write a two column proof. fill in the missing reasons for the correct statements. given: ABCD is a rectangle. L, M, N, and P are the midpoints of AB, BC, CD, and DA respectively. prove: NM≈PL

Answer:[tex]\sqrt{6}[/tex]

Step-by-step explanation:

The distance between 2 points is given by:

[tex]\sqrt{(x2-x1)+(y2-y1)}[/tex]

Let (6,3) be (x1, y1) and (8,7) (x2,y2).

=[tex]\sqrt{(8-6)+(7-3)}[/tex]

=[tex]\sqrt{2+4}[/tex]

=[tex]\sqrt{6}[/tex]

Hope this helps :)

[tex]\sqrt{p^1^2-16p^6+80}[/tex]

A pic down below is given:

Answer:

Domain is x-value and range is y-values

Step-by-step explanation:

x = k - 2, y = 8 - 2k, z = k is the general solution of the given system, where k is an arbitrary, if k = 1

x = -1, y = 6, z = 1 is the solution.

Ax = [tex]\left[\begin{array}{ccc}1&1&1\\1&2&3\\1&4&7\end{array}\right][/tex] [tex]\left[\begin{array}{ccc}x\\y\\z\end{array}\right][/tex]

and b = [tex]\left[\begin{array}{ccc}6\\14\\30\end{array}\right][/tex]

the augmented matrix is [A:B] = [tex]\left[\begin{array}{ccc}1&1&1:6\\1&2&3:14\\1&4&7:30\end{array}\right][/tex]

we need to reduce the augmented matrix [A:B] to row echelon form by applying elementary row transformations only.

operating R₂→R₂-R₁ , R₃→R₃-R₁

[A:B] = [tex]\left[\begin{array}{ccc}1&1&1:6\\0&1&2:8\\0&3&6:24\end{array}\right][/tex]

operating, R₃→R₃-3R₃

~  [tex]\left[\begin{array}{ccc}1&1&1:6\\0&1&2:8\\0&0&0:0\end{array}\right][/tex]

which is the row echelon, form of the matrix [A:B]

we have rank of [A:B] = the number of the non zero rows in echelon form = 2

also by the same elementary transformation we get,

A ~ [tex]\left[\begin{array}{ccc}1&1&1\\0&1&2\\0&0&0\end{array}\right][/tex]

∴ rank of A = 2

since rank A = rank  [A:B] = 2 < number of unknowns

therefore, the given equation are consistent and will have an infinite number of solutions.

We see that the given system of equations is equivalent to the matrix equation

[tex]\left[\begin{array}{ccc}1&1&1\\0&1&2\\0&0&0\end{array}\right][/tex]  [tex]\left[\begin{array}{ccc}x\\y\\z\end{array}\right][/tex]  =  [tex]\left[\begin{array}{ccc}6\\8\\0\end{array}\right][/tex]

which gives the equations x + y + z = 6 ........(1)

and y + 2z = 8 .......(2)

from (2), y = 8 - 2z, putting the value of y in (1) we get,

x = 6 - y - z = 6 (8 - 2z) z = z - 2

taking z = k, we get x = k - 2, y = 8 - 2k, z = k is the general solution of the given system, where k is an arbitrary,

if k = 1

x = -1, y = 6, z = 1 is the solution.

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The probability of the intersection of two events occurring can never be more than the probability of the union of two events occurring.

False.

It should be stated that the likelihood of the intersection of two events occurring is always less than the likelihood of the events occurring together.

It is always less likely than or equal to the likelihood of either event occurring alone for an intersection of two events, which is the chance that both occurrences take place.

In other words, the probability of the intersection and the probability of the union are subsets of one another.

The chance of the intersection of two events occurring can never be greater than the likelihood of the union of two events occurring, hence that is the right statement.

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Mr. Titus travels a total of 7476 miles annually between Charlotte, North Carolina, and New York City.

Expression in maths is defined as the relation of numbers variables and functions by using mathematical signs like addition, subtraction, multiplication, and division.

Given that twelve times a year, Mr. Titus makes the trip from Charlotte to New York City and back. Each round trip covers a total distance of 623 miles.

The total distance will be calculated as:-

Distance = 12 x 623

Distance = 7476 miles

Therefore, Mr. Titus' annual mileage between Charlotte, North Carolina, and New York City is 7476 miles.

