All rational numbers can be written as complex numbers in the form a +bi.
For the number 18, what is the value of a and b?

O a=0 and b = 18
O a=18 and b= 1
O a = 1 and b = 18
O a 18 and b = 0

By applying the distributive property of multiplication, the students that are correct in their approach to solving the problem are: Nico, Raj and Sandra.

In order to open the bracket and isolate the variable x, we would first of all multiply both sides by 5/2 as follows:

2/5(5 + x) = 8

Multiplying both sides by 5/2, we have:

5/2 × 2/5(5 + x) = 8 × 5/2

5 + x = 40/2

5 + x = 20

Subtracting 5 from both sides, we have:

5 + x - 5 = 20 - 5

x = 15

In order to open the bracket and isolate the variable x, we would first of all multiply both sides by 1/2 and then 5 as follows:

2/5(5 + x) = 8

Multiplying both sides by 1/2, we have:

1/2 × 2/5(5 + x) = 8 × 1/2

1/5(5 + x) = 4

Multiplying both sides by 5, we have:

5 × 1/5(5 + x) = 4 × 5

5 + x = 20

Subtracting 5 from both sides, we have:

5 + x - 5 = 20 - 5

x = 15

In order to open the bracket and isolate the variable x, we would apply the distributive property of multiplication:

2/5(5 + x) = 8

2/5 × 5 + 2/5 × x = 8

2 + 2x/5 = 8

Subtracting 2 from both sides, we have:

2 - 2 + 2x/5 = 8 - 2

2x/5 = 6

Multiplying both sides by 5/2, we have:

5/2 × 2x/5 = 5/2 × 6

x = 30/2

x = 15.

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The equivalent ratio is 12: 18

The ratio is 12:_ = 16: 24

12/x = 16/ 24

x≠0, because the denominator can never be 0.

Solve the equation

12/x = 16/24

12/x = 2/3

x = 18

Therefore the equivalent ratio is 12:18.

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Answer:

[tex]\frac{2y^5}{x^6}[/tex]

you have chosen the correct answer

The integer represents the new temperature is (-8) F.

An integer is the number zero, a positive natural number or a negative integer with a minus sign. The negative numbers are the additive inverses of the corresponding positive numbers.

Given:

At 2 a.m. temperature = -3F

Then temperature decreased 12°F = -12 F

and then increase  7°F = +7F

Now, the temperature is

= (-3) - 12 + 7

= -3 -5

=-8 F

Hence, the temperature is (-8) F

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The 3 angles in a triangle always add up to be 180.

Call the smallest angle as x
-> The 3 angles are x, 4/3x and 5/3x
-> 4x = 180
-> 45

So, the sizes of the 3 angles are 45, 60 and 75.

An nth- degree polynomial function with real coefficient for N = 3 ; 3, 2i are zeros ; f(-1) =20 is given by f(x) = (-1)( x³ -3x²+4x -12).

As given in the question,

Number of zeros of the polynomial function N = 3

Real and complex zeros = 3, 2i , -2i

Function value f(-1) = 20

f(x) = k (x-3)(x-2i)(x+2i)

⇒f(x) = k(x-3)(x²-4i²)

⇒f(x) =k(x-3)(x²+4)

⇒f(-1) = k(-1-3)((-1)² +4)

⇒ 20 =k(-4)(5)

⇒k =-1

Now , f(x) = (-1)((x-3)(x²+4)

               = (-1)(x³ -3x²+4x -12)

Therefore, nth- degree polynomial function with real coefficient for N = 3 ; 3, 2i are zeros ; f(-1) =20 is given by f(x) = (-1)( x³ -3x²+4x -12).

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Answer:

11.34

Step-by-step explanation:

14% of 81 =

 14% × 81 = 

14/100 × 81 = 

(14 ÷ 100) × 81 =

 14 × 81 ÷ 100 =

 1,134 ÷ 100 = 

11.34

Answer:

84 people

Step-by-step explanation:

14 percent means that for each 100, there are 14 of something.

