Copy the problem and write a statement/reason proof

It is given that ABCD is a rectangle. We have to give reasonings for the statements.

What is the rectangle?

A rectangle is a four-sided polygon with four right angles. The opposite sides of a rectangle are equal in length (congruent) and the opposite angles are equal in measure (congruent). The opposite sides are parallel to each other. A rectangle can be defined as a special case of parallelogram where all angles are right angles.

Given: ABCD is a rectangle

Prove: triangle ADC is congruent to triangle BCD

1. Given ABCD is a rectangle

2. By definition of rectangle, opposite sides are congruent (AD is congruent to BC)

3. By definition of rectangle, opposite angles are right angles (angle ADC and angle BCD are right angles)

4. By definition of right angle, adjacent angles are congruent (angle ADC is congruent to angle BCD)

5. By reflexive property, an object is congruent to itself (DC is congruent to DC)

6. By SAS Congruence (Side-Angle-Side), if two triangles have two congruent sides and the included angle congruent, the two triangles are congruent. Since AD=BC and angle ADC= angle BCD, and DC=DC, then triangle ADC is congruent to triangle BCD.

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The line that is parallel to y = 1/5x + 4, is A. 5 y - x = 6.

Parallel lines are any two or more lines that all lie in the same plane and never cross one another. They are equally spaced apart and have the same incline. No matter how far we extend a parallel line, it will never meet another parallel line.

As mentioned parallel lines will have the same slope so the line that is parallel to y = 1/5x + 4 would have the same slope of 1 / 5.

Converting the first option to slope intercept form gives:

5 y - x = 6

5 y = 6 + x

y = 6 / 5 + x / 5

y = 1.2 + 1 / 5 x

This slope is the same as y = 1/5x + 4 so they are parallel.

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The area of the irregular figure is 65.12 cm².

We know that a shape is said to be irregular if the shape does not fit into any of the known patterns of shape that we have. In this case, we have a kind of shape that is made up of the rectangle and the semi circle.

We know that we can be able to obtain that area of the rectangle by the use of the formula;

A = l * w

A = area

l = length

w = width

We then have;

A = 8 cm * 5 cm

= 40 cm^2

For the semi circle;

A =  (π r²)/2

A = (3.14 (4²))/2 = (3.14*16)/2 = 50.24/2 = 25.12cm²

Total area of the figure = 40 cm² + 25.12 cm² = 65.12 cm²

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[tex](\stackrel{x_1}{-2}~,~\stackrel{y_1}{8})\qquad (\stackrel{x_2}{4}~,~\stackrel{y_2}{8}) \\\\\\ \stackrel{slope}{m}\implies \cfrac{\stackrel{\textit{\large rise}} {\stackrel{y_2}{8}-\stackrel{y1}{8}}}{\underset{\textit{\large run}} {\underset{x_2}{4}-\underset{x_1}{(-2)}}} \implies \cfrac{0}{4 +2} \implies \cfrac{ 0 }{ 6 } \implies \text{\LARGE 0}[/tex]

Answer: 9/20

Step-by-step explanation:

45/100 ÷ 5/5 = 9/20

To convert 0.45 into a fraction, we can consider it as 45/100. Then to get the simplest form of the fraction, we divide both the numerator and denominator by their greatest common factor which is 5. So, the simplest form of the fraction is 9/20. Therefore Matt ate 9/20 of his birthday cake.

Answer:
16.01 gallons of fuel.

Step-by-step explanation:

So we already know that there were initially 1.9 gallons. We have to add 14.11 gallons of fuel to the starting amount.

14.11 + 1.9 = 16.01 gallons

I hope this was able to help you :D

To find out how much fuel is in Leila's car now, we need to add the amount of fuel she just put in to the amount that was already in the car.

Leila put 14.11 gallons of fuel in the car and there were 1.9 gallons in the car to begin with.

So, 14.11 gallons + 1.9 gallons = 16.01 gallons

This is the correct answer because 14.11 gallons is the fuel Leila put into her car and 1.9 gallons is the fuel that was already in the car. Adding these two values together gives the total amount of fuel in the car now, which is 16.01 gallons.

