Find the absolute value of the complex number.
2+i

Answer: 163$

Step-by-step explanation:

Answer:

33.  AB = √45.  CD = √40.  Not congruent.  AB is greater.

34.  EF = 5.  GH = √41.  Not congruent.  GH is greater.

Step-by-step explanation:

[tex]\boxed{\begin{minipage}{7.4 cm}\underline{Distance between two points}\\\\$d=\sqrt{(x_2-x_1)^2+(y_2-y_1)^2}$\\\\\\where $(x_1,y_1)$ and $(x_2,y_2)$ are the two points.\\\end{minipage}}[/tex]

Given endpoints:

Substitute the given endpoints into the formula and solve:

[tex]\begin{aligned}\overline{AB}&=\sqrt{(x_B-x_A)^2+(y_B-y_A)^2}\\&=\sqrt{(-3-0)^2+(8-2)^2}\\&=\sqrt{(-3)^2+(6)^2}\\&=\sqrt{9+36}\\&=\sqrt{45}\\& \approx 6.7\; \sf (1 \; d.p.)\end{aligned}[/tex]

Given endpoints:

Substitute the given endpoints into the formula and solve:

[tex]\begin{aligned}\overline{CD}&=\sqrt{(x_D-x_C)^2+(y_D-y_C)^2}\\&=\sqrt{(0-(-2))^2+(-4-2)^2}\\&=\sqrt{(2)^2+(-6)^2}\\&=\sqrt{4+36}\\&=\sqrt{40}\\& \approx 6.3\; \sf (1 \; d.p.)\end{aligned}[/tex]

Therefore, the segments at not congruent.

[tex]\textsf{As\; $\sqrt{45} > \sqrt{40}$ \; then \; $\overline{AB} > \overline{CD}$}.[/tex]

Therefore, the length of segment AB is greater.

Given endpoints:

Substitute the given endpoints into the formula and solve:

[tex]\begin{aligned}\overline{EF}&=\sqrt{(x_F-x_E)^2+(y_F-y_E)^2}\\&=\sqrt{(5-1)^2+(1-4)^2}\\&=\sqrt{(4)^2+(-3)^2}\\&=\sqrt{16+9}\\&=\sqrt{25}\\&=5\end{aligned}[/tex]

Given endpoints:

Substitute the given endpoints into the formula and solve:

[tex]\begin{aligned}\overline{GH}&=\sqrt{(x_H-x_G)^2+(y_H-y_G)^2}\\&=\sqrt{(1-(-3))^2+(6-1)^2}\\&=\sqrt{(4)^2+(5)^2}\\&=\sqrt{16+25}\\&=\sqrt{41}\\& \approx 6.4\; \sf (1 \; d.p.)\end{aligned}[/tex]

Therefore, the segments at not congruent.

[tex]\textsf{As\; $\sqrt{41} > 5$ \; then \; $\overline{GH} > \overline{EF}$}.[/tex]

Therefore, the length of segment GH is greater.

The total number of toys is 45 Samuel if Samuel has a collection of toy cars. His favorites are the 27 red ones.

It's the ratio of two integers stated as a fraction of a hundred parts. It is a metric for comparing two sets of data, and it is expressed as a percentage using the percent symbol.

It is given that:

Samuel has a collection of toy cars. His favorites are the 27 red ones.

Let Samuel has x number of toys:

From the equation:

60% of x = 27

(60/100)x = 27

0.6x = 27

x = 27/0.6

x = 45

Thus, the total number of toys is 45 Samuel if Samuel has a collection of toy cars. His favorites are the 27 red ones.

The complete question is:

Samuel has a collection of toy cars. His favorites are the 27 red ones which make up 60% of his collection. How many toy cars does Samuel have?

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Plotting the graph of the quadratic function  g(x)=-1/5x^2 + 4x + 1 the range is

The range of the quadratic function is seen at the vertex were the maximum or minimum y value is seen

The graph of the function  g(x)=-1/5x^2 + 4x + 1 is plotted and attached

From the graph the vertex coordinates is v(-10, -16). The y coordinates of the vertex is -19 and this is the minimum values for y

Therefore the range is y ≥ -19

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The function f has domain : [-4, 5], range : [0, 9], zero : (3, 0), the function is increasing in intervals at [-4, 0] U [3, 5], decreasing in intervals at (0, 3], the relative minimum values of f : (3, 0), and relative maximum values of f : (5, 9).

The domain of the function includes all possible x values of a function, and the range includes all possible y values of the function.

The function f is given in the graph.