This is the most common method to calculate 14% of 600. 600 is the Whole, 14 is the Percent, and the Part is what we are calculating. Below is the math and answer to "What is 14% of 600?" using the percent formula.

Percent Formula:

(Whole × Percent)/100 = Part

(600 × 14)/100 = 84

14% of 600 = 84

1. The money that the gym employee earns in 1 month is $1500.

2. The money that the gym employee earns in 5 months is $7500.

The gym employee earns the same amount each month and after working for three months, he earned $4,500.

In this case, the amount that he earns monthly will be:

= Total amount / Number of months

= $4500 / 3

= $1500

He earns $1500 monthly.

The money that the gym employee earns in 5 months will be:

= 5 × $1500

= $7500.

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The order from lowest to highest is  -5, -3, -2, -1 .

What is ascending order ?

Numbers can be arranged in ascending order, from least value to highest value. The arrangement is left to right. Increasing order is another name for ascending order.

6-8=-2

7-12=-5

1-4=-3

0-1=-1

Order : -5, -3, -2, -1

Avoid becoming confused by the values following the negative sign. The value of a number decreases with increasing size after a negative sign.

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Given:

Two different congruency mapping

To find:

a) a rule for the congruence mapping that will move a figure 5 units to the right and 3 units up

b) a rule for congruence mapping that reflects a figure across the y-axis

Answer:

there are different kind of sequence number and just multiply the fractions.

Step-by-step explanation:

multiply fractions aND you will get the answer.

The given number [tex]\frac{16}{11}[/tex] is an improper fraction.

Proper fraction = A fraction with a smaller numerator than denominator is said to be a correct fraction. A fraction whose numerator is the same as or bigger than its denominator is said to be inappropriate. Proper fractions include 3/4, 2/11, and 7/19.

Improper fraction = A fraction is called improper if the numerator is greater than the denominator. Examples are 9/2, 8/5, 10/3, etc.

When we divide 16 by 11 we get a quotient of 1 and a remainder of 5.

This fraction after solving can be represented as [tex]11\frac{1}{6}[/tex] which is a mixed fraction.

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The meaning of vertical intercept in this context can be inferred from the options to mean that the helicopter took off from a height of 50 ft.

In a linear problem or a graph, the vertical intercept, which is also known as the y-intercept, refers to the value of y when the value of x is 0.

Assuming y in this problem refers to the height and x refers to the minutes, the vertical intercept would be the height at 0 minutes.

If the vertical intercept is 50 ft then it means that the helicopter took off from 50 feet because at takeoff, the value of x would be 0 minutes.

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Answer:

Weight on Mars:  1,475.32 kg

Step-by-step explanation:

The formula is Weight on Mars= (Weight on Earth/9.81m/s2) * 3.711m/s2.

If a space rover has a mass of 3900 kg on Earth, the mass on Mars when it lands will be 3900kg.

Mass is a dimensionless quantity representing the amount of matter in a particle or object. The standard unit of mass in the International System (SI) is the kilogram.

Given,

The mass of a space rover is 3900 kg.

We need to check what is its mass in Mars.

The mass of space rover  in Mars will also be same 3900 kg because the mars is same quantity it wont change according to place or time, it remains constant. Where as weight would be changed.

The mass of the object is always constant, anywhere it is on the Earth or Moon or any other planet.

Hence, If a space rover has a mass of 3900 kg on Earth, the mass on Mars when it lands will be 3900kg.

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Answer:

C. between 14.1 and 14.2

Step-by-step explanation:

√100 × 2

√(10 × 10) × 2

10√2 = 14.14

I hope this helps!

Answer:

C. Between 14.1 and 14.2
10√2 ≈ 14.142135624

Step-by-step explanation:

Answer:

this appears to already be in standard form?

