6. Justify the last two steps of the proof.
Given: ABCD is a parallelogram.
Prove: A4BC = ACDA
A
B
1. ABDC is a parallelogram.
2. AB DC and BC= DA
3. AC = CA
4. JABC = ACDA
D
1. Given
2. Opposite sides of a parallelogram are congruent.
3.
C
4.
?

No. For example, thirteen hearts could be selected: 2, 3, 4, 5, 6, 7, 8, 9, 10, J, Q, K, A. No two of these are of the same denomination.

What is a denomination?

A denomination is a classification system that identifies the nature or worth of an object. Denomination frequently relates to currency.

Here, we have

13 cards are randomly selected from a standard 52-card deck.

This is not necessary.

All 13 cards may be of different denominations.

At least 2 need not be of the same denomination.

Hence, thirteen hearts could be selected: 2, 3, 4, 5, 6, 7, 8, 9, 10, J, Q, K, A. No two of these are of the same denomination.

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Answer:

Answer choice (C) -$19.56 is your answer. After the check was cashed she had negative -19.56

Step-by-step explanation:

Kathy had $45.67 in her checking account. She wrote a check for $65.23. What was her balance after the check was cashed? A. $110.90 B. $39.56 C. -$19.56 D. -$110.90

Answer:

[tex]\frac{x}{3} \leq 5[/tex]

Hope this helps! :)

The price of new car is reduced by $825 from the original price $12,500 which implies the price of car after reduction is $11,625 i.e

The percentage reduction is 7 .

Percentage is calculated by dividing the value by total value and then multiply with 100.

We have given that,

The price of a new car = $12,500

After the some reduction in price

then the price of car = $11,625

The reduction in total price of car = original price - price after reduction

= $12,500 - $11,625

= $875

Now, we have to calculate the reduction of price in percentage.

Using the percentage reduction formula,

P% = (original price - price after reduction )× 100 /original price

=> percentage reduction = ( 875/12500)×100

=> percentage reduction = 875/125 = 7

Hence, the reduction is 7% .

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The largest product we can get is: 26244,

What is integers?

Integers are whole numbers that are either positive, negative, or zero. They are the building blocks of the number system and are used to represent quantities or perform calculations. Integers are represented in the form of digits and can either be written in the form of standard numbers, Roman numerals, or in the form of exponential notation. Integers are used in many areas of mathematics and are a fundamental concept in the study of algebra, geometry, and calculus. Integers are also used in everyday life, such as in accounting and finance, where they represent monetary values.

We know that for 28,
(k-2)*2 <= k
2k-4 <= k
k <= 4

So, we should only consider numbers less than or equal to 4.

Now, 4 can be replaced by 2*2 and there is no point in taking 1 since it will not increase product result.

So, we are left with 2 and 3. Some possible solutions are:

{3,3,3,3,3,3,3,3,2,2} or {3,3,3,3,3,3,2,2,2,2,2} etc.

Out of all these, the maximum product we can get is from {3,3,3,3,3,3,3,3,2,2} which is: 26244

So, The largest product we can get is: 26244

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Muscular strength can be measured based on the amount of weight lifted.

Muscular strength can be measured based on the amount of weight lifted. The upper-body and lower-body strength are measured separately. Muscular strength is typically measured which is known as a One Rep Max (1RM).

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The area of the trapezium, if  CD = 8 cm, BD = 6 cm, AE = 9 cm, is  30 cm².

The measurement that expresses the size of a region on a plane or curved surface is called an area. Surface area refers to the area of an open surface or the boundary of a three-dimensional object, whereas the area of a plane region or plane area refers to the area of a form or planar lamina.

Given:

CD = 8 cm,

BD = 6 cm,

AE = 9 cm,

Here you can see that the triangle AEC and triangle BDC are similar, so the ratio of sides of a triangle are also equal,

BD / AE = CD / CE

6 / 9 = 8 / CE

CE = 9 × 8 / 6

CE = 12 cm

Thus, DE = CE - CD.

DE = 12 - 8 = 4 cm

Calculate the area as shown below,

[tex]Area = (BD+AE) / 2 \times DE[/tex]

Area = (6 + 9) / 2 × 4

Area = 15 / 2 × 4

Area = 30 cm²

Therefore, the area of the trapezium, if  CD = 8 cm, BD = 6 cm, AE = 9 cm, is  30 cm².

