The coordinates of the vertices of trapezoid ABCD are A (2,6), B (5,6), C (7,1), and D (-1,1). The coordinates of the vertices of trapezoid A'B'C'D' are A' (-6, -2),B' (-6, -5), C' (-1, -7), and D' (-1, 1). Which statement correctly describes the relationship between trapezoid ABCD and trapezoid A'B'C'D' ?

A. Trapezoid ABCD ≅ trapezoid A'B'C'D'
You can reflect trapezoid ABCD across the x-axis and then across the y-axis.


B. Trapezoid ABCD ≅ trapezoid A'B'C'D'
You can rotate trapezoid ABCD 180°about the origin and then translating it 4 units left.


C. Trapezoid ABCD ≅ trapezoid A'B'C'D'
You can reflect trapezoid ABCD across the x-axis and then rotating it 90°clockwise.

Answer:

union and the second question is intersection

Step-by-step explanation:

Answer:

The union of two sets A and B is the set of elements that are present in A, in B, or in both A and B.

The intersection of two sets A and B is the set of elements that are present in A, in B.

Answer: (B) 4√2

Step-by-step explanation:

45-45-90 is a special triangle because the side lengths are congruent and the hypotenuse is √2 times the side lengths.

So, m√2 = 8

           [tex]m=\dfrac{8}{\sqrt2}[/tex]

           [tex]m=\dfrac{8}{\sqrt2}(\dfrac{\sqrt2}{\sqrt2})[/tex]

           [tex]m=\dfrac{8\sqrt2}{2}[/tex]

           [tex]m=4\sqrt2[/tex]

Answer:

The speed of the car is 42 miles per hour

Step-by-step explanation:

Step 1:

(Blank) x s = (Blank)

Let us evaluate this. Something times s miles per hour is going to gives us? 126 miles. So, our second blank would be 126 since that's our total:

(Blank) x s = 126

Step 2:

On the other hand, our first blank would be 3. Why? Because that's the amount of time it takes us to go 126 multiplied by s miles per hour; Our new equation is:

3 x s = 126

Step 3:

We can simplify this equation to:

3s = 126

Step 4:

We now have a one step equation. Divide each side by 3 to get s by itself.

[tex]\frac{3s}{3} =\frac{126}{3}[/tex]

Step 5:

We end up getting:

s = 42

That means that the car is traveling at 42 miles per hour. If the car continues at that rate for 3 hours, the car would have traveled 126 miles.

Hope this helps!

Answer:

3 X S = 126

Step-by-step explanation:

because the variable (s) is speed then we must know that 126 is tyhe total that it is driving in 3 hours so 3 time S is 126

Answer:

$875.00

Step-by-step explanation:

If you want to find out how much commission Anil earned in commissions last month, you must multiply $12,500 by .07 (7%) and it equals $875.00.

Hope that helps!

Answer:

336$

Step-by-step explanation:

Given: Each invitation costs a total of 3$.

Given: There were a total of 112 invitations made.

So, the question is asking you to find the total amount spent making the invitations. To do so we need to find the product/sum. Product in mathematical terms is used to describe the answer to a multiplication problem. Sum on the other hand is used to describe the answer to an addition problem. Now you could just add, but multiplication is a better way of simplifying the problem. So instead of saying 3 + 3 + 3 + 3.. or 112 + 112 + 122, we say 122 x 3 = x.

Now that we've created the equation, we can find the answer.

122 x 3 = 336

Answer: Andri spent 336$ on materials for her invitations.

Good luck! c:

(x, y) → (x, y + n) - translate the graph n units up

(x, y) → (x, y - n) - translate the graph n units down

(x, y) → (x - n, y) - translate the graph n units left

(x, y) → (x + n, y) - translate the graph n units right

---------------------------------------------------------------------------

Look at the picture.

(x, y) → (x - 5; y + 4)

To find the sales tax on a $60 bill with a 5% rate, convert the percentage to a decimal (0.05) and multiply by the total amount ($60). The sales tax is $3.

The sales tax on a total bill can be calculated by converting the percentage rate of the sales tax into a decimal and then multiplying it by the total amount of the bill.

In this case, the total cost is $60 and the sales tax rate is 5%. First, convert 5% into a decimal by dividing it by 100, which gives us 0.05. Then, multiply this decimal by the total bill amount to find the amount of sales tax. The calculation would be as follows:

$60 × 0.05 = $3

Therefore, the sales tax for a $60 bill at a 5% rate is $3.

Answer:

184.85 square mm

Step-by-step explanation:

The area of a sector of a circle is [tex]\frac{1}{2} r^{2} \theta[/tex], where r is the radius and [tex]\theta[/tex] is the angle in radians subtended by the arc at the centre of the circle.