Step-by-step explanation:

standard form has x and y on one side of the =

The equation for the line parallel to y=1/4x+1 that passes through the point (6,-2) is x-4y=14 as the slope for both lines are equal and using slope-point form of equation.

The definition of an equation in algebra is a mathematical statement that demonstrates the equality of two mathematical expressions. For instance, the equation 3x + 5 = 14 consists of the two expressions 3x + 5 and 14, which are separated by the 'equal' sign.

The equation of a straight line that passes through a given point and is inclined at a specific angle to the x-axis can be found using the point slope form.

Here,

The slope for the line will be 1/4 and the given points will be (6,-2) so the equation for the line is

y-y1=m(x-x1)

y+2=1/4(x-6)

4y+8=x-6

x-4y=14

Given that both lines have an equal slope and using the slope-point form of equation, the equation for the line parallel to y=1/4x+1 passing through the point (6,-2) is x-4y=14.

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The number of binder on the bookshelf is one

The given parameters are:

Width of the bookshelf = 31 3/4 inches

Width of the binders = 28 inches

From the question, we understand that the binders are stacked side by side

This means that the quotient of the width of the bookshelf and the width of the binder will give the number of binders

So, we have

Number of binders = Width of the bookshelf/Width of the binders

This gives

Number of binders = (31 3/4)/28

Evaluate the quotient

Number of binders = 1.13

Approximate

Number of binders = 1

Hence, there is only one binder on the bookshelf

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1. The value of x in the triangle is B. 22.5°.

2. The value of x in the triangle is B. 22.5°.

3. The value of the limit illustrated is D. 32

1. It should be noted that the total angle in a triangle is 180°. The three angles given are illustrated as:

Angle 1 = 3x

Angle 2 = x + 30°

Angle 3 = 180° - 120° = 60°

The value of x will be:.

3x + x + 30 + 60 = 180

4x + 90 = 180

4x = 180° - 90°

4x = 90°

x = 90/4.

x = 22.5°

2. Note that the question was repeated. Therefore, the answer is illustrated above The value of x is 22.5°.

3. x³ + 7x² - 4

when x = 2

x³ + 7x² - 4

= 2³ + 7(2)² - 4

= 8 + 28 - 4

= 32

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Answer:

d

Step-by-step explanation:

because you're already given the hypotenuse "c" and a side length "a"

so

8^2+ y^2=12^2

Answer: Yes it does.

Step-by-step explanation:

Answer:

(a²b)³(b²c²)=a⁶b⁵c²

Answer:

option C

Step-by-step explanation:

due to the vertical line test it only passes through the x point once

Distance from point (0, -3) to the line y = x - 1 = [tex]\sqrt{2}[/tex]

Given:

Point =(0,-3) => x = 0; y = -3

Line = y = x - 1 => a= 1, b= -1, c=-1

How is the distance from the point to the line calculated?

Let us consider the distance to be d,

[tex]d= \frac{ax+by+c}{\sqrt {a^{2}+b^{2}} } \\\\=\frac{1(0)-1(-3)-1}{\sqrt{2} } \\\\=\frac{2}{\sqrt{2} } = \sqrt{2}[/tex]

What is the distance from a point to a line?

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Answer:

y = [tex]\frac{2}{5}[/tex] x - 3

Step-by-step explanation:

the equation of a line in slope- intercept form is

y = mx + c ( m is the slope and c the y- intercept )

here m = [tex]\frac{2}{5}[/tex] and line crosses the y- axis at (0, - 3 ) ⇒ c = - 3

y = [tex]\frac{2}{5}[/tex] x - 3 ← equation of line

The percentage of puffin eggs that hatch given in decimal form by the quadratic function, f(x) = -0.379•(x - 46)² + 2.62•(x - 46) - 3.61, gives;

a. At 51 °F, 1.5% of the eggs will hatch

b. The temperature at which the maximum percentage of puffin eggs will hatch is approximately 49.5 °F

