Which statement is true?

The first step in the construction of a line perpendicular to line AB and passing through an external point m is:

a. place the compass needle on m and keeping the compass width the same, draw two arcs that intersect the line AB

To construct a perpendicular line, a compass and a scale are used.

Consider a line AB and an external point M.

Step 1:

Place the compass needle on M and keeping the compass width the same, draw two arcs that intersect the line AB.

Step 2:

Name the two intersecting points on line AB as X and Y.

Draw the arcs from these two points to the opposite side of point M with the same compass width.

Step 3:

Name the intersecting point of two arcs as N.

Draw a line connecting the two points M and N using scale.

Step 4:

Using a protractor, measure the angle of the line MN with the line AB.

The angle must show 90°.

Thus, the line MN perpendicular to line AB and passing through an external point M is constructed.

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Answer:

a. place the compass needle on m and keeping the compass width the same, draw two arcs that intersect the line AB

Step-by-step explanation:

Answer:

9.2195445 (9.22 rounded)

Step-by-step explanation:

#1: Use the distance formula to determine the distance between the two points:

Distance = [tex]\sqrt{(x_{2}-x_{1})^{2}+(y_{2}-y_{1})^{2}}[/tex]

#2: Substitute the actual values of the points into the distance formula:

[tex]\sqrt{((-4)-3)^{2}+(5-(-1))^{2}}[/tex]

#3: Simplify:

- Subtract 3 from -4: [tex]\sqrt{(-7)^{2}+(5-(-1))^{2}}[/tex]

- Raise -7 to the power of 2: [tex]\sqrt{49+(5-(-1))^{2}}[/tex]

- Multiply -1 by -1: [tex]\sqrt{49+(5+1)^{2}}[/tex]

- Add 5 and 1: [tex]\sqrt{49+6^{2}}[/tex]

- Raise 6 to the power of 2: [tex]\sqrt{49+36}[/tex]

- Add 49 and 36: [tex]\sqrt{85}[/tex] (Decimal form: 9.2195445 (9.22 rounded))

The distance between the two points (3,1) and (4,-5) is 9.22.

Answer:

e(x)=0 will be  your answer

Step-by-step explanation:

First of all it is important to know about the fair game.  A game is said to be fair if it has equal chances of winning for both the parties.

In Statistical terms, this can be said as expected value =0

If E(X) = 1 where X is from the player, then organizer of the game would have more chances of losing.

Similarly if E(X)>0where X is from the player, then organizer of the game would have more chances of losing.

Also if E(X)>1, where X is from the player, then organizer of the game would have more chances of losing.

Hence a fair game is one where

Answer: A. E(X) = 0

Step-by-step explanation:

Answer:

D

Step-by-step explanation:

A' represents everything outside of the circle A

B represents the space within circle B

A' intersection B is everything not in A that is in B.

Answer: $92.30

Step-by-step explanation:

Finding the area of one of the triangles formed by the diagonal,[tex]s=\frac{9+12+19}{2}=20\\\\A=\sqrt{(20)(20-9)(20-12)(20-19)}=4\sqrt{110}[/tex]

Therefore, the area of the entire parallelogram is [tex]8\sqrt{110}[/tex].

Therefore, the cost is [tex](8\sqrt{110})(1.1) \approx 92.30[/tex]

Answer:

$92.30   i got it right.

Step-by-step explanation:

edg 2023 its right.

The additional number of people is [4, 13]

Brittany and four of her friends are five people.

So, we have:

n = 5

The conditions are given as

Let the additional number of people be x

So, we have the following inequalities

x + 5 ≥ 9 and x + 5 ≤ 18

Subtract 5 from both sides

x ≥ 4 and x ≤ 13

Express as interval notation

[4, 13]

Hence, the additional number of people is [4, 13]

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The number of possible combinations would be 56.

Permutation is the changing of the order in which things have been arranged or the arranging of things in a certain order.

Analysis:

Total number of fiction books available = 8

number of fiction books Ruthie wants = 1

Number of combination for Ruthie = 8C1 = 8 ways

Total number of non fiction books available = 7

number of non fiction books needed by Ruthie = 1

possible combination = 7C1 = 7 ways

Total number of magazines available = 3 ways.

Total possible combinations for all the Reading materials = 8 x 7 x 1 = 56 ways.

number of magazines Ruthie wants = 3C3 = 1 way

In conclusion, the number of possible combinations of The reading materials is 56.