Since, diameter = 40.6 mm

So, radius(r)=20.3 mm and  [tex]\theta[/tex]=[tex]\frac{2 \pi}{7}[/tex] radians

So, area of sector= [tex]\frac{1}{2} r^{2} \theta[/tex]

=[tex]\frac{1}{2} (20.3)^2 (\frac{2 \times 3.14}{7})[/tex]

=184.85 square mm

The area of the sector using given data is equal to 184.96 mm².

The area of a sector with a central angle of 2π7 radians and a diameter of 40.6 mm.

To solve this, we need to find the radius of the circle, which is half the diameter, and then use the formula for the area of a sector, which is ½ ×r² × θ, where θ is the angle in radians.

First, find the radius: r = ½ × diameter = 0.5 × 40.6 mm = 20.3 mm.

Then, substitute the values into the formula for the area of a sector:

Area = ½ × (20.3 mm)² × (2π7)

        = 1/2 × (20.3)² × (2 × 3.14 /7)

        = 1/2 × 412.09 × 0.89714

        = 184.96 mm²

Rounded to the nearest hundredth, the area of the sector is 184.96 mm².

Answer:

(1)

Closed circle graph

(2)

Closed circle graph

Step-by-step explanation:

(1)

we are given

[tex]|x|=1[/tex]

we know that absolute value is always positive

so, we can write as

[tex]-x=1[/tex]

[tex]x=-1[/tex]

[tex]x=1[/tex]

So, value of x are

[tex]x=-1,x=1[/tex]

so, graph will be of closed circle

(2)

we are given

[tex]|x|=2[/tex]

we know that absolute value is always positive

so, we can write as

[tex]-x=2[/tex]

[tex]x=-2[/tex]

[tex]x=2[/tex]

So, value of x are

[tex]x=-2,x=2[/tex]

so, graph will be of closed circle

Answer:

|x| = 1

Closed circles on -1 and 1.

|x| = 2

Closed circles on -2 and 2.

(See attachments.)

Answer:

Toy Cars=6 and total spending by Mr.Lee=$156

Step-by-step explanation:

Let us first consider

Number of Airplanes=A Cars=C and Trains=T

Now how to start with the problem ? Just start reading it step by step. First statements says that The number of airplanes is 2/3 of The number of cars.

Now how to convert it into an mathematical expression?

here the word "=" is of most important, The number of airplanes "is" whenever you encountered "is" just place a "="

so the first statement can be converted into mathematical expression as,

A=2/3*C  (The number of airplanes is 2/3 of The number of cars.)

Now as per the second condition we can write it in mathematical form as,

C=3/5*T (The number of cars is 3/5 the number of trains).

and the third condition as,

C=3/5*T (The number of cars is 3/5 the number of trains).

Now , we have expressed the statements in mathematical expressions. we have three expressions.

Now It is also given that total number of Toys=20 so we can write it as,

A+C+T=20. ............(1)

Till now we have expressed everything in the question in mathematical form.

now for solving such type of question we need to express the expression giving total in a single entity, expressed it in terms of Airplanes,Cars or Trains,

here we are expressing it in terms of Cars so we can rewrite it (1) as,

2/3*C+C+5/3*C=20 (A=2/3*C and C=3/5*T so T=5/3*C)

by solving this we will get C=6

Total number of car toys, answer of first part

now put this value of C in expression 1,

2/3*C+C+T=20

so the value of T will be 10. T=10

and the total is toys are 20 so 20-10+6=4

Means Airplanes are 4.

Now the cost for each toy is.

A=$12,C=$8 and T=1/2 A i.e T=$6.

So the total cost would be,

4*12+6*8+10*6=$156

$156 answer of second part

I Hope this will help you to solve such kind of Problems.

Mr. Lee buys 6 toy cars for his store. The total cost for all the toys he purchased is $156. This includes the cost of toy airplanes, cars, and trains, with each toy tailoring a specific price.

The student wants to know how many toy cars Mr. Lee bought and the total cost of all toys he purchased for his store. We start with the relationships provided: the number of airplanes is 2/3 the number of cars, and the number of cars is 3/5 the number of trains. We also know that the total number of toys is 20. Let A be the number of airplanes, C be the number of cars, and T be the number of trains. So, we have A = (2/3)C and C = (3/5)T.

From these ratios, we can express airplanes and trains in terms of cars: A = (2/3)C, T = (5/3)C. The equation A + C + T = 20 becomes (2/3)C + C + (5/3)C = 20. Simplifying this, we get (10/3)C = 20, so C = 6. Thus, Mr. Lee buys 6 cars. The number of airplanes, A = (2/3) * 6 = 4, and the number of trains, T = 20 - A - C = 20 - 4 - 6 = 10.