According to the given function, the required solution would be as:

The domain and range of f will be :

domain : [-4, 5]

range : [0, 9]

The zero of f will be :

(x, y) = (3, 0)

The function is increasing in intervals at [-4, 0] U [3, 5]

The function is decreasing in intervals at (0, 3]

The relative minimum values of f : (3, 0)

The relative maximum values of f : (5, 9)

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Answer:

B

Step-by-step explanation:

given 1 pound = 16 ounces , then

5 pounds = 5 × 16 = 80 ounces

Answer:

-2w-20

Step-by-step explanation:

The rule that describes ( -1, 1), (1, 2), (3, 3), (5, 4) is c. Output = (0.5)(Input) + 1.5

A function can be defined as the outputs for a given set of inputs.

The inputs of a function are known as the independent variable and the outputs of a function are known as the dependent variable.

Given, On a coordinate plane, points are at ( -1, 1), (1, 2), (3, 3), (5, 4).

By observing the given options we conclude that it is Output = (0.5)(Input) + 1.5 to confirm let's put the values.

Given when input is - 1 output is 1.

∴ 1 = 0.5(-1) + 1.5.

1 = - 0.5 + 1.5.

1 = 1  ( satisfied).

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Answer:

12x^5+18x^2+10x^3+15

Step-by-step explanation:

first you apply the distribution property (FOIL) and you get

12x^5+18x^2+10x^3+15

a. Creating a system of equations, the length of each plan A's workout is 3/4 hour, while the length of each plan B's workout is 3/4 hour.

b. x = -8, y = 2.

Write equations of a system that represents the information given and solve accordingly.

Let the length of plan A = x

Length of plan B = y

Equation for Monday would be:

9x + 7y = 12 --> eqn. 1

Equation for Tuesday:

3x + 5y = 6 --> eqn. 2

Multiply eqn. 1 by 3 and eqn. 2 by 9

27x + 21y = 36 --> eqn. 3

27x + 45y = 54 --> eqn. 4

Subtract the equations:

-24y = -18

y = -18/-24

y = 3/4

Plan B's length of workout is: 3/4 hour.

Substitute y = 3/4 into equation 2:

3x + 5(3/4) = 6

3x + 15/4 = 6

3x = 6 - 15/4

3x = 9/4

12x = 9

x = 9/12

x = 3/4

Length of plan A's workout is: 3/4 hour.

b. 2x + 4y = -8 --> eqn. 1

-2x + 3y = 22 --> eqn. 2

Add both equations together:

7y = 14

y = 2

Substitute y = 2 into equation 1:

2x + 4(2) = -8

2x + 8 = -8

2x = -8 - 8

2x = -16

x = -16/2

x = -8

The solution is: x = -8, y = 2.

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You got to set it up to boys to girls

Answer:

0,1

Step-by-step explanation:

simplest form

The distance on the map, in cm, given the real distances, and the scale of the map are:

A scale of 1 : 200, 000 means that every 1 cm on the map is 200, 000 cm on the ground.

To find the distance on the map of 10 km, first convert it to cm:
= 10 km x 100, 000 cm per km

= 1, 000, 000 cm

The distance on the map is therefore:

= 1, 000, 000 / 200, 000 cm scale

= 5 cm on map

The distance of 15 km on the map is:

= (15 km x 100, 000) / 200, 000

= 7.5 cm

The distance of 4 km is:

= (4 x 100, 000) / 200, 000

= 2 cm

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The net value of the items purchased is ₹ 900.

Raman purchased books and stationery items and paid the total amount of rupees 963.

Paid tax = 7%

Let the net value of the items purchased be `x.

VAT = 7%

Selling price = ₹x + (7% of x)

                    = ₹x+ ₹ ( 7/100 * x)  

                    =₹( x +7 x /100)

                    = ₹ 107 x /100

But Raman purchased books and stationery items for ₹963.

107x/100 = ₹963

               x =  963 x 100/107

               x = 900

Hence the answer is the net value of the items purchased is ₹ 900.

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Answer:

Step-by-step explanation:

y=7x is the equation that shows how the total cost of the party favors, y, depends on the number of guests, x

Two or more expressions with an Equal sign is called as Equation.

Given,

Andrew has picked out some party favors.

He calculates that they will cost $7 per guest.

We need to find the equation that shows how the total cost of the party favors, y, depends on the number of guests, x

So y=7x where y is the total cost and x is the number of guests and 7 is the cost per guest.

If there are 2 guests then the total cost will be 14.

Hence y=7x is the equation that shows how the total cost of the party favors, y, depends on the number of guests, x

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Answer:156

Step-by-step explanation:

Answer:

480 lbs

Step-by-step explanation:

First, find the ratio of weight on the moon to weight on the earth. I will put the two known values in a fraction like this:

[tex]\frac{25}{150}[/tex]

Now, I can create a proportion, making sure to keep the same types of measurements in the numerator and denominator. I will use w for the unknown weight on earth.

