Answer: A one-to-one correspondence between the parts of two figures is such that the corresponding parts are equal, then the figures are congruent.
The question pertains to geometric concepts of congruence, one-to-one correspondence, included side, included angle, and vector concepts in mathematics, such as orthogonal and parallel vectors, which are key concepts in solving geometry and trigonometry problems.
Explanation:The question refers to several key concepts in geometry. When each member of a set, such as angles of a triangle, can be paired with one and only one member of another set, we have a one-to-one correspondence. This correspondence can be applied to situations such as pairing angles or sides of one geometric figure with another.
For example, let's consider two triangles. If each angle of the first triangle corresponds to an angle of the second triangle, and all pairs of corresponding elements (angles or sides) are equal, then those two triangles are congruent. This is the basic principle of congruence in geometry.
The angle formed by two sides of a triangle is called an included angle. The side of a triangle that is formed by the common side of two angles is an included side. In a right triangle, like in Figure 5.17, we see the terms adjacent side, opposite side, and hypotenuse, which are used for trigonometric calculations such as sine, cosine, and tangent.
The Pythagorean Theorem plays a crucial role for right-angled triangles, stating that the square on the hypotenuse is equal to the sum of squares on the other two sides. Also, the question talks about parallel and orthogonal vectors. Two vectors are said to be parallel if they have identical directions, while orthogonal vectors are perpendicular to each other, with directions differing by exactly 90°.
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Solve the following equation; domain 0< x < 360; 3 cot x + sqrt 3 = 0
< is less than or equal too (I don't have the symbol on my keyboard. )
sqrt = square root.
Solve the equation 3 cot x + √3 = 0 by isolating cot x, and recognizing that tan x = -√3. The equation has solutions x = 120° and x = 300° in the given domain.
To solve the equation 3 cot x + √3 = 0 for the domain 0 ≤ x ≤ 360°, we can follow these steps:
Isolate cot x by moving √3 to the other side: 3 cot x = -√3.Divide both sides by 3: cot x = - (√3 / 3).Recall that cot x is the same as 1 / tan x, hence 1 / tan x = - (√3 / 3), which implies that tan x = -√3.Determine the angles where tan x = -√3. Tan x = -√3 at x = 120° and x = 300° within the specified domain.Thus, the solutions to the equation 3 cot x + √3 = 0 in the domain 0 ≤ x ≤ 360° are x = 120° and x = 300°.
Find the constant of variation for the relationship shown in the following table:
x 1 2 3 4
y 5 10 15 20
1
2
5
10
Graph the data in the table. Which kind of function best models the data? Right in equation to model the data.
A. Exponential y=2.5^x
B. Quadratic y=-2.5x^2
C. Quadratic y=2.5x^2
D. Linear y=2.5x
Answer:
c
Step-by-step explanation:
it is a parabola which has a standard equation of
y = x^2. option a is an exponentially positive curve. option b is a negative parabola. option d is a linear graph which isn't a parabola
Find the arc length of a central angle of pi/6 in a circle whose radius is 10 inches.
Answer:
= 5/3 * pi inches
or approximately 5.235987756 inches
Step-by-step explanation:
The formula for arc length = r * theta where theta is in radians
arc length = 10 * pi/6
= 10/6 * pi
= 5/3 * pi
or approximately 5.235987756 inches
Answer: 5.23 inches
Step-by-step explanation:
Let the length of the arc intersected by a central angle x be l.
Given:- Central angle[tex]x=\frac{\pi}{6}\text{ radians}[/tex]
Radius r= 10 inches
We know that ,
[tex]l=x\ r\\\\\Rightarrow\ l=\frac{\pi}{6}\times10\\\\\Rightarrow\ l=\frac{3.14\times10}{6}= 5.2333333333\approx5.23\text{ inches}[/tex]
Thus, the length of the arc of a central angle [tex]\frac{\pi}{6}\text{ radians}[/tex] is 5.23 inches.
