Kelly and Daniel wrote the following proofs to prove that vertical angles are congruent. Who is correct?
Line segment NT intersects line segment MR forming four angles. Angles 1 and 3 are vertical angles. Angles 2 and 4 are vertical angles. Kelly's Proof Statement Justification ∠2 = ∠4 Vertical angles are congruent. ∠1 = ∠3 Vertical angles are congruent. Vertical Angles are congruent. Vertical Angle Theorem Daniel's Proof Statement Justification ∠1 + ∠2 = 180° Definition of Supplementary Angles ∠1 + ∠4 = 180° Definition of Supplementary Angles ∠1 + ∠2 = ∠1 + ∠4 Transitive Property of Equality ∠2 = ∠4 Subtraction Property of Equality
Both Kelly and Daniel are correct.
Neither Kelly or Daniel is correct.
Kelly is correct, but Daniel is not.
Daniel is correct, but Kelly is not.

The fencing that is needed to enclose the garden is 36 meters.

Let the width be represented by x.

Let the length be represented by x+2.

The area is given as 80m².

Therefore, the length and width will be calculated thus;

x(x + 2) = 80

x² + 2x - 80 = 0

x² + 10x - 8x - 80 = 0

x(x + 10) - 8(x + 10) = 0

x - 8 = 0

x = 8

The width is 8 meters and the length is 10m.

The perimeter will be:

= 2(8m + 10m)

= 2 × 18m

= 36m

In conclusion, the correct option is 36 meters.

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Answer: AA'+BB'+CC'+DD'+EE'=31.5 inches.

Step-by-step explanation:

As we know a translation is a transformation that maintain distance.

therefore ,if line segment YZ was used to translate ABCDE then

⇒ YZ=AA'=BB'=CC'=DD'=EE'=6.3 inches

Thus AA'+BB'+CC'+DD'+EE' =5 times YZ=5×6.3=31.5 inches.

Translation is a function that moves an object for a particular distance such that every point of the object must be moved in the same direction and for the same distance.

40hrs*60mins/1hr=2400mins

2400mins*60secs/min=144,000secs

First we can calculate how many seconds there are in an hour:​

​Since 1 hour has 60 minutes and each minute has 60 seconds.

​Then 1 hour = 60 minutes * 60 seconds/1minute = 3,600 seconds.

​Now we have to multiply x 40 to calculate how many seconds there are in 40 hours.

​In a 40-hour work week = 40 hours * 3,600 seconds/1hour = 144,000 seconds

​Answer : 144,000 seconds there are in a 40-hour work week

​Hope this helps!​​​​

​[tex]\textit{\textbf{Spymore}}[/tex]​​​​​​​

Answers

C = 58.84

B = 97.16°

Explanation

The sine rule states:

SinA/a = sinB/b

∴ sin24 / 77 = sinC / 162

 sinC = (162 × sin24)/77

         = 65.89/77

         = 0.85573

C = 58.84°

Angles in a triangle add up to 180°

∴ B + 24 + 58.84 = 180

  B = 180 - 24 - 58.84

      = 180 - 82.84

      = 97.16°

      =

Using the Law of Sines, which states that the ratio of a side length to the sine of its opposite angle is the same for all sides, you can solve for the missing angle. Rearrange the formula to sinC = c * sinA / a, then take the inverse sine of both sides to find the measure of the missing angle.

To find the missing angle m∠C using the Law of Sines, you first need to know the lengths of the sides of the triangle and one of the angles. The Law of Sines states that the ratio of the length of a side of a triangle to the sine of its opposite angle is the same for all three sides of the triangle. In other words, if a, b, and c represent the lengths of the sides and A, B, and C represent the measures of the opposite angles, we have: sinA/a = sinB/b = sinC/c.

To solve for m∠C, you rearrange the Law of Sines to: sinC = c * sinA / a. After that you take the inverse sine (or arcsin) of both sides to find m∠C = arcsin(c * sinA / a). Notice that you are assuming that the sine of the missing angle is positive, which is valid for angles less than 180 degrees.

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Hey there!!

Equation Given : x + 3x - 36

In order to solve this, we will need to combine the like terms.

What are like terms?

Like terms are terms which have the same variable, in the equation given, the variable mentioned is x and hence, the like terms are x and 3x.

Now, we will need to combine x and 3x.

Let's take x as 1x and 3x as 3x.

Now, we will need to add both these like terms.

1x + 3x

x will be common, we will need to add 1 and 3

1 + 3 is 4 and hence, 1x + 3x = 4x

Hence, the final equation would be :

4x - 36

Hence, the answer is option ( c )

Hope my answer helps!

Answer:

4x-36 C

Step-by-step explanation:

Answer:

Jerry does [tex]2.11[/tex] cases per hour (Rounded to 2 decimal places). As we cannot do 0.11 cases. We can say Jerry does 2 cases per hour.