Answer: The length of a side of a regular pentagon can be found using the formula, side = 2r * sin(π/5), where r is the radius of the circle that the pentagon is inscribed in. Using this formula, the length of a side of the pentagon is approximately 4.08 cm or 40.8 mm (rounded to the nearest mm).

Answer:

The expression that represents the given situation is 6P - 16.

Step-by-step explanation:

The teacher got six boxes of pencils, and each box contains P pencils. Since the teacher used 16 pencils in the first month of school, the total number of pencils left after the first month can be represented by the expression 6P - 16.

This expression means that the teacher started with 6 boxes of pencils, each containing P pencils, for a total of 6P pencils. But since the teacher used 16 pencils in the first month, the total number of pencils left after the first month is 6P - 16.

The equation that can be used to solve for the number of points that Jan scored in the game is:

x + 2x + (x-10) = 70

Given that Jan scored twice as many points as Tritt, we can use the equation

2x = Tritt.

Given that Jan scored ten points fewer than Sarah, we can use the equation

x = Sarah - 10.

Also, we know that the total number of points scored by all three players is 70, so we can use the equation:

x + Tritt + Sarah = 70

If we replace Tritt with 2x and Sarah with x-10, we get:

x + 2x + (x-10) = 70

So the equation that can be used to solve for the number of points that Jan scored in the game is:

3x -10 = 70

We get x = 30, which means Jan scored 30 points in the game.

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Answer: i know what school ur from my school page looks the same (we in CCA) XDD

anyways this question is very vague. but i think its c.

Step-by-step explanation:

again its very vague but i tried i think its c

The population growth rate can be calculated using the equation x = x₀ (1+r)ⁿ. The population after 8 years will be 66 frogs.

The population growth is the increase in population after the specified number of years. Lets look into the data which is given.

The initial population is 6 tree frogs.

Population growth percent = 35%    

Rate of growth, r = 35/100 = .35

The population growth is calculated using the equation,  x = x₀ (1+r)ⁿ

     x₀ is  initial population

     r is the rate

    n is the number of years.

x = 6 (1+r)⁸ = 66.19

So the population of frog after 8 years will be 66.

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Answer: -2

Step-by-step explanation:I'am in a rush right now sorry

The range of the values of x is 7<x<2.

In the given quadrilateral we can see that 2 of its sides are equal and the diagonal of the quadrilateral divides the quadrilateral into 2 triangles.

we can label the diagonal as "b" and the equal sides as "a".

when we apply the cosine law on the upper triangle, we get,

(2x-4)² = a² + b² - 2abcos45°

=(2x-4)² = a² + b² - 2ab×1/√2

=(2x-4)² = a² + b² - √2ab

Similarly, applying the cosine law on the lower triangle,

10² = a² + b² - 2abcos60°

= 10² = a² + b² - 2ab×1/2

= 10² = a² + b² - ab

we can clearly see from the above 2 equations formed by applying cosine law to the triangles that,

(2x-4)²<10²

2x-4<10

2x<14

x<7

and we know that 2x-4 has to be positive So,

2x-4>0

2x>4

x>2

combining these inequalities we get,

7<x<2

which gives the range, where x will belong

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Answer:

Step-by-step explanation:

The answer that thay already gave is backwards its actully 2<x<7 in acellus

Answer:

Step-by-step explanation:

After solving, total 360 different executive boards can there be.

In the specified office have one member of the executive board is the president, another is the vice president, a third is the secretary, and the last one the treasurer.

So there are total 6 members.

The total number of members in executive board = 4

So, the ways of selecting different executive boards = [tex]^{6}P_{4}[/tex]

The ways of selecting different executive boards = [tex]\frac{6!}{(6-4)!}[/tex]

The ways of selecting different executive boards = [tex]\frac{6!}{2!}[/tex]

The ways of selecting different executive boards = [tex]\frac{6\times5\times4\times3\times2!}{2!}[/tex]

The ways of selecting different executive boards = 6 × 5 × 4 × 3

The ways of selecting different executive boards = 360

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To learn more about

The complete question is:

From a committee of 6 members, suppose that each member of the executive board also has a specified office: one member of the executive board is the president, another is the vice president, a third is the secretary, and the last one the treasurer. How many different executive boards can there be?