Now let's calculate the total cost. Each toy airplane costs $12, each toy car costs $8, and each toy train costs half as much as an airplane, which is $6. The total cost is 4 airplanes * $12 + 6 cars * $8 + 10 trains * $6, which equals $48 + $48 + $60, resulting in a total of $156 spent by Mr. Lee.

Answer:

21

Step-by-step explanation:

since its a rectangle there are two lengths of six. If you add them together you get 12. subtract the total perimeter of 54 by the 12 and get 42. Since there is 2 sides left divide by 2. You should get 21 for the width of the rectangle

Answer:

thats wrong

Step-by-step explanation:

Answer:

Sam picked 27

Step-by-step explanation:

41-8=33

33+27=60

Answer:

27.

Step-by-step explanation:

So there was 41 peaches, and they sold 8 so that's 41 - 8 which is 33 peaches. But now there is 60, so you do 60 - 33 gives you how many were picked and 60 - 33 is 27.

To scale down Tom's photo with the original dimensions of 20 cm by 30 cm to a width of 5 cm, the new length should be 7.5 cm. This is calculated using a proportion that maintains the original aspect ratio.

To determine the new length that a photo should be when scaling down, we will maintain the ratio of the original width to the original length. Tom's photo has a width of 20 centimeters and a length of 30 centimeters. If he wants to reduce the width to 5 centimeters, we calculate the new length by setting up a proportion and solving for the missing value:

We set up the following proportion:
20/5 = 30/new length

To solve for new length, we cross-multiply:
(20) * (new length) = (5) * (30)

Then,
new length = (5 * 30) / 20

So,
new length = 150 / 20 = 7.5

Therefore, the new length that Tom should have for his wallet-sized photo is 7.5 centimeters when the width is 5 centimeters.

Final answer:

To find the population of Smallville and population density per square mile, divide the total population by the area of the town.

Explanation:

The population of Smallville:

Population of Smallville: 72450

Area of Smallville: 5 miles x 1 mile = 5 square miles

Population density in Smallville:

Population density = Population / Area = 72450 / 5 = 14490 people per square mile

We are given that AB ≅ CB and AD ≅ CD.

We know that BD ≅ BD, so ΔABD ≅ ΔCBD by SSS.

Then ∠1 ≅ ∠2 by CPCTC; and ∠3 ≅ ∠4, also by CPCTC.

Since ∠1 ≅ ∠2, BD is the bisector of (∠1+∠2) = ∠ABC.

Since ∠3 ≅ ∠4, BD is the bisector of (∠3+∠4) = ∠ADC.

From (5), we know BD is the angle bisector of ∠ABC. ΔABC is isosceles, so the bisector of the apex angle is also an altitude and median. That is, point M on BD and AC must be the midpoint of AC by the definition of a median.

Answer:

Area of triangle is 25.

Step-by-step explanation:

We have been given an isosceles right triangle

Isosceles triangle is the triangle having two sides equal.

Figure is shown in attachment

By Pythagoras theorem

[tex]BC^2=AC^2+AB^2[/tex]

AD is altitude which divides the triangle into two parts

DC=5 implies BC =10 since D equally divides BC

Let AC=a implies AB=a being Isosceles

On substituting the values in the Pythagoras theorem:

[tex]10^2=a^2+a^2[/tex]

[tex]100=2a^2[/tex]

[tex]\Rightarrow a^2=50[/tex]

[tex]\Rightarrow a=\pm5\sqrt{2}[/tex]

WE can find area of right triangle by considering height AB and AD

Area of triangle ABC is:

[tex]\frac{1}{2}\cdot BC\cdot AD[/tex]     (1)

[tex]\Rightarrow \frac{1}{2}\cdot 10\cdot AD[/tex]

And other method of area of triangle is:

[tex]\frac{1}{2}\cdot AB\cdot BC[/tex]       (2)

Equating (1) and (2) we get:

[tex]\frac{1}{2}\cdot 10\cdot AD=\frac{1}{2}\cdot a\cdot a[/tex]

[tex]\Rightarrow AD=\frac{a^2}{10}[/tex]

[tex]\Rightarrow AD=\frac{50}{10}=5[/tex]

Using area of triangle is: [tex]\frac{1}{2}\cdot BC\cdot AD[/tex]

Now, the area of triangle ABC=[tex]\frac{1}{2}\cdot 5\cdot 10[/tex]

[tex]\Rightarrow 25[/tex]

Answer:

8x(4+z) and 32x+8z, = Not equivalent

9(g+h) and 9g+9h = Equivalent

Step-by-step explanation:

Answer:

[tex]\frac{1}{2} QP = UT[/tex]

Step-by-step explanation:

We are given  a ΔPQR  in which S is the mid point of QP  , T is the mid point of  QR , U is the mid point of PR

i) is true

⇒ [tex]\frac{1}{2} QP = UT[/tex]

Using mid segment theorem which states that In a triangle, the line joining the midpoints of any two sides will be parallel to the third side and that same line joining the midpoints is also half of length of third side .

