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On a map of North Carolina, the distance between Raleigh and Charlotte is 1 point
3 inches. The scale on the map is 1 inch = 40 miles. What is the actual
distance?

Answer: 56

Step-by-step explanation:

Answer:

564643

Step-by-step explanation:

Answer:

In the real number system, there is no solution to the equation x^2=-1x

2

=−1x, squared, equals, minus, 1. In this lesson, we will study a new number system in which the equation does have a solution.

The backbone of this new number system is the number iii, also known as the imaginary unit.

i^2=-1i

2

=−1i, squared, equals, minus, 1

\sqrt{-1}=i

−1

​

=isquare root of, minus, 1, end square root, equals, i

By taking multiples of this imaginary unit, we can create infinitely many more new numbers, like 3i3i3, i, i\sqrt{5}i

5

​

i, square root of, 5, end square root, and -12i−12iminus, 12, i. These are examples of imaginary numbers.

However, we can go even further than that and add real numbers and imaginary numbers, for example 2+7i2+7i2, plus, 7, i and 3-\sqrt{2}i3−

2

​

i3, minus, square root of, 2, end square root, i. These combinations are called complex numbers.

Defining complex numbers

A complex number is any number that can be written as \greenD{a}+\blueD{b}ia+bistart color #1fab54, a, end color #1fab54, plus, start color #11accd, b, end color #11accd, i, where iii is the imaginary unit and \greenD{a}astart color #1fab54, a, end color #1fab54 and \blueD{b}bstart color #11accd, b, end color #11accd are real numbers.

\begin{array}{ccc} \Large\greenD a&\Large+&\Large \blueD bi \\ \uparrow&&\uparrow\phantom{i} \\ \text{Real}&&\text{Imaginary} \\ \text{part}&&\text{part} \end{array}

a

↑

Real

part

​

+

​

bi

↑i

Imaginary

part

​

\greenD aastart color #1fab54, a, end color #1fab54 is called the \greenD{\text{real}}realstart color #1fab54, start text, r, e, a, l, end text, end color #1fab54 part of the number, and \blueD bbstart color #11accd, b, end color #11accd is called the \blueD{\text{imaginary}}imaginarystart color #11accd, start text, i, m, a, g, i, n, a, r, y, end text, end color #11accd part of the number.

The table below shows examples of complex numbers, with the real and imaginary parts identified. Some people find it easier to identify the real and imaginary parts if the number is written in standard form.

Complex Number Standard Form \greenD a+\blueD b ia+bistart color #1fab54, a, end color #1fab54, plus, start color #11accd, b, end color #11accd, i Description of parts

7i-27i−27, i, minus, 2 \greenD {-2}+\blueD 7i−2+7istart color #1fab54, minus, 2, end color #1fab54, plus, start color #11accd, 7, end color #11accd, i The real part is \greenD{-2}−2start color #1fab54, minus, 2, end color #1fab54 and the imaginary part is \blueD 77start color #11accd, 7, end color #11accd.

4-3i4−3i4, minus, 3, i \greenD 4 + (\blueD{-3})i4+(−3)istart color #1fab54, 4, end color #1fab54, plus, left parenthesis, start color #11accd, minus, 3, end color #11accd, right parenthesis, i The real part is \greenD{4}4start color #1fab54, 4, end color #1fab54 and the imaginary part is \blueD{-3}−3start color #11accd, minus, 3, end color #11accd

9i9i9, i \greenD 0+\blueD9i0+9istart color #1fab54, 0, end color #1fab54, plus, start color #11accd, 9, end color #11accd, i The real part is \greenD{0}0start color #1fab54, 0, end color #1fab54 and the imaginary part is \blueD 99start color #11accd, 9, end color #11accd

-2−2minus, 2 \greenD {-2}+\blueD0i−2+0istart color #1fab54, minus, 2, end color #1fab54, plus, start color #11accd, 0, end color #11accd, i The real part is \greenD{-2}−2start color #1fab54, minus, 2, end color #1fab54 and the imaginary part is \blueD 00start color #11accd, 0, end color #11accd

Step-by-step explanation:

plz brian list and allways happy to help.