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Answer:

-16x² + 10x - 14.

Step-by-step explanation:

To find the composition of two functions, (f g)(x), we first evaluate g(x) and then substitute the result into f(x).

So, let's first evaluate g(x):

g(x) = 8x² - 5x + 7

Next, substitute g(x) into f(x):

(f g)(x) = f(g(x)) = f(8x² - 5x + 7) = -2(8x² - 5x + 7) = -16x² + 10x - 14

Therefore, (f g)(x) = -16x² + 10x - 14.

Answer: 6x - 3

Step-by-step explanation:

I believe this question is asking you to expand the equation

Distribute the 3 to both terms on the inside to get: 3(2x -1) = 6x-3

Answer:

Step-by-step explanation:

i believe its 5x?

sorry if im wrong but i times 3 x 2 then 6 -1 or you can do 3 x 2 then 3 x -1 to get 6x and -3

Check the picture below.

The vertical difference in height between

i. A and B = 1.55

ii. B and C = 1.27

iii. A and C. = 2.82

the angle of elevation from A to C

The vertical difference in height is worked using SOH CAH TOA

Sin = opposite / hypotenuse - SOH

Cos = adjacent / hypotenuse - CAH

Tan = opposite / adjacent - TOA

The directions describes a right angle triangle o

A and B

sin 15 = vertical difference / 6

vertical difference = 6 sin 15

vertical difference = 1.55

B and C

sin 25 = vertical difference / 3

vertical difference = 3 sin 25

vertical difference = 1.27

A and C

A to B + B to C

= 1.55 + 1.27

= 2.82

angle of elevation from A to C

sin x = 2.82 / 5

x = arc sin (2.82/5)

x = 34.33 degrees

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Answer:B

Step-by-step explanation:

R^2=Q^2-P^2

R^2=2025

R=45

Answer:

b) 45cm

Step-by-step explanation:

by pythagoras theorem:

R² = P² - Q²

R² = 53² - 28² = 2809 - 784

R² = 2025

R = √2025

R = 45cm

Hope this helps!

Step-by-step explanation:

Rather than give you the full answer, let me point out the things that you need to know to work this out for yourself.

The surface area of the solid is the sum of all of the areas of its faces.

The area of a right triangle is a well-known formula. You should already know this.

If carpeting cost AED 12 per square meters for the bedroom of 75m by 50m, it will cost AED 45,000 to lay carpet for Linda's entire bedroom.

To calculate the cost of laying carpet for Linda's bedroom, we need to know the area of the bedroom and the cost per square meter of the carpeting.

Linda's bedroom is a rectangle with a length of 75 meters and a width of 50 meters. To calculate the area of the bedroom, we multiply the length by the width:

Area = length x width = 75 meters x 50 meters = 3750 square meters

Now that we know the area of the bedroom is 3750 square meters, we can find the total cost of the carpeting by multiplying the area by the cost per square meter. The cost per square meter is given as AED 12, so:

Total cost = area x cost per square meter = 3750 square meters x AED 12/square meter

Multiplying the area by the cost per square meter gives us:

Total cost = AED 45,000

Therefore, it will cost AED 45,000 to lay carpet for Linda's entire bedroom.

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It will take 20 pounds for both charges to be the same.

An equation containing variables with its highest power as one is called linear equation.

To ship a package,

UPS charges $4 for the first pound and $0.50 for each additional pound.

FedEx charges $6 for the first pound and $0.40 for each additional pound.

These can be written in the linear equation form as,

Let p be the pound charges by both UPS and FedEx,

then, 4+0.50p-------(1)

6+0.40p-----(2)

When the charges are same, (1)=(2)

4+0.50p = 6+0.40p

⇒0.10p=2

⇒p=20

Hence, this means that, it will take 20 pounds for both charges to be the same.

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Answer:

О m³   (cubic meters)

Step-by-step explanation:

The volume formula is length * width * height

Example:

volume = 3m * 5m * 4m

volume = 60m³

The solution is, О m³   (cubic meters), is the correct label to show volume.

In mathematics, volume is the space taken by an object. Volume is a measure of three-dimensional space. It is often quantified numerically using SI derived units or by various imperial or US customary units. The definition of length is interrelated with volume.

here, we have,

to find the correct label to show volume.

now, we know that,

The volume formula is length * width * height

as we know that,

the standard unit for length is meter (m).

now, we have,

length has unit m

width (= length) has unit m

and, height (=length)  has unit m

so, we get,

Volume = length * width * height

             = m * m* m  (as unit)

             = m³

Example:

volume = 3m * 5m * 4m

volume = 60m³

Hence, The solution is, О m³   (cubic meters), is the correct label to show volume.