So, by refering image we can see that UT is the line joining the two mid points . So, by using above theorem    1/2QP=UT and UT is parallel to PQ

Thus, (i) statement is true

⇒[tex]\frac{1}{2} QP = UT[/tex]

Answer:

it's A and D

Step-by-step explanation:

Answer:

A, B, C, D

Step-by-step explanation:

A polynomial is 2 or more terms connected by operations where at least one has a variable with a power or exponent. Each has two or more terms with variables with a power. We can rewrite square roots and fractions as an exponent power.

Her Pop music which started at 3 hours increases by 5% which is written as 0.05 as a decimal.

You need to multiply the number of hours of pop music by 5% every month to find the new total and then add that to the 2 hours of classical.

The equation would be: f(x) = 3(1.05)x + 2

Answer:

f(x) = 3(1.05)x + 2

Step-by-step explanation:

i took the test and got it right

Answer:

21x+35[tex]\geq[/tex]160

Step-by-step explanation:

(Amount)(time)+(starting total)[tex]\geq[/tex]total

(21)(x)+(35)[tex]\geq[/tex]160

21x+35[tex]\geq[/tex]160

Answer:

A prom ticket at Valley high school cost $160. Bryan is going to save money for his ticket by walking his neighbor’s dog for $21 per week. Bryan has already has saved $35. Which inequality could be used to find the minimum number of weeks Bryan must walk the dog to earn enough to pay for his prom ticket?

A) 21x + 35 ≥ 160  

B) 21x + 35 ≤ 160  

C) 35x + 21 ≥ 160  

D) 35x + 21 ≤ 160

Step-by-step explanation:  THE ANSWER is A

The answer is x = 3, because x = 3 has an undefined slope (m = 0 or is imaginary), and it contains 3, 0 which makes 3, 0 a solution.

Answer: x=3

Step-by-step explanation:

The graph never crosses the y axis.

The point (3,0) is on the graph.

So are all points (3,y) with y any real number.

There can't be a slope because x never changes.

Answer:

c

Step-by-step explanation:

Option (C) No; because x and y could be additive inverses of each other is correct.

A number is a mathematical entity that can be used to count, measure, or name things. For example, 1, 2, 56, etc. are the numbers.

It is given that:

The expression is x + y

The expression can be defined as the combination of constants and variables with mathematical operators.

If x + y is rational, must x and y each can be or cannot be rational because x and y could be additive inverses of each other.

As we know, the arithmetic operation can be defined as the operation in which we do the addition of numbers, subtraction, multiplication, and division. It has a basic four operators that is +, -, ×, and ÷.

Thus, option (C) No; because x and y could be additive inverses of each other is correct.

Learn more about the number here:

brainly.com/question/17429689

#SPJ2

The number of bags that can be filled completely is 105 and the 3 rocks will be left over.

Division is the process of dividing a number by a given number.

Given that, the number of rocks is 1578 and the number of rocks in each bag is 15.

To find the number of bags, divide the number of total rocks by the number of total rocks in each bag:

1578/15

= 105.2

≈ 105

Now, the number of rocks in 105 bags is:

105 ×15

= 1575

So, the number of rocks left is:
1578 - 1575

= 3

Hence, the number of bags that can be filled completely is 105 and the 3 rocks will be left over.

To learn more about division, click here:

https://brainly.com/question/10571790

#SPJ5

Answer:

8+8i

Step-by-step explanation:

remove parenthesis

3+i+5+7i

add like terms

8+8i

not sure if you wanted it foiled or like that

Answer: x = 9 (choice D)

Assuming this is a geometric kite, then this means that triangle ABD is a reflection over the line BD to get triangle BCD. Furthermore, this points to AB and BC being the same length

AB = BC

3x - 5 = 22 .... substitution

3x - 5+5 = 22+5 .... add 5 to both sides

3x = 27

3x/3 = 27/3 ..... divide both sides by 3

x = 9

The lines j' and k' are parallel lines.

                Option: B is the correct answer.

We are given Line j ans Line k such that both are parallel to each other.

Now as we know that the translation transformation just change the position of the location but does not changes it shape.

As both the lines were parallel to each other so on translating both of them they just shifted some units to the right but the behavior remains the same.

Also, from the figure attached to the answer we may observe that the two lines are parallel to each other as the distance between the two lines at each point is constant.

            Hence, the correct answer is:

                       Option: B