT

Step-by-step explanation:

From the question we are told that

Sample space

Math majors are 3

computer science majors are 3

Generally the sample space is

Mathematically the sample space required on Monday is given as  \(S_m= 3c_1 * 3C_2\)

where \(S_m\) =sample space on Monday

Therefore,

\(P_1\) = \(\frac{3C_1 *3C_2}{6C_3}\)

\(P_1=\frac{3*3}{20}\)

\(P_1=\frac{6}{20}\)

b)

Generally the the equation is given as

\(P_2 =P(\frac{x \cap y}{y})\)

where

x  is  selecting two math major and 1 computer science major on Monday

y is at leas one math major selected

\(P_2 =\frac{^3C_1*^3C_2}{^3C_1*^3C_2 + ^3C_2*^3C_1 +^3C_3*^3C_0}\)

\(P_2 =\frac{3*3}{3*3 + 3*3 +^1*1}\)

c)

Generally in representing independent events

\(P_3=p(x \cap y)\)

=>\(p(x) * p(y)\)

Mathematically

\(n(x)= ^3C_1 *^3C_2\)

\(n(y)={^3C_1*^3C_2 + ^3C_2*^3C_1 +^3C_3*^3C_0}\)

therefore

\(n(x \cap y) =^3C_1 *^3C_2\)

This does not satisfy the two equations stated above therefore NOT INDEPENDENT

Answer: 40 years old.

Step-by-step explanation:

Let man's age = a

Let son's age = b

Since a man is 4 times as old as his son, therefore

a= 4b

In 5 years, he will only be 3 times as old as his son, therefore

a+5=3(b+5)

Apply substitution method :

4b+5=3b+15

b=10

a=40

The number of gallons is 4.1

From the information given, we have that;

1 gallon of paint is equivalent to 150 square feet

Since we have 2 doors, the area of a rectangular prism is

Area = lw

Area =20(15)

Area = 300 (2) = 600 ft²

For the window, we have;

Area = 3(5) = 15

The total area of the wall is;

Total area = 615 ft²

Then, if;

1 gallon = 150 square feet

x = 615  square feet

cross multiply

x = 4. 1 gallons

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Step-by-step explanation:

√a = 1√a so we can solve them easily:

b) 3√7 -√7= 3√7 - 1√7 =( 3-1)√7= 2√7

d) 5√6 - 2√6+√6= (5-2+1)√6 = 4√6

g) √2+2√2= 3√2

j) √5+5√5 - 3√5 = 3√5

k) 2√3 + √3 - 5√3= -2√3

I) 5√11 + 7√11 - √11 = 11√11

Answer

Q. 37)      E. 50

Q. 38)     A.   28

Step-by-step explanation:

For   37)    the answer is   E  .  50  

While in 38)  the values of the angles are wrong .    

Angle  QPR must be  36   and angle  RSQ  must be  64  .  The answer is  A.  28

The length of line x in the figure of the cube given is 19.

Calculate the length of the base of the cube, which is the diagonal of the lower sides :

base length = √10² + 6²

base length = √136

The length of x is the diagonal of the cube

x = √(√136)² + 15²

x = √136 + 225

x = √361

x = 19

Therefore, the length of line x in the figure given is 19.

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Answer:

49*0.53=25.97 :)

(edited) ;)

Step-by-step explanation:

53 percent of 49 is approximately equal to 25.97.  the correct answer is option B) 25.97.

To find 53 percent of 49, we can calculate it by multiplying 49 by 0.53 (which is equivalent to 53 divided by 100).

49 * 0.53 = 25.97

Therefore, 53 percent of 49 is approximately equal to 25.97.

So, the correct answer is option B) 25.97.

Options A) 2.597, C) 259.7, and D) 2,597 are not correct since they either incorrectly place the decimal point or exaggerate the value by orders of magnitude. The accurate value is 25.97.

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Answer:

1000

Step-by-step explanation:

Answer: C i took the test

" If you buy a new cell phone, your opportunity cost is the time you could spend talking on the phone."

Step-by-step explanation:

I took the test and got an A hope this helps.