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Answer:

13 square units

Step-by-step explanation:

The composite figure can be decomposed into

2 semicircles each of diameter 3

1 rectangle of height 1 and length 5

1 square of side 1

Radius of each semicircle = 3/2 = 1.5 units
Area of a semicircle of radius r = 1/2 area of circle of radius r = 1/2 x π x r²
Two semicircles make a circle

So area of the two semicircles = 2 x (1/2 x π x r²) = πr² = π x 1.5²
= 2.25π = 7.07

= 7 square units rounded to nearest whole number

Area of the rectangle = width x length = 1 x 5 = 5 square units

Area of square of side 1 = 1 x 1 = 1 square unit

Total area of shaded area = 7 + 5 + 1 = 13 square units

Answer:

Step-by-step explanation:  (10)(A) Add and subtract polynomials of degree one and degree two. (10)(B) Multiply polynomials of degree one and degree two. (10)(C) Determine the quotient

Hope it helps =}

Answer:

b

Step-by-step explanation:

The soap used by the machine last year is 5399.76 gallons.

The denominator of a percentage (also known as a ratio or fraction) is always 100. Sam, for instance, would have received 30 out of a possible 100 points if he had received 30% on his arithmetic test. In ratio form, it is expressed as 30:100 and in fraction form as 30/100. In this case, the percentage symbol "%" is read as "percent" or "percentage." This percent symbol can always be changed to a fraction or decimal equivalent by using "divided by 100."

Let the soap used last year = x.

Then, according to the given condition:

4,508.8 = x (1 - 16.5%)

4,508.8 = x (83.5/100)

x = 4,508.8(100) / 83.5

x = 5399.76

Hence, the soap used by the machine last year is 5399.76 gallons.

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At 9:00 a.m., the rate of people entering the amusement park is 533 people per hour, while the rate of people leaving the amusement park is 67 people per hour.

(1) At 9:00 a.m., the rate of people entering the amusement park is given by the derivative of the entering function, which is:

f'(t) = 400 + 200cos(πt/12).

At t = 9, this rate is 400 + 200cos(π*9/12) = 400 + 200cos(3π/4) ≈ 533 people per hour.

(2) At 9:00 a.m., the rate of people leaving the amusement park is given by the derivative of the leaving function, which is:

g'(t) = 200 - 200cos(πt/12).

At t = 9, this rate is 200 - 200cos(π*9/12) = 200 - 200cos(3π/4) ≈ 67 people per hour.

the complete question is :

both are measured in people per hour and the time t is measured in hours after midnight. these functions are valid for , the hours during which the park is open. at time , there are no people in the park. (1) how fast are people entering the amusement park at 9:00 a.m.? (2) how fast are people leaving the amusement park at 9:00 a.m.?

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Given:-

By using formula:-

Solution:-

[tex] \: [/tex]

[tex] \: [/tex]

[tex] \: [/tex]

[tex] \: [/tex]

hope it helps! :)

The student must she score on the fourth test in order to raise her test average 4 points is 4 points.

An average is a single number taken as representative of a list of numbers, usually the sum of the numbers divided by how many numbers are in the list.

Given that, a student has completed 3 tests in biology class, we need to find that how many points above her present test average must she score on the fourth test in order to raise her test average 4 points,

Let the required point be x,

According to question,

x+4×3 / (3+1) = 4

x+12 = 16

x = 4

Hence, the student must she score on the fourth test in order to raise her test average 4 points is 4 points.

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the first choice is the right answer

please check my working for guidance

As per the ratio, the number of men on the sight-seeing tour is 4.

In the given sight-seeing tour, we are told that there were 14 people in total. We are also given the ratio of women to children, which is 5 to 2. This means that for every 5 women on the tour, there were 2 children.

To find the number of men on the tour, we need to first find the number of women and children. We can do this by dividing the total number of people by the ratio of women to children.

Let's use a variable to represent the number of sets of 5 women and 2 children. We'll call this variable "x".

So, the number of women on the tour is 5x and the number of children is 2x.