[tex]\frac{25}{150}=\frac{80}{m}[/tex]

Now, I will simplify the fractions as much as I can.
[tex]\frac{1}{6}=\frac{80}{m}[/tex]

Now, I can see a correlation. 1 times 80 is 80, so 6 times 80 is m. Simplified, here is the answer!

[tex]6*80=m\\480=m\\m=480[/tex]

Answer:

480 pounds

Step-by-step explanation:

we times for objects on earth and divide for objects on the moon by the same number

150

[tex]150 \div x = 25[/tex]

150/-25=-x

-6/-1= -x/-1

6=x

[tex]150 \div 6 = 25[/tex]

so when in object is on earth you multiple by x Wich 6

[tex]80 \times 6 = 480[/tex]

you can also cross multiply

Answer:

which of the following ratios are connected to 5/20?

multiple choice

a 1/5

c 20/100

d 25/100

d is the option 25/100 and

b 1/4

Answer:

Arithmetic

Step-by-step explanation:

The difference between consecutive terms is 5. Thus, this is an arithmetic sequence with a common difference of 5.

If the actual length of the pool table is 6 feet , then the length of the pool table in the drawing is 12 inches   .

In the question,

it is given that ,
Barbara drew an scale drawing of the game room.

the scale that she used is 1 feet in the actual length is represented by 2 inches in the drawing ,

which means ,

1 feet = 2 inches

to find the length of 6 feet in the drawing ,

6 feet = 6 × 2 inches

= 12 inches

Therefore , If the actual length of the pool table is 6 feet , then the length of the pool table in the drawing is 12 inches   .

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Answer:

Step-by-step explanation:

We have to the graph from x = -4 to x = 2

2y + x + 3 = 0

Rearrange the equation to make y the subject

2y = -x - 3

y = (-1/2)x -3/2

-3/2 is the y intercept

the gradients is -1/2

since the value is negative, the graph will be sloping downwards

Point your pen at y = -3/2 on the y axis (-3/2 is -1.5)

go 1 point down and 2 points to the right, make a point and connect these 2 dots and make a line across the graph.

Do the same with the other equation:

3y - x + 1 = 0

3y = x - 1

y = (1/3)x -1/3

y intercept is -1/3

gradient is 1/3

point your pen at -1/3 on the y axis, go 1 point up and 3 points to the right

and mark this point and connect these 2 points and make a line across the graph.    

By solving a system of equations we can see that each goat costs $30 and each sheep costs $25.

Let's define the variables:

x = cost of a goat

y = cost of a sheep.

We can write the system of equations with the given info:

6*x + 5*y = 305

2*x + 9*y = 285

If we subtract 3 times the second equation from the first one, we get:

(6*x + 5*y) - 3*(2*x + 9*y) = 305 - 3*285

-22*y = -550

y = -550/-22 = 25

Now that we know the value of y we can try to find the value of x:

2*x +9*25 = 285

2*x = 285 - 9*25 = 60

x = 60/2 = 30

These are the costs of each animal.

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Answer: 2>=n

Step-by-step explanation:

3n-6 +2 >= 5n-8

3n-4 >= 5n-8

-4>= 2n -8

4>=2

2>=n

Hope this helped!!

Answer:

2.8 pounds per hour

Step-by-step explanation:

[tex] \frac{3.5}{1.25} = \frac{350}{125} = \frac{14}{5} = 2.8[/tex]

========================================================

Explanation:

A thing that jumps out at me right away is the presence of x/3 on both sides. When subtracting x/3 from both sides, these terms cancel out and we're left with this equation

5 = 6 + (x/9)

Let's say w = x/9. We now have this equation 5 = 6 + w. Subtract 6 from both sides to isolate w and you should get w = -1

Then plug in w = x/9 and solve for x.

w = -1

x/9 = -1

x = 9*(-1)

x = -9

We get exactly one solution and it is x = -9

--------------

Check:

5 + x/3 = x/3 + 6 + x/9

5 + (-9)/3 = (-9)/3 + 6 + (-9)/9

5 - 3 = -3 + 6 - 1

2 = 3 - 1

2 = 2

We get the same thing on both sides, which leads to a true statement. This causes a domino effect to lead the first equation to be true when x = -9. Therefore, the solution is confirmed.

The measure of angle 2 is 75°

From the question, we have

∠1= 105°

∠2= 180°- 105° (Linear pair)

∠2=75°

Subtraction:

Subtraction represents the operation of removing objects from a collection. The minus sign signifies subtraction −. For example, there are nine oranges arranged as a stack (as shown in the above figure), out of which four oranges are transferred to a basket, then there will be 9 – 4 oranges left in the stack, i.e. five oranges. Therefore, the difference between 9 and 4 is 5, i.e., 9 − 4 = 5. Subtraction is not only applied to natural numbers but also can be incorporated for different types of numbers.