The probability of the car encountering it's first red light on the third day, i.e., P(Y = 3) will be 0.1479

According to the question,

we have to calculate the probability of the car encountering it's first red light on the third day, i.e., P(Y = 3)

Here,

Probability of encountering a Red light = 0.35, since traffic light at the intersection is red 35% of the time.

And Y is the number of days that pass up to and including the first time the car encounters a red light, i.e.,

The distribution here is a geometric one, where

P(Y = 3)

= P(Not red light in initial 2 lights) x P(red light in third light)

= [(1 - 0.35)² X 0.35]

= 0.1479

so, the probability of the car encountering it's first red light on the third day, i.e., P(Y = 3) will be 0.1479.

Note:

mean and variance of this question is not possible to find out.

the complete question ends till the probability to find the first red light on the third day.

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Answer: its 15

Step-by-step explanation:

Using subtraction and division operations, the amount you receive for each soup mix sold is $6.

Subtraction and division operations are two of the four basic mathematical operations. The other two are multiplication and addition.

Mathematical operations combine variables, numbers, and mathematical operands to solve mathematical problems.

The number of soup mixes sold = 16

The total sales revenue = 16x + 96

The amount for the company that makes the soup = 16x

The amount that the seller receives = 96 (16x + 96 - 16x)

The amount the seller receives per soup mix = The total revenue received divided by the number of units sold

= 6 (96/16)

Thus, for each soup mix that you sell, you receive $6.

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The  true statements about the unit prices :

spring water has a lower unit price of $0.11/ounce and fresh water has a lower unit price of $0.12/ounce

The correct answer: option (A) and option (C)

We use the unitary method in order to determine the unit price.

Here, 16-ounce bottle of spring water is $1.76. A 20-ounce bottle of fresh water is $2.40

Let us assume that the unit price of spring water be 'm' and the unit price of freshwater be 'n'.

By unitary method the unit price of spring water would be,

m = 1.76/16

m = 0.11

This means,  1 ounce bottle of spring water is $0.11

And the unit price of freshwater be:

n = 2.40 / 20

n = 0.12

i.e., the unit price of freshwater is $0.12

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The complete question is:

A 16-ounce bottle of spring water is $1.76. A 20-ounce bottle of fresh water is $2.40. which statement about the unit prices is true?

A)spring water has a lower unit price of $0.11/ounce

B) spring water has a lower unit price of $0.12/ounce

C)fresh water has a lower unit price of $0.12/ounce

D)fresh water has a lower unit price of $0.11/ounce

The length of Mian in inches is 23 and the length of Udon in inches is 11

An equation is a mathematical statement that shows that two mathematical expressions are equal.

Given that, Aria has two pet snakes, Mian and Udon. The combined length of the two snakes is 34 in and Udon is 12 inches shorter than Mian.

Let Mian be represented by M and that of Udon by U,

Therefore, according to question, establishing the equation,

M + U = 34

M - U = 12

Adding both the equations,

2M = 46

M = 23

U = 11

Hence, the length of Mian in inches is 23 and the length of Udon in inches is 11

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The probability that they are sitting around a round table in age order is 1/12. There are 10 ways for five people to sit in age order.  

Probability is a numerical description of how possible an event to happen. Probability of an event can be expressed as

P(A) = n(A) / n(S)

Where

Five people all of different age are sitting around a round table.

Find the probability they are sitting in age order!

Let's name the 5 people 1, 2, 3, 4, 5.

There are two ways in putting them in the age order, ascending or descending.

There are 10 ways that they are sitting around a round table in the age order.

n(Age order) = 10

The total arrangements for 5 people sitting around a round table is

5! = 1 × 2 × 3 × 4 × 5

5! = 120 ways

n(S) = 120

The probability that they are sitting in age order would be

P(Age order) = n(Age order) / n(S)

P(Age order) = 10/120

P(Age order) = 1/12

Hence, the probability that five people are sitting around a round table in age order is 1/12.

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Answer: -48x-32

Step-by-step explanation:

New weight = 225 x (1 - (16 / 100)) = 225 x 0.84 = 189 pounds.

So, after dieting and exercising, Jim now weighs 189 pounds.