Now, we can set up an equation to find the value of x:

5x + 2x = 14

This equation represents the total number of women and children on the tour, which is equal to 14.

Simplifying the equation, we get:

7x = 14

Dividing both sides by 7, we get:

x = 2

This means that there were 2 sets of 5 women and 2 children on the tour. So, the number of women is:

5x = 5(2) = 10

The number of children is:

2x = 2(2) = 4

Now, we can find the number of men by subtracting the number of women and children from the total number of people:

14 - 10 = 4

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The percentage of the shipping crate when compared to the total weight of the shipment would be = 16%

The weight of two granite specimen = 22 pounds

The weight of the crate = 20 pounds

The weight of shipping crate = 8 pounds

The total weight of the whole shipment = 22+20+8 = 50 pounds.

Therefore the percentage of shipping crate as compared to the total weight;

= 8/50 × 100/1

= 800/50

= 16%

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Answer:

1m/sec

Step-by-step explanation:

Mr. Hall spent 3 seconds to increase his speed to 3m/sec increasing 1m/sec, don't over think it.

Answer:

Step-by-step explanation:

Given room looks like a rectangular room.Let w be the wide and l be long of the rectangular room respectively.Given,w=10 feet and l=24 feet.

we know area of the rectangular room= l*w

So,area=10*23

area=230 sq.feet

Given,cost of trim=$0.85 per foot

So,total cost =230* 0.85

=195.5

So,Jennifer charges $195.5 to buy enough

Answer:

See proof below

Step-by-step explanation:

We will use the SAS condition for congruency of two triangles

SAS (Side-Angle-Side)

If any two sides and the angle included between the sides of one triangle are equivalent to the corresponding two sides and the angle between the sides of the second triangle, then the two triangles are said to be congruent by SAS rule.

In the two triangles ΔHIK and ΔJIK we have
m∠4 = m∠3  (given)

HK ≅ KJ

IK is the common side

So the two sides HK and IK are equal and the included angles ∠4 and ∠3 are also equal

So by SAS, the two triangles are equal

So m∠2 = m∠1

which means IK bisects ∠HIK

The solution of the system of equation y - 10 = 2x and 1/2 y = x + 5 is

The simultaneous equation is solved by substitution method as follows

y - 10 = 2x and

1/2 y = x + 5

Isolate y in the first equation to get

y = 2x + 10

substitute y in 1/2 y = x + 5

1/2 (2x + 10) = x + 5

x + 5 = x + 5

x = 0

substitute x = 0 into y = 2x + 10

y = 2(0) + 10

y = 10

hence the solution is (0, 10)

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1. 121 degree. 2. 15 degree. The side of the dilated triangle increases by scale factor. Here, 1.5, thus: 3. LM = (20)(1.5) = 30 4. MN = 26(1.5) = 39 5. RT = 57/1.5 = 38. 6. Triangle RST is congruent to triangle LMN.

Transformations involve the reflection, refraction, or translation of forms on a coordinate plane. Felix Klein put forth a novel perspective on geometry in the 19th century called transfinite geometry. The majority of geometric principles depend on the transmissions of objects.

Transfrmatiions enable the modification of any image in a coordinate plane. You can better understand the graphics in video games by using the mathematical laws of transmission.

As a result, the red triangle is a dilation of the blue triangle.

When triangle is dilated the angles remain the same. Thus,

1. 121 degree.

2. 15 degree.

The side of the dilated triangle increases by scale factor. Here, 1.5, thus:

3. LM = (20)(1.5) = 30

4. MN = 26(1.5) = 39

5. RT = 57/1.5 = 38

6. Triangle RST is congruent to triangle LMN.

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The requried solutions are as follows,
(1) the original price is $450.   (2)  the original price is $172.40.

Sale price is defined as the price of a product marked including of various price cut such as discounts.

Here,
If the percent of discount is 80% and the sale price is $90, we can use the following formula to find the original price x (let)

Sale price = Original price - Discount

$90 = x - 0.8x

Simplifying the right-hand side:

$90 = 0.2x

x = $450

Therefore, the original price is $450.

If the percent of discount is 15% and the sale price is $146.54, we can use the same formula:

Sale price = Original price - Discount

$146.54 = x - 0.15x

Simplifying the right-hand side:

$146.54 = 0.85x

x = $172.40

Therefore, the original price is $172.40.

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