Step-by-step explanation:

to find the number of cases per hour, we have to divide the number of cases by number of hours taken for those cases,

Number of cases per hour = [tex]\frac{5cases}{2\frac{3}{8} hours}[/tex]

                                             =[tex]\frac{5}{\frac{19}{8} } \\[/tex] cases per hour

                                             =[tex]\frac{5*8}{19}[/tex] cases per hour

                                             =[tex]\frac{40}{19}[/tex] cases per hour

                                              =[tex]2.11[/tex] cases per hour (Rounded to 2 decimal places)

As we cannot do 0.11 cases. We can say Jerry does 2 cases per hour.

C = 14π cm ( in terms of π )

the circumference (C) of a circle is calculated using the formula

C = πd ( where d is the diameter )

C = 14π cm ≈ 3.14 × 14 - 43.96 cm

Solution is given in attachment below.

Two factors of x²-12x+36 are

(x-6) and (x-6)

Solution;

x²-12x +36

x²-6x -6x +36  ( split -12x in two parts such that if add them we will get-12x and if multiply will get 36x²)

Taking x common from first two terms and 6 from next two terms

x(x-6) -6(x -6)

taking (x-6) common

(x-6)(x-6)

Answer:

[tex]x^2 - 12x + 36 = (x-6)(x-6) = (x-6)^2[/tex]

Step-by-step explanation:

We are given the following expression:

[tex]x^2 - 12x + 36[/tex]

We need to factor the given expression.

We will do this with the help of technique of splitting the middle term.

Factorization can be done as:

[tex]x^2-12x + 36\\=x^2 - 6x-6x+36\\=x(x-6)-6(x-6)\\=(x-6)(x-6)\\=(x-6)^2[/tex]

Thus, the factored form of given expression is:

[tex]x^2 - 12x + 36 = (x-6)(x-6) = (x-6)^2[/tex]

Answer:

The right graph is A.

Step-by-step explanation:

When x=0, -5y=15, y=-3

That means (0,3) is on that line.

When y=0, 4x=15, x=15/4

That means (15/4,0) is on that line too.

Based on the two points, the graph is A.

Answer:

ans is A

Step-by-step explanation:

heres another way to solve this

convert the eqn to standard form:

4x-5y = 15

15+5y = 4x

5y = 4x - 15

y = 4x/5 - 3

with y=mx+C, where m is slope and C is y-intercept

slope is 4/5 positive and y-intercept is -3

the ans is a

Using proportion concepts, it is found that the equivalent statement is:

(F) The price now is 66 2/3 % of what it was before

The statement is:

"price decreased by 1/3"

It decreases by 1/3, thus it is [tex]\frac{2}{3} = 0.6667 = 66\frac{2}{3}\%[/tex] of what was before, which means that the equivalent statement is given by option F.

As for the other statements, they do not have the correct percentage or ratio, which we found above.

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Answer:

Correct choice is D

Step-by-step explanation:

Consider regular 60 sided polygon (regular means all sides are of equal length). Connect the center of this polygon with each polygon's vertex. You get 60 equal isosceles triangles with base that is polygon's side. The measure of the angle opposite to the base is

[tex]\dfrac{360^{\circ}}{60}=6^{\circ}.[/tex]

Rotating the polygon by 6° over the center, each such triangle will map onto the previous triangle. Thus, the least angle by which a regular 60-gon can be rotated so that it maps onto itself is 6°.

Answer:

The commutative property lets you group like terms together:

... 5x +3x +9x +20 +7

Step-by-step explanation:

If we divide the expression into 4 groups:

...[5x] +(20) +(3x +9x) +[7]

according to the commutative property of addition, we can swap the groups in curved parentheses.

... [5x] +(3x +9x) +(20) +[7]

_____

The distributive property lets you combine x terms:

... (5 +3 +9)x +27

... 17x +27 . . . . . . the simplified form of the expression

Answer:

B. (x-8)(x-5).

Step-by-step explanation:

Given  : Equations .

To find : Which of the given expressions results in 0 when evaluated at x = 5.

Solution : We have given equations

We need the result zero.

We can see from the given equation (x-8) (x-5)

If we plug x = 5.

(5 -8 )( 5 -5).

-3 (0).

0. (  multiply with zero to any number it will always be zero )

Therefore, B. (x-8)(x-5).

Formula: P(A or B)=P(A)+P(B)-P(A or B)  

p(c)=7/18

p(s)=6/18

p(c or s)=2/18

0.39+0.33-0.11=

answer:0.61

Formula: P(A or B)=P(A)+P(B)-P(A or B)  

p(c)=7/18

p(s)=6/18

p(c or s)=2/18

0.39+0.33-0.11=

answer:0.61

1 [tex]\frac{1}{2}[/tex] dozen

1 dozen = 12

to convert to dozen, divide 18 by 12

[tex]\frac{18}{12}[/tex] = [tex]\frac{3}{2}[/tex] = 1 [tex]\frac{1}{2}[/tex] dozen

Sarah bought 1.5 dozen of eggs as 1 dozen of eggs has 12 eggs as defined "Twelve objects, twelve shapes, or twelve numbers make up a dozen. Doz or dz are used to shorten it. One of the oldest common units of measurement is the dozen".