Answer: 189 pounds

Step-by-step explanation:

If he lost 16% of his weight, Jim is now 84% of his original weight.

84% = 0.84

225 x 0.84

189 pounds

Answer:111

Step-by-step explanation: how to do it:is try

Answer: f(k) = 3k - 5

Step-by-step explanation:

For f(x) functions, you're simply plugging in whatever value is in the parenthesis. For example, if you were asked to find f(1), you would plug in 1 for x.

f(1) = 3(1) - 5 = -2. In this case, you're just plugging in a different variable.

The length of the line segment is given by the distance equation

D = 7.2 units

The distance of a line between 2 points is always positive and given by the formula

Let the first point be A ( x₁ , y₁ ) and the second point be B ( x₂ , y₂ )

The distance between A and B is D , and the distance D is

Distance D = √ ( x₂ - x₁ )² + ( y₂ - y₁ )²

Given data ,

Let the distance of the line segment between two points be D

Now , the equation will be

Let the first point be represented as P ( 1 , 6 )

Let the second point be represented as Q ( 7 , 2 )

Now , distance between P and Q is D , and the distance D is

Distance D = √ ( x₂ - x₁ )² + ( y₂ - y₁ )²

D = √ ( 1 - 7 )² + ( 6 - 2 )²

On simplifying the equation , we get

D = √ ( -6 )² + ( 4 )²

D = √ ( 36 + 16 )

D = √ 52

D = 7.2 units

Hence , the distance is 7.2 units

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The solution of the system of linear equations is :-

x = 6 hours .

y = 330 miles.

Now, According to the question:

Let x be the number of hours that have elapsed since Zac started traveling .

Let y be the number of miles traveled .

We know that,

Speed = Distance / Time.

so,

Speed of Zac = D / T = 123.75 / 2.25 = 55 miles / hour.

Speed of Lynn = D / T = 105 / 1.75 = 60 miles / hour.

then, Distance travelled by Zac in x hours = S * T

y = 55 × x

y = 55x miles

and, Distance travelled by Lynn in (x - 0.5) hours = S * T

y = 60 × (x - 0.5)

y = 60x - 30

Therefore, a system of linear equations that represents the distance each of them has traveled since Zac left on his trip are :-

y = 55x ----------- Eqn.(1)

y = 60x - 30 ------------- Eqn.(2)

Now, putting value of Eqn.(1) in Eqn.(2) , we get,

55x = 60x - 30

60x - 55x = 30

5x = 30

x = 6 hours.

Putting value of x in Eqn.(1),

y = 55 * 6

y = 330 miles.

Hence, the solution of the system of linear equations is :-

x = 6 hours .

y = 330 miles.

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The length of median A is 11.7.

The point of intersection of a triangle's medians is its centroid (the lines joining each vertex with the midpoint of the opposite side).

If the triangle has its vertices as   (x_1, y_1), (x_2, y_2) , \: (x_3, y_3), then the coordinates of the centroid of that triangle is given by:

[tex](x,y) = \left( \dfrac{x_1 + x_2 + x_3}{3} + \dfrac{y_1 + y_2 + y_3}{3} \right)[/tex]

Given;

The sides of triangle

a = 4, b = 5 and c = 6

The median of triangle =½√(2b2+2c2-a2).

=(2*5*5+2*6*6-4*4)

=(50+72-16)

=[tex]\sqrt{138}[/tex]

=11.7

Therefore, the median of triangle will be 11.7

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(a) The study is observational type.

(b) Stratified sampling can be used for carrying out this study.

(a) In the given problem, We want to hear students' opinions about the new housing structure and ensure that the survey reflects all students' views equally. The critical thing to note here is that you need to collect opinions. Not the reason behind the opinion. So researchers don't care how the data goes up. So this is an observational study.

(b) In the case of sampling strategy we can use stratified sampling. Stratified sampling refers to a type of sampling technique. In stratified sampling, researchers divide the population into separate groups called strata. A probability sample (often a simple random sample) is then drawn from each group. The same number of samples can be used each year.

Therefore, To make sure the survey equally represents opinions from students from all years (a) the study is the observational type and (b) Stratified sampling can be used for carrying out this study.

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