9514 1404 393

Answer:

  (3/2)√2 ≈ 2.1213 units

Step-by-step explanation:

The distance d from point (x, y) to line ax+by+c = 0 is given by ...

  d = |ax +by +c|/√(a^2 +b^2)

We can write the equation of the line as ...

  x + y -4 = 0

so the distance is ...

  d = |x + y - 4|/√(1^2 +1^2)

For point (x, y) = (2, -1), the distance is ...

  d = |2 +(-1) -4|/√2 = 3/√2 = (3√2)/2

The distance from A(2, -1) to the line y = -x +4 is (3√2)/2 units.

f ( x ) = - ( x + 1)^2 + 4

_____________________

Vertex = ( - 1 , 4 )

♡♡♡♡♡♡♡♡♡♡♡♡

Domain = R

♡♡♡♡♡♡♡♡♡♡♡♡

Range = ( - infinite , 4 ]

For this problem you will need to use the quadratic formula. [tex]x=\frac{-b+-\sqrt{b^2-4ac} }{2a}[/tex] (the + and - are together. basically the plus is on top and the minus is on bottom. you should have seen it in your notes hopefully). a = 1, b = 8, and c = 10. from there you just plug everything in and solve.

Answer:

OK so this may or may not help u ...

this can be taken as the straight line with equation

y = mx + c

here f(x) is taken to be y

the attached pic is the graph of this function

so I think the value of x before it explodes would be 18.875

and x represents the time

and f(x) represents height so we see that the highest possible value of f(x) from the graph is 302

Answer:

$8

Step-by-step explanation:

7/7 = 1

56/7 = $8

Answer:

18.0625 ft²

Step-by-step explanation:

4.25 × 4.25

18.0625 ft²

Answer:

x=4

Step-by-step explanation:

4x+7=23

4x=23-7

4x=16

x=16÷4

x=4

Answer:

4

Step-by-step explanation:

4 x 4 + 7 = 23

Answer:

Danton vendeu 310 instrumentos musicais.

Step-by-step explanation:

Selton vendeu 62 instrumentos esse mês.

Danton:

Quintuplo do que seu irmão Selton, ou seja:

62*5 = 310.

Danton vendeu 310 instrumentos musicais.

Answer:

See the steps below:)

Step-by-step explanation:

Expression is equivalent to (2x+3)(3x²−2x+5) is 6x³+5x²+4x+15.

An expression can be of many types numerical expressions, Algebraic expressions.We can also form these mathematical expressions from a given statement or by observing a real world scenario.

Equivalent expressions are same expressions in different forms.To check whether an expression is equivalent to another expression or not we just need to do some algebraic manipulations.Like distributing or taking common and other algebraic and arithmetic operations.

According to the given problem we have to write an expression which is equivalent to the expression (2x+3)(3x²-2x+5).

(2x+3)(3x²-2x+5)

= (2x+3)(3x²-2x+5)

=2x(3x²-2x+5)+3(3x²-2x+5)                                (now we will distribute)

=6x³-4x²+10x+9x²-6x+15

=6x³+5x²+4x+15.

Learn more about equivalent expressions here :

https://brainly.com/question/3644212

#SPJ6

Answer:

200 grams

Step-by-step explanation:

Let us represent

The number of grams of

30% smarties = x

20% smarties = y

Hence:

x + y = 500

x = 500 - y

Hence:

30% × x + 20% × y = 24% × 500

0.3x + 0.2y = 120

Substitute 500 - y for x

Hence:

0.3(500 - y) + 0.2y = 120

150 - 0.3y + 0.2y = 120

Collect like terms

- 0.3y + 0.2y = 120 - 150

- 0.1y = -30

y = -30/0.1

y = 300

Solving for x

x = 500 - y

x = 500 - 300

x = 200

Hence,

The number of grams of

30% smarties = x = 200 grams

20% smarties = y = 300 grams

Therefore:

the mass of the 30% mix is required to make a 500 gram mixture that will have 24% Smarties by mass is 200 grams