Comparing a physical quantity to a known standard quantity of the same kind is the process of measurement. For instance, measuring length with Vernier Calipers and determining wire diameter with a screw gauge.

One of the most basic and straightforward traditional units of measurement is the dozen. The 12-base number system is referred to as duodecimal or dozenal. A dozen is a collection of precisely twelve figures, shapes, or things. You can spell it out as doz or dz. So, a dozen is equal to twelve. The counting of the finger bones with the thumb is thought to have marked the beginning of the dozen. It has to do with nature. Twelve moon cycles or zodiac signs, 12 months, and two cycles of 12 hours each make up a day. These days, many household items and other items are sold by the dozen.

12 eggs=1 dozen

18 eggs=

=18*1/12

=18/12

=3/2

=1.5 dozen.

Given that a dozen of eggs has 12 eggs by definition, Sarah purchased 1.5 dozen eggs. "A dozen is made up of twelve things, twelve shapes, or twelve numbers. It can be abbreviated with doz or dz. The dozen is one of the earliest common units of measurement ".

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1) The probability of getting a queen is 187/10000 which is 0.0187 = 1.87%

2) The probability is 449 / 479 which is 0.937 = 93.7%

You may need to round the answers. It doesn't say if they need to be rounded or not.

Hi ShadowHawk,

1) If you conduct an experiment and randomly pull a card from a deck of cards 10,000 times, getting a Queen of Hearts 187 times, what is the experimental probability of drawing a Queen of Hearts the next time?

187/10,000 = 1.87% = 1.9%

2) If a kicker has kicked a ball 479 times for the extra point and scored the point 449 times, what is the experimental probability of the kicker making the next field?

449/479 = 93.7% = 94%

Answer:

option 2=11/20  is the answer.

Step-by-step explanation:

given that there are 20 cards numbers 1,2... 20.

A card is randomly drawn.

We have to find the probability of drawing either 1 or even card.

P(drawing even card) = no of even cards/total cards = 10/20= 0.5

P(drawing one) = no of 1's/total cards = 1/20 = 0.05

P(drawing both one and even card) = 0 (since impossible)

Hence P(drawing even or one) =0.5+0.05-0

=0.55

= 11/20

Hence option 2 is the answer.

Answer : 11/20

There are 20 cards labeled from 1 to 20 in a bag. A card is randomly selected from the bag.

Total number of outcomes = 20

outcomes of an even number ={2,4,6,8,10,12,14,16,18,20}

So number of outcomes of even number = 10

outcomes of a 1 ={1}

So number of outcomes of a 1 = 1

Number of outcomes of even number and a 1 = 10+1 = 11

Probability ( any event) =number of favorable outcomes divide by total  number of outcomes

Probability (getting an even number or a 1) = [tex]\frac{11}{20}[/tex]

Answer: So, the probability will be

[tex]P( \text{getting a blue ball })=\frac{30}{70}=\frac{3}{7}[/tex]

Step-by-step explanation:

Since we have given that

Number of blue balls =30

Number of red balls = 40

Number of white balls = 30

Since there are 100 balls in total ,

As we have given that there is no white ball chosen.

So, only 70 balls are left with us , from which we choose a blue ball

So, the probability will be

[tex]P( \text{getting a blue ball })=\frac{30}{70}=\frac{3}{7}[/tex]

The conditional probability of picking a blue ball given that a white ball was not picked is 0.43. This is calculated by dividing the number of blue balls by the total remaining balls after excluding the white balls.

To solve this question, we need to understand the concept of conditional probability. Given that we have 30 blue balls, 40 red balls, and 30 white balls, we have a total of 100 balls in the bag. The problem states that a white ball was not chosen. From that, we have eliminated the 30 white balls from the total, leaving us with 70 balls (30 blue and 40 red).

In the case of the conditional probability of choosing a blue ball, given that a white ball was not chosen, we are just focused on the remaining 70 balls. So, the probability is calculated by dividing the number of blue balls by the total remaining balls. Hence, the conditional probability is 30/70 = 0.43 (approximately).

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Answer:12/4

Step-by-step explanation:

Answer:

 Length of one side of Keisha's kitchen = 15 feet.

Explanation:

  Let the side of square be a. The area of a rectangle is breadth x width. Here breadth = width = side of square

 Area of square = a x a = [tex]a^2[/tex]

It is given that area of Keisha's kitchen is known, so she can find side of the square by finding square root of the area.

So we have area = 225 feet squared = [tex]a^2[/tex]

So length of one side of Keisha's kitchen = [tex]\sqrt{225} =15[/tex]feet

The length of one side of Keisha's kitchen is 15 feet, as the area of a square is found by squaring the side length and the square root of 225 is 15.

Keisha's kitchen is shaped like a square, which means all four sides of the kitchen are of equal length. Given that the area of the kitchen is 225 square feet, we need to find the length of one side. The formula below is used to find the area of a square:

So, let’s set up the equation:

Or in mathematical terms:

To find the side length, we need to take the square root of 225:

Knowing that [tex]\sqrt{225}[/tex] = 15, we have:

Therefore, each side of Keisha's kitchen is 15 feet long.