The letter "-" stands for subtraction. Minuend, subtrahend, and difference are the three numerical components that make up the subtraction operation. A minuend is the first number in a subtraction process and is the number from which we subtract another integer in a subtraction phrase.

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Answer:

=============================

The given translates as:

Use given x - intercepts to get the equation:

Use the coordinates of P to find the value of a:

The equation of this parabola is:

Answer:

[tex]\textsf{Intercept form}: \quad y=-\dfrac{2}{7}(x+4)(x-7)[/tex]

[tex]\textsf{Standard form}: \quad y=-\dfrac{2}{7}x^2+\dfrac{6}{7}x+8[/tex]

Step-by-step explanation:

[tex]\boxed{\begin{minipage}{6 cm}\underline{Intercept form of a quadratic equation}\\\\$y=a(x-p)(x-q)$\\\\where:\\ \phantom{ww}$\bullet$ $p$ and $q$ are the $x$-intercepts. \\ \phantom{ww}$\bullet$ $a$ is some constant.\\\end{minipage}}[/tex]

If the x-intercepts are (-4, 0) and (7, 0) then:

Substitute the values of p and q into the formula:

[tex]\implies y=a(x-(-4))(x-7)[/tex]

[tex]\implies y=a(x+4)(x-7)[/tex]

To find a, substitute the given point on the curve P (3, 8) into the equation:

[tex]\implies 8=a(3+4)(3-7)[/tex]

[tex]\implies 8=a(7)(-4)[/tex]

[tex]\implies 8=-28x[/tex]

[tex]\implies a=\dfrac{8}{-28}[/tex]

[tex]\implies a=-\dfrac{2}{7}[/tex]

Substitute the found value of a into the equation:

[tex]\implies y=-\dfrac{2}{7}(x+4)(x-7)[/tex]

Expand to write the equation in standard form:

[tex]\implies y=-\dfrac{2}{7}(x^2-3x-28)[/tex]

[tex]\implies y=-\dfrac{2}{7}x^2+\dfrac{6}{7}x+8[/tex]

The number that will be next in the series will  be  63 .

In the question ,

a recurrence relation is given that is  0, 3, 8, 15, 24, 35, 48, ? .

we have to find the number that will come in place of question mark .

On carefully examining the series , we can see that

3 - 0 = 3

8 - 3 = 5

15 - 8 = 7

24 - 15 = 9

35 - 24 = 11

48 - 35 = 13

we can se that increments 3,5,7,9,11,13,... form an Arithmetic Progression

with first term as 3 and common difference as 2 ,

So ,the next increment will be 13+2 = 15

let the next term be "x" .

x - 48 = 15

x = 15 + 48 = 63

the number in place of ? is 63 .

Therefore , The number that will be next in the series will  be  63 .

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Answer:

Step-by-step explanation:

The average annual rainfall for a town is 43.2 inches.

This is converted to average monthly as:

The difference is:

Answer:

Yeah, they exceeded by 0.4 inches.

Step-by-step explanation:

It is given that,

→ the average monthly rainfall for the previous 9 months was 4 inches.

The monthly rainfall in 12 months,

→ 43.2 inches ÷ 12 months

→ 43.2/12

→ 3.6 inches

Then the difference will be,

→ 4 inches - 3.6 inches

→ 4 - 3.6

→ 0.4 inches

Hence, the difference is 0.4 inches.

(a)The probability that the friend is between 25 and 30 minutes late is 1/2.

(b) It is 10 A.M. There is a 10% probability the friend will arrive within 1 minute.

What is probability?

Uniform distribution

a = 0

b = 10

a) P(friend is between 25 and 30 minutes late) = (30 - 25)/(b - a)

= 5/(10-0)

= 1/2

b) Let the time for arrival be A minutes

(A - 0)/(b-a) = 0.10

A = 0.10 x (10 - 0)

A = 1 minute

Hence, The probability that the friend is between 25 and 30 minutes late is 1/2 and It is 10 A.M. There is a 10% probability the friend will arrive within 1 minute.

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Answer:

A ≈ 6538.35 cm²

Step-by-step explanation:

Calculating the area (A) using Heron's formula

A = [tex]\sqrt{s(s-a)(s-b)(s-c)}[/tex]

where s is the semi perimeter and a, b, c the 3 sides

here

s = 380 ÷ 2 = 190

given perimeter = 380 and unequal side is 150 , then

equal sides = (380 - 150) ÷ 2 = 230 ÷ 2 = 115 cm

then a = 150, b = 115 , c = 115

A = [tex]\sqrt{190(190-150)(190-115)(190-115)}[/tex]

   = [tex]\sqrt{190(40)(75)(75)}[/tex]

   = [tex]\sqrt{42750000}[/tex]

   ≈ 6538.35 cm² ( to 2 dec. places )