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The answer to this Question based on Linear equation is 28 and 45

What is Linear Equation?

It is a equation in which the degree of each and every variable is 1 only is called linear equation

Solution:

Let the time taken to complete maths homework be x and time to complete science homework be y

first we know that total time taken was 1 hr 15 minutes means 75 minutes which in turn means x + y = 75

and from 2nd relation that we are given

x = 2y - 9

now we got the 2 linear equations now we just need to solve them to get our final answer

putting this equation in first equation we got we get

2y - 9 + y = 75

3y - 9 = 75

3y = 84

y = 28

and hence x = 2y - 9

x = 56  - 9

x = 45

hence time to complete maths was 45 minutes and time to complete science is 28 minutes

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On an average, 1.67 people will have to be stopped by the reporter before he finds his first democrat.

A supporter of democracy, Democratic Party subscriber, a democratic government, or a system of government where the people rule, may be referred to as a Democrat, Democrat, or Democratic.

The central value of a set of data is expressed mathematically as the average of a list of data. It is defined mathematically as the ratio between the total number of units in the list and the sum of all the data. The term "mean" in statistics also refers to the average of a given set of numerical data.

For instance, (2+3+4)/3 = 9/3 = 3 is the average of 2, 3, and 4. As a result, in this instance, 3, which also includes 2, 3, and 4, serves as the central value. Finding the average value of a group of numbers is what average means, then.

Average is calculated by dividing the total number of values by the sum of the individual values.

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Answer:

Without knowing the values of the variables in the given expression, it is impossible to determine the value of the expression. In general, the expression is a combination of a number (A), two variables (b and c), and an exponent (2). The value of the expression will depend on the values of these variables and the operations that are performed on them. For example, if A=3, b=2, and c=4, then the value of the expression would be:

(3^2 * 2 * 4^2) - 5

Which is equal to 29. However, if the values of the variables were different, then the value of the expression would also be different. Therefore, it is impossible to determine the value of the expression without knowing the values of the variables.

Step-by-step explanation:

Answer:

(3^2 * 2 * 4^2) - 5, hope it helps.

The first step is converting both the velocity and the wind in vector form, as follows:

Then the true speed of the plane is given by the addition of these two vectors, as follows:

[tex]\vec{v_1} + \vec{v_2} = \sqrt{|v_1|^2 + |v_2|^2 + 2 \cdot |v_1| \cdot |v_2| \cdot \cos(\theta)}[/tex]

The magnitudes of each vector are given as follows:

The angle between these two vectors is given as follows:

[tex]\theta = 100^\circ - 42^\circ = 58^\circ[/tex]

Thus the resulting speed is obtained as follows:

[tex]\vec{v_1} + \vec{v_2} = \sqrt{180^2 + 30^2 + 2 \cdot 180 \cdot 30 \cdot \cos(58^\circ)} = 197.54[/tex]

The resulting angle of the plane is then obtained as follows:

[tex]\angle = \arctan\left(\frac{|v_1| \cdot \sin(\theta) + |v_2| \cdot \sin(\theta_2)}{|v_1| \cdot \cos(\theta) + |v_2| \cdot \cos(\theta_2)}\right)[/tex]

Hence:

[tex]\angle = \arctan\left(\frac{180 \cdot \sin(58^\circ) + 30 \cdot \sin(42^\circ)}{180 \cdot \cos(58^\circ) + 30 \cdot \cos(42^\circ)}\right)[/tex]

[tex]\angle = 59.87^\circ[/tex]

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Answer:

  197.5 km/h

Step-by-step explanation:

You want the resultant speed with an airplane at a speed of 180 km/h at 100° is acted upon by a wind at a speed of 30 km/h at 42°. Angles are bearings CW from north.

A vector calculator makes short work of this. The resultant speed is ...

  197.5 km/h at 92.6°

The law of cosines can be used to find the side opposite the known angle in the triangle with sides 30 km/h and 180 km/h. The known angle is ...

  180° -(100° -42°) = 122°

So, the resultant speed is ...

  c = √(a²+b²-2ab·cos(C))

  = √(30² +180² -2(30)(180)·cos(122°)) ≈ √39023.13

  c ≈ 197.543

The true speed of the plane is about 197.5 km/h.