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Answer:

1. 4x²-6x-4

2. 8x³+4x²-8x-4

3. x⁵-x⁴+3x³+x²+12

Step-by-step explanation:

1. (4x+2)(x-2)

apply foil method (a+b)(c+d)=ac+ad+bc+bd

(4x+2)(x-2)=4x.x + 4x(-2) + 2x + 2(-2)

2. (4x²-4) (2x+1)

apply the same method as question no.1

(4x²-4) (2x+1)=4x².2x + 4x².1 + -4.2x-4.1

3. (x²+3) (x³-x²+4)

Distributive parentheses

(x²+3) (x³-x²+4)= x².x³ + x²(-x²) + x².4+ 3x³+3(-x²) +3.4

Answer:

a) 10√3 + 5√3 + 10√3 + 5√3 = 30√3 cm

b) (√10 + √2) + (√10 - √2) + (√10 + √2) + (√10 - √2)

= 4√10 cm

c) Simplifying √72: √36 x √2 = 6√2

   Simplifying √18: √9 x √2 = 3√2

   Finding the perimeter: 6√2 + 3√2 + 6√2 + 3√2 = 18√2 cm

Answer:

See below

Step-by-step explanation:

y = -6x^2 + 24x-100

solve for 'x'

y + 100 =   -6x^2 + 24x   = -6(x^2-4x)    complete the square for x

(y+100) /(-6 ) =    (x-2)^2 -4                     add 4 to both sides

(y+100)/(-6) +4   = (x-2)^2                       sqrt both sides

sqrt [  ( y+100)/(-6) + 4  ]  + 2 = x           change  x and y

y = ± sqrt [ (x+100)/(-6) + 4 ] + 2            simplify (if needed)

y  = ± sqrt( -x/6 -12.666)  + 2

Probability of someone over age 30 winning the tickets is; 38.46%

We are given;

Number of People over 30 years of age = 15

Number of people between 20 and 30 years old = 14

Number of People under 20 years old = 10

Total number of people in the group = 15 + 14 + 10 = 39

Thus;

Probability of someone over age 30 winning the tickets = 15/39 = 38.46%

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Using limits, it is found that the correct statement defining the sequence is:

The sequence converges to 1.

The numerator starts at 3 and increases by 1, while the denominator starts at 4 and increases by 1, hence the rule is:

[tex]\sum_{n = 0}^{\infty} \frac{3 + n}{4 + n}[/tex]

To verify if it converges, we find the limit as n goes to infinity, hence:

[tex]\lim_{n \rightarrow \infty} \frac{3 + n}{4 + n} = \lim_{n \rightarrow \infty} \frac{n}{n} = \lim_{n \rightarrow \infty} 1 = 1[/tex]

Hence the sequence converges to 1.

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Answer:

B i took quiz

Step-by-step explanation:

Step-by-step explanation:

3) Triangle QTR is similar to triangle STP (AA)

4) RT/PT = QR/PS (corresponding sides of similar triangles are proportional)

Using it's concept, the domain of the function shown in the graph is:

B. [tex]-6 \leq x \leq 6[/tex].

The domain of a function is the set that contains all possible input values for the function. In a graph, the domain is the set that contains all values of x.

From this graph, the function is defined for values of x between -6 and 6, hence the domain is given by:

B. [tex]-6 \leq x \leq 6[/tex].

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The correct statement about when a scatterplot is constructed is  the independent variable is the input variable and should be represented by the x-axis. Option A

From the given steps, we can see that when a scatter plot is constructed,  the independent variable is the input variable and should be represented by the x-axis.

Hence, the correct statement about when a scatterplot is constructed is  the independent variable is the input variable and should be represented by the x-axis. Option A

The complete question is;

Which statement is correct when a scatterplot is constructed? The independent variable is the input variable and should be represented by the x-axis.

The independent variable is the input variable and should be represented by the y-axis.

The dependent variable is the input variable and should be represented by the x-axis.

The dependent variable is the input variable and should be represented by the y-axis.

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Answer: A; The independent variable is the input variable and should be represented by the x-axis.

Step-by-step explanation:

I just know

Using proportions, the lengths of the unknown sides are given as follows:

A proportion is a fraction of a total amount, and the measures are related using a rule of three.