The maximum percentage of eggs that hatch is approximately 91.8 %

A quadratic function is a polynomial of the second degree (degree 2) such that the highest power of the variables in a quadratic function is 2

The quadratic function is presented as follows;

f(x) = -0.379•(x - 46)² + 2.62•(x - 46) - 3.61

Where;

f(x) = The percentage of the eggs that hatch

x = The mean sea surface temperature of the area in degrees Fahrenheit

a. The percentage of the eggs that will hatch at 51° is therefore;

f(51) = -0.379•(51 - 46)² + 2.62•(51 - 46) - 3.61 = 0.015

The percentage of the eggs that hatch at 51° d is f(51) = 0.015 × 100% = 1.5%

b. The temperature for which the percentage of hatched puffin eggs is a maximum, is given by the maximum value of the quadratic function as follows;

At the maximum value of the quadratic function, f(x) = a•x² + b•x + c, we have;

x = -b/(2•a)

Therefore, where we have;

f(x) = -0.379•(x - 46)² + 2.62•(x - 46) - 3.61

At the maximum value;

x - 46 = -2.62/(2×(-0.379)) = 1310/379

Which gives;

Second part;

The percentage of eggs that hatch at the temperature that gives the maximum percentage of eggs is the maximum percentage of eggs, which is found as follows;

f(46 + 1310/379) = -0.379•(1310/379)² + 2.62•(1310/379) - 3.61 ≈ 0.9179683

The maximum percentage of puffin eggs is therefore;

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Exponential function:

A mathematical function with the formula f (x) = an x is an exponential function. where an is a constant known as the function's base and x is a variable. The transcendental number e, or roughly 2.71828, is the exponential-function base that is most frequently encountered.

Given,

The value of this exponential function :

14 × 14 = 196

The value of this exponential function :

4 × 4 × 4 × 4 × 4 = 1024

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Given in the question the matrix

A  =   [ 1    -1         B =  [ 1    5        C = [ 1     2

          -2    3 ]                8   -8 ]              3     4]

after solving AX + B = C, we get the value of x

x  =         [ 1        -21/5

              -1           8/5]  ..........(ii)

Given A =   [ 1    -1         B =  [ 1    5        C = [ 1     2

                   -2    3 ]               8   -8 ]              3     4]

find x, if AX + B = C

AX + B = C

AX = C -B =      [ 1     2                        [ 1    5  

                                           -    

                         3     4]                         8   -8 ]

AX =   [ 1-1        2-5      =      [ 0   -3

          3-8        4+8 ]           -5    12]

X = A -1        [ 0   -3

                    -5    12]   .........(i)

A =   [1     1            |A|  = {3*1 - 1 *(-2)}

       -2    3]                  = 5

A-1  = [tex]\frac{adj A}{|A|}[/tex]

Adj  A = [cofactor A]^1 =       [ [tex]a_{11}[/tex] = 3        [tex]a_{12}[/tex]  = 2

                                               [tex]a_{21}[/tex]  = -1           [tex]a_{22}[/tex]  = 1 ] ^1

adj A = [ 3  -1            A -1 =  1/5    [ 3    -1

             2    1]                               2     1]

x = 1/5   [3     -1                 [ 0     -3

              2     1]                 -5      12]

   = 1/5 [ 5    -21        =     [ 1        -21/5

             -5     8]              -1           8/5]  ..........(ii)

Hence, required solution of the given matrix is equation (ii)

Therefore, Given the matrix A  =   [ 1    -1         B =  [ 1    5        C = [ 1     2

                                                         -2    3 ]                8   -8 ]              3     4]

after solving AX + B = C, we get the value of x

x  =         [ 1        -21/5

              -1           8/5]  ..........(ii)

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Answer:

D = 1.9

You can find for d by using the associative property of division (divide instead of multiply):

5.7 divided -3 = 1.9

Step-by-step explanation:

Hope it helps! =D