Answer:

14.75 feet below ground level.

Step-by-step explanation:

90.5-105.25=-14.75

The answer is neither. Option C

A linear number pattern is a sequence of numbers whose difference between all the terms is the same. When you count, the difference between each successive number is 1. You start with 1, then you add 1 to get 2. Then you add another 1 to get 3. And you keep repeating this addition of 1 process to get the rest of the terms.

Exponential notation is used to represent very large numbers and very small numbers. When representing very large numbers, the exponential notation will have a positive exponent; when representing a really small number, the exponential notation will contain a negative exponent.

From the question, the pattern of the number takes non of the pattern or neither linear or exponential

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Answer:

1. 43, 45, and 47

2. 50, 52, and 54

3. 47 years old

4. 106 degrees

5. 66 degrees

Step-by-step explanation:

1. Let's assume that the first number in the three consecutive odd numbers is x.

We can write an equation to express this now. \(x + (x+2) = (x+4) + 41\).

Combining like terms, we get \(2x+2 = x+45\). Subtracting by (x+2) on each side, we get \(x = 43\). Since the smallest number is 43, we can find the two larger numbers as well, since they are 2 more than one another. Therefore, the numbers are 43, 45, and 47.

2. Let's assume that the first number in the three consecutive even integers is x.

We can write an equation to express this now. \(x + (x+2) = (x+4)+48\)

Combining like terms, we get \(2x+2 = x+52\). Subtracting by (x+2) on each side, we get \(x = 50\). Since the smallest number is 50, we can find the two larger numbers as well, since they are 2 more than one another. Therefore, the numbers are 50, 52, and 54

3. We can write his current age in years as x. Next year, his age will be x+1. We know that the sum of his current age and his age next year is 73, so we can write an equation to express this.

\(x + (x+1) = 73\). Therefore, 2x + 1 = 73, or 2x = 72. This means that x = 36, or his current age is 36. In 11 years, his age will be 36 + 11 = 47 years old.

4. \((21x+1) + (14x+4) = 180\). Combining like terms, we get \(35x + 5 = 180\) Subtracting by 5 on both sides, we get \(35x = 175\) This means that \(x = 5\). Now, we can find the degree measures of both angles and find the larger one. The degree measure of the angle on the left is 21(5) + 1 = 106 degrees, and the degree measure of the angle on the right is 14(5) + 4 = 74 degrees. Therefore, the degree measure of the larger angle is 106 degrees.

5. We know that the sum of the angles in a triangle is 180 degrees. Therefore, we can sum the angles up and equate them to 180 degrees.

(x-24) + (2x-108) + (1/3x+12) = 10/3x - 120 = 180. Adding 120 to both sides, we get 10/3x = 300. Multiplying both sides by 3/10, we get x = 900/10 = 90. Therefore, plugging in x = 90, we get 66 degrees.

Answer:

2.22

Step-by-step explanation:

To get 2 2/9 in decimal form, we basically convert the mixed number to a fraction and then we divide the numerator of the fraction by the denominator of the fraction. Here are the detailed math steps we use to convert 2 2/9 mixed number to decimal form:

Step 1: Multiply the whole number by the denominator:

2 × 9 = 18

Step 2: Add the product you got in Step 1 to the numerator:

18 + 2 = 20

Step 3: Divide the sum from Step 2 by the denominator:

20 ÷ 9 = 2.222222

That's it! The answer to 2 2/9 in decimal form is displayed below:

2 2/9 ≈ 2.22

Answer:

y = \(\frac{1}{2}\)x - 5

Step-by-step explanation:

Use rise over run to find the slope, which will get you 1/2 as the slope

The y-intercept is at (0, -5) so put -5 in the equation

Answer: y= 1/2x + -5

Step-by-step explanation: slope is 1/2 because the line is going up one and over 2 (rise over run),  the y intercept is -5 because that is where the line hits on the y axis

Answer:

u funkin this is ur test idiot

Answer: 42

Step-by-step explanation:

Lwh equals volume

6*3*2 equals 36

2*3*1 equals 6

36 + 6 equals 42