Question:
1. What is the value of x? Show your work to justify your answer. (2 points)
2. What is the value of the exterior angle? Show your work to justify your answer. (2 points)
Answer:
1. [tex]x=56^o[/tex]
2. Exterior angle = [tex]116^o[/tex]
Step-by-step explanation:
1.
We can see from our given diagram that (2x+4) degrees is the measure of exterior angle of triangle PQR.
Since the measure of exterior angle of a triangle equals to the sum of the opposite interior angles. So measure of our given triangle's exterior angle will be equal to sum of measure of angle P and angle Q.
We can represent this information as:
[tex](2x+4)^o=60^o+x^o[/tex]
[tex]2x^o+4^o=60^o+x^o[/tex]
Let us subtract [tex]x^o[/tex] from both sides of our equation.
[tex]2x^o+4^o-x^o=60^o+x^o-x^o[/tex]
[tex]x^o+4^o=60^o[/tex]
Let us subtract [tex]4^o[/tex] from both sides of our equation.
[tex]x^o+4^o-4^o=60^o-4^o[/tex]
[tex]x=56^o[/tex]
Therefore, value of x is 56 degrees.
2. Since the measure of exterior angle of our given triangle is 2x+4, let us substitute x=56 in our expression to find the measure of exterior angle.
[tex]\text{Measure of exterior angle}=(2x+4)^o[/tex]
[tex]\text{Measure of exterior angle}=(2*56+4)^o[/tex]
[tex]\text{Measure of exterior angle}=(112+4)^o[/tex]
[tex]\text{Measure of exterior angle}=116^o[/tex]
Therefore, the measure of exterior angle of our given triangle is 116 degrees.
I’m so confused and I need help!!
Someone please help me because I need to get it done
WILL MARK BRAINLIEST. Which of the following demonstrates how the first 21 (on the left side of the triangle) is calculated using the combination pattern?
Answer:
That would be C.
Step-by-step explanation:
7C2 = 7! / (7-2)! * 2!
7C2 = 7*6*5*4*3*2*1 / 5*4*3*2*1 * 2*1
= 7*6 / 2
= 21
A zoo has a limited daily supply of leaves to feed elephants and giraffes. Every day, each giraffe eats the same amount of leaves, and each elephant eats 47\text{ kg}47 kg of leaves. Let EE represent the number of elephants and GG represent the number of giraffes that the zoo can feed with its daily supply of leaves. 47E+24G \leq 50047E+24G?500 According to the inequality, what is the zoo's daily supply of leaves, and how many \text{kg}kg of leaves does each giraffe eat per day?
Answer:
The zoo's daily supply of leaves is 500 kg leaves at most.
Each giraffe eats 24 kg leaves per day.
Step-by-step explanation:
We have been given an inequality: [tex]47E+24G\leq 500[/tex], where E represents the number of elephants and G represents the number of Giraffes. Every day, each giraffe eats the same amount of leaves, and each elephant eats 47 kg of leaves.
We can see that each elephant eats 47 kg of leaves per day, which is represented by 47E in our given inequality. The amount of leaves eaten by a giraffe is 24 kg, which is represented by 24G in our given inequality, therefore, each giraffe eats 24 kg leaves per day.
We can see that total amount of leaves eaten by E elephants and G giraffes is less than or equal to 500, which means that zoo's daily supply of leaves is at most 500 kg.
Answer:
1. Daily supply of leaves is 500 kg;
2. Each giraffe eats 24 kg of leaves per day.
Step-by-step explanation:
Let E represent the number of elephants and G represent the number of giraffes that the zoo can feed with its daily supply of leaves.
If each elephant eats 47 kg of leaves, then E elephants eat 47E kg of leaves.
Consider inequality
[tex]47E+24G \leq 500.[/tex]
The first term of this inequaliy represents the number of kilograms all elephants in zoo eat per day. The second term 24G represents the number of kilograms all giraffes in zoo eat per day. The sum 47E+24G represents the number of kilograms all elephants and giraffes in zoo eat per day (together). This amount of leaves should be less or equal than 500 kg. This means that all elephants and giraffes cannot eat more than 500 kg of leaves per day.