__

Additional comment

You will notice that we used bearing angles directly in the calculator computation. As long as angles are consistently measured, it doesn't matter how they're measured.

When plotting the vectors on the Cartesian plane, we need to subtract the bearing angles from 90° to make them correspond to the vectors plotted on a map with north at the top.

The value of the form 4^4 plus 3 is 259

Scientific notation can simply be defined as a way of expressing numbers with extreme values in a convenient form.

It is also known as standard index form,  standard form and scientific form.

It is commonly used for complex calculations with very long numbers.

It is also described as a method of expressing numbers in the terms of a decimal number.

Given the expression;

4^4 plus 3

4^4 is represented as 4 × 4 × 4 × 4

Multiply the values

256 + 3

Add the values

259

Hence, the value is 256

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Answer: X[12)

Step-by-step explanation:

-6x+9<2-5(x+1)

-6x+9<-5(x+1)+2

-6x+9<-(5x+5)+2

Answer:

4i/7

Step-by-step explanation:

Answer:

88

Step-by-step explanation:

If your data analysis shows that there is a chance that a hypothesis is false, the standard practice is to reject it. It is b). False.

Scientists can either reject the null hypothesis (which implies that there is a clear, causal connection between the two observations) or. not proving the null hypothesis (meaning the test has not identified a consequential relationship between the two phenomena). If the test statistic is greater than the crucial value in an upper-tailed test, the decision rule requires that researchers reject H0.

If the test statistic is less than the crucial value in a lower-tailed test, the decision rule requires that the investigators reject H0. Checking for sufficient evidence to refute the null hypothesis is the aim of hypothesis testing. To determine whether there is sufficient evidence to reject the null hypothesis, in other words. If there is insufficient support, we cannot rule out the null hypothesis.

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The inequality to graphed.

y < (-1/2)x + 4

It shows a relationship between two numbers or two expressions.

There are commonly used four inequalities:

Less than = <

Greater than = >

Less than and equal = ≤

Greater than and equal = ≥

We have,

The equation of the line from the graph.

y = mx + c

Two coordinates from the graph:

(8, 0) and (0, 4)

m = 4/-8

m = -1/2

Now,

(8, 0) = (x, y)

0 = (-1/2)8 + c

c = 4

Now,

y = (-1/2)x + 4

Thus,

y < (-1/2)x + 4 is the inequality that will graph the given graph.

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Given any set of seven integers there are no two numbers that have same remainder when divided by 6.

The remainder is the value left after the dividion. If a number is not completely divisible by another number then we are left with a value once the division is done. This value is called the Remainder.

Given any set of seven integers, there must be at least two numbers that have same remainder when divided by 6.

So there can be six remainders when divided by 6 i.e. 0,1,2,3,4 and 5.

According to the Piegeonhole principle,

in any set of seven integers two must have the same remainder when divided by seven.

Consider the set of integers 0,1,2,3,4,5 and 66. All of these have different remainders upon division by 8.

Hence there need not be two numbers such that they have same remainders when divided by 6.

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The exact circumference of the circle with radius 17 millimeters is 34π   millimeters , the correct option is (b) .

In the question ,

it is given that ,

the radius of the circle is given as = 17 millimeter

we have to find the exact circumference of the circle,

we know that the formula to find circumference of the circle is ;

circumference = 2×π×r

Substituting the value of radius in the circumference formula ,

we get ;

circumference = 2×π×17

Simplifying  further ,

we get ,

= 34π

Therefore , the exact circumference of the circle is = 34π .

The given question is incomplete the complete question is

What is the exact circumference of a circle with a radius of 17 millimeters ?

(a) 17π millimeters

(b) 34π millimeters

(c) 68π millimeters

(d) 8.5π millimeters

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Answer:

7x

Step-by-step explanation:

When combining like terms, you keep the bases the same and add the constants.

the "x's" are the base and the constants are 5 and 2:

(5 + 2)x = 7x

A recipe calls for 170,100 milligrams of raisins.

What are units ?

Units are the measuring and contrasting devices for many things. When all measurement units are identical, comparisons are simple. Depending on how they are used, several units can be categorized.