In this problem, the triangles are similar, hence the lengths of it's sides follow the proportion given next:

[tex]\frac{2x}{4} = \frac{5}{x - 3}[/tex]

Applying cross multiplication:

2x(x - 3) = 20

2x² - 6x - 20 = 0

x² - 3x - 10 = 0

(x - 5)(x + 2) = 0.

Then the positive solution is:

x - 5 = 0 -> x = 5.

And the lenghts are:

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Using it's concept, the probabilities are given as follows:

19. A. 1/3.

20. F. 1/6.

A probability is given by the number of desired outcomes divided by the number of total outcomes.

In this problem, there are 1 + 1 + 3 + 4 + 3 = 12 papers. 4 have a score of 6, hence, in item 19, the probability is:

p = 4/12 = 1/3.

Which means that option A is correct.

2 papers have a score greater than 12, hence the probability in item 20 is given by:

p = 2/12 = 1/6.

Which means that option F is correct.

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Hello,

John : n

Brad : n + 12

n + n + 12 = 84

2n + 12 = 84

2n = 84 - 12

2n = 72

n = 72/2

n = 36

John $36 and Brad $36 + $12 = $48

Answer:

jhon =36 brad=48

Step-by-step explanation:

B=J+12

J+B=84

12+J+J=84

2J=72

J=36

B=J+12=36+12=48

Answer:

B. The coefficient of the second term is -5.

and

D. The coefficient of the fourth term is -10.

Step-by-step explanation:

The coefficient is the number being multiplied by a variable.

Hope this helps!

Answer:

Tick:

- the coefficient of the second term is -5

- the coefficient of the fourth term is -10

Explanation:

The coefficient of an expression is simply the number placed before and multiplying the variable (e.g. 10x ; the coefficient is 10, the variable is x)

Hope this makes sense. Feel free to inquire further if need be!

- profparis

Answer:

x - 11

Step-by-step explanation:

The area of the triangle is 557. 7cm²

In order to determine the area of a triangle, we have to know the size of the base and the size of the height

The formula for finding the area of a triangle is given as = half the base multiplied by the height

In mathematical form, it is written as;

Area = 1/ 2 × base × height

From the figure given, we have their lengths to be'

base = 57. 2 m

height = 19. 5 m

Let's substitute the values

Area = 1/ 2 × 57. 2 × 19. 5

Area = 1/ 2 × 1115. 4

Find the ratio

Area = 557. 7 m²

The area of the triangle is 557. 7cm²

Hence, the area of the triangle is 557. 7cm²

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For easy estimation, option A = nearest hundred,B = nearest ten, C = nearest hundred and D= nearest thousand.

3529 and 3689

3529 to the nearest hundred = 3500 and,

3689 to the nearest hundred = 3700

∴ Required sum = (3500+3700) = 7200

33 and 99

33 to the nearest ten = 30 and,

99 to the nearest ten = 90

∴ Required sum = (30+90) = 120

120777 × 523

777 to the nearest hundred = 800 and,

523 to the nearest hundred = 500

∴ Required sum = (800+500) = 1300

1300495420 and 123512

495420 to the nearest thousand = 495000 and,

123512 to the nearest thousand = 124000

∴ Required sum = (495000 + 124000 ) = 619000

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16 tiles will fit end to end on a 4 foot wall.

In unitary method we will learn how to find the value of a unit from the value of a multiple and the value of a multiple from the value of a unit.

When we go to the market to buy any article, we ask the shopkeeper to tell the price of the article. This is called unit price. We calculate the price of number of articles, we want to buy, with the help of this unit price. Sometimes, we calculate unit price when the price of a multiple is given.

1 tile in 1/4 foot

So in 4 foot wall the number of tiles = 4/(1/4) = 16 tiles.

Thus 16 tiles will fit end to end on a 4 foot wall.

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The age of the grandfather in years according to the task content is; 84.

It follows that the age of the grandfather and granddaughter are; x and y respectively.

Hence, the two equations which follow are;

x = 12y

x + y= 91

Hence, the age of the grandfather, x can be evaluated as follows;

x = 12(91-x)

13x = 1092

x = 1092/13

x = 84 years.

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Answer:

Step-by-step explanation:

your answer will be 110degrees

Answer:

30.7

Step-by-step explanation:

It's 30.7 because 707/23

Answer:

16261 u3

Step-by-step explanation:

V = (base area)(height)=(707)(23)= 16261 u3

Hope this helps