Answer:

$1012993.2

Step-by-step explanation:

Given data

Cost of home V= $899,000

Rate of increase= 1%

Time= 12 years

The exponential growth function is expressed as

A=V(1+r)^t

A=899000(1+0.01)^12

A= 899000(1.01)^12

A= 899000*1.1268

A=$1012993.2

Hence the cost of the home will be $1012993.2

Answer:

1.95secs

Step-by-step explanation:

Given the height of the float expressed as h(t) = -16t2 - 3t + 55.

The floats reach the swimmer at h(t) = 0

Substitute

0 = -16t^2 - 3t + 55.

16t^2 + 3t - 55 = 0

Using the general formula;

t = -3±√3²-4(16)(-55)/2(16)

t = 3±√9+3520/32

t = 3±√3529/32

t = 3+59.41/32

t = 62.41/32

t = 1.95

Hence it will take 1.95secs

Answer:

48

Step-by-step explanation:

Answer:

she will pay 25% of the cost

Step-by-step explanation:

Well .35 is 35%

35+40 = 75

100-75 = 25

25%

Answer:

y=15x+125

Step-by-step explanation:

Hope this helps!

Answer:

the answer is c !

Step-by-step explanation:

Answer:

Step-by-step explanation:

Step 1: Find the slant height

10^2 + 28^2 = c^2

884 = c^2

c = [tex]\sqrt{884}[/tex]

Step 2: Find the lateral area

LA = pi * radius * slant height

LA = pi * 10 * [tex]\sqrt{884}[/tex]

LA (rounded to the nearest tenth) = 297.3pi in^2

Step 3: Find the area of the base circle

A = pi * r^2

A = pi * 10^2

A = 100pi in^2

Step 4: Add the areas together

SA = 297.3pi + 100pi

SA = 397.3pi in^2

Hope this helps!! :)

Answer:

(7,-19)

Step-by-step explanation:

Just took the final got it correct

Answer:

160 cm i think

Step-by-step explanation:

Answer:

45%

Step-by-step explanation:

Counting the marbles, there are 5 green, 6 blue and 9 red.

Which means the odds of drawing a red to a non red are 11:9

In fraction form that would be 9 marbles out of 20 are red. 9/20

Since the fraction cannot be simplified, we can go to decimal form.

9/20=.45

.45=45%

The answer is 45%.

Answer:

45%

Step-by-step explanation:

Total = 20

Red = 9

9/20 = 0.45

Therefore 45 % is the correct option :))

Answer:

90

Step-by-step explanation:

Formula is:

2(wl + hl +wh)

plug in values and calculate

Answer:

The area of the pentagon is approximately 21 square units

Step-by-step explanation:

The radius of the circle in which the regular pentagon is inscribed, r = 3

The area of a pentagon, 'A', inscribed in a circle with radius, r is given as follows;

A = 5×(1/2) ×2×r·sin(32°)×r·cos(32°) = (5/2)×r²×sin(72°)

Therefore, the area of the pentagon, A = (5/2)×3²×sin(72°) ≈ 21.3987716166 ≈  21

The area of the pentagon, A ≈ 21 square units.

Answer:

a) 40 caramelos

b) 13 bolas

Step-by-step explanation:

A) En cada caja hay 5 caramelos. Si tengo 8 cajas, ¿cuántos caramelos tengo?

1 caja = 5 caramelos

8 cajas = x

Multiplicar cruzada

x × 1 caja = 8 cajas × 5 caramelos

x = 8 cajas × 5 caramelos / 1 caja

x = 40 caramelos

b) Romina tiene 9 bolas y Lidia 4 veces más que ella. ¿Cuántas bolas tiene Lidia?

Romina = 9 bolas

Lidia = 4 bolas más que ella

Lidia = 9 bolas + 4 bolas

= 13 bolas