Measurement is the process of comparing an unknown quantity to an already known quantity. A numerical value with specific units is the measurement's output. Any given object can have its length, mass, capacity (volume), and temperature measured.

1 ounce = 28.35 grams

6 ounces = 6*28.35 grams  = 170.1 grams

1 gram = 1,000 milligrams

170.1 grams  = 170.1 * 1,000 milligrams = 170,100 milligrams

So, a recipe calls for 170,100 milligrams of raisins.

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Answer:

A recipe calls for 170,100 milligrams of raisins.

Step-by-step explanation:

I took the exam and got it right

The numbers in the increasing order are:

(x-1)>(x+1)>(x+2)

In mathematics, factorization is the process of dividing a large number into smaller ones that, when multiplied together, give you the original number. The factorization of the integer 12, for instance, might be represented as 3 times 4. In the context of integers, factorization was first studied by Greek mathematicians. They established the basic theorem of mathematics, which states that every positive integer can be factored into a product of prime numbers but cannot be factored further into integers larger than 1. Up to the order of the factors, this factorization is also distinct.

It has also been studied for ages how to factor polynomials.

The given equation is:

x³+2x²-x-2

Now, we have to do factorization for the given equation.

(x+1)(x²+x-2)

(x+1)(x²+2x-x-2)

(x+1)(x(x+2)-1(x+2))

(x+1)(x-1)(x+2)

This is the factorized form of the given equation.

Therefore, the numbers in the increasing order are:

(x-1)>(x+1)>(x+2)

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Answer: Her brother is 5 years old.

Step-by-step explanation:

s = 2b

4b + 3b = 35

7b = 35

First, I used s to represent Sarah's age. We are told that she is twice her brother, I used b to represent her brother's age. The sum of twice her age is 4 times her brother's age (2b + 2b) and 3 times her brother's age is 3b.

The earliest finish time for the activity 10-11(far right-hand side) is 23 if the earliest start time of activity 8-10 and activity -10 is 12 and 13 respectively.

The depicted graph represents the critical path method(CPM)

Given,

Earliest start time of 8-10 = 12

Earliest start time of 9-10 = 13

From the network, it is observed that at 10, two networks are connecting, we need to take the largest earliest finish time from both the activities as earliest start time for 10-11.

Earliest finish time = earliest start time + activity duration

Earliest finish time for 8-10 = 12+4=16

Earliest finish time for 9-10 = 13+2=15

From above two times, 8-10's earliest finish time is the greatest. So, consider 16 as earliest start time for 10-11.

Now,

Earliest finish time for 10-11= earliest start time + activity duration=16+7=23

Thus, the earliest finish time for 10-11 is 23.

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There are "P(20, 10) - P(15, 10)" options (ways) to distribute the coupons so that at least one woman receives a coupon.

What do you mean by permutation?

A permutation of a set in mathematics is, broadly speaking, the rearrangement of its elements if the set already has an ordered structure into a sequence or linear order. The act or procedure of altering the linear order of an ordered set is referred to as a "permutation."

There are P(20, 10) ways to distribute the coupons if they are different, with the only restriction being that no more than one coupon can be given to a shopper. To ensure that all of the coupons go to the guys, there are P(15, 10) ways to distribute them. In order to ensure that at least one coupon is given to a woman, there are P(20, 10) - P(15, 10) options to distribute the coupons.

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Complete Question

10 coupons are given to 20 shoppers in a store. Each shopper can receive at most one coupon. 5 of the shoppers are women and 15 of the shoppers are men.

If the coupons are different, how many ways are there to distribute the coupons so that at least one woman receives a coupon?

Answer:

A ; B ; D

Step-by-step explanation:

5t + 9

for commutative property

9 + 5t

5t = 5 x t

5 · t + 9

(5 x t) + 9

Answer:

D. One solution

Step-by-step explanation:

6-3x=4-x-3-2x

Combine your like-terms.

6-3x=1-3x

Subtract 1 to both sides (on the right side it cancels out).

5-3x=3x

Add 3 on both sides (on the left side it cancels out).

5=6x

Divide both sides by 6.

x=0.83

Answer: 216 times

Step-by-step explanation:

18 * 12

Answer:

yes

Step-by-step explanation:

2x+4=3x-2

4=x-2

6=x

x=6

Answer:

Yes, It equals 6.