Joe gets paid 4 pounds to walk a dog. He wants to save 11 pound? How many times does he need to walk the dog.
Answer:
He needs to walk the dog 3 times as 3 times 4 = $12
Step-by-step explanation:
For each of the following equations say whether it is a horizontal or vertical line and state the slope of the line.
1. x = - 2
2. y = -8
3. x = 15
4. y = -4
Answer:
1. vertical line. slope is undefined.
2. horizontal line. slope of 0
3. vertical line. slope is undefined.
4. horizontal line. slope of 0
Step-by-step explanation:
In which expression is 13y a term?
a- 13y/4 −2y
b- 8+13y −yz
c- 4+ 13yz
d- 13+y
Answer:
Option b is the correct choice.
Step-by-step explanation:
We are asked to find the which of our given expressions has 13y as a term.
Since we know that a term can be a signed number, a variable, or a constant multiplied by a variable or variables as 2a or 5b. In term 2a, 2 is coefficient and a is a variable.
We can see that in 13y, 13 is coefficient and y is variable.
Let us see our given choices one by one.
a. [tex]\frac{13y}{4}-2y[/tex]
Let can write our 1st term as:
[tex]\frac{13}{4}y-2y[/tex]
We can see that both of our terms have y variable, but our 1st term has a coefficient 13/4 and 2nd term has a coefficient of -2. As none of these terms have 13 as a coefficient, therefore, option a is not a correct choice.
b. [tex]8+13y-yz[/tex]
We can see that 8 is a constant, while 13y and -yz are terms. Since our expression has 13y as a term, therefore, option b is the correct choice.
c. [tex]4+13yz[/tex]
We can see that 4 is a constant and 13yz is a term as it has variables yz. Since our given term has two variables, therefore, option c is not a correct choice as well.
d. [tex]13+y[/tex]
We can see that 13 is a constant and y is term of our given expression. Since our expression don't have 13 as coefficient, therefore, option d is not a correct choice.
b- 8+13y −yz. In the provided options, 13y is a standalone term in expression option b, which is 8+13y−yz. A term is part of an algebraic expression separated by plus or minus signs.
Explanation:The student is asking to identify in which expression 13y is a term. The correct answer is option b, which is 8+13y−yz. In this expression, 13y is a separate term that is being added to 8 and subtracted by yz.
It's important to recognize that in algebraic expressions a term is a single mathematical expression that can be a number, a variable, or the product of numbers and variables separated by a plus (+) or minus (−) sign. In the case of 13y, it is a term because it is separated by addition or subtraction in the expression. Other options include division or other variables combined with 'y', which do not present '13y' as a standalone term.
What is the sum of the first ten terms in the geometric series 4 – 12 + 36 – 108 + ...?
The sum of the first ten terms in the geometric series 4 – 12 + 36 – 108 + ... will be the negative 59048.
What is the sum of the geometric series?The series is given below.
4 – 12 + 36 – 108 + …
The complete series wall be
4 – 12 + 36 – 108 + 324 – 972 + 2916 – 8748 + 26244 – 78732
Then the sum of the first ten terms in the geometric series will be
⇒ 29524 – 88572
⇒ – 59048
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Tracy started a savings account that is set up so that the simple interest earned on the investment is moved into a separate account at the end of each year. Tracy invests $5,000 at 4.5%, what is the total simple interest accumulated in the checking account after 2 years? (1 pt) * a) $4.50 b) $45 c) $450 d) $4,500 e) $45,000
Given:
Tracy invests $5,000 at 4.5% and the simple interest earned on the investment is moved into a separate account at the end of each year.
To Find:
The total simple interest accumulated in the checking account after 2 years.
Answer:
$450 is the total simple interest accumulated in the checking account after 2 years.
Step-by-step explanation:
The principal sum invested by Tracy is $5000.
The rate of simple interest is given to be 4.5% and the time period given is 2 years.
To calculate the total amount of interest accrued we use the formula
[tex]\frac{P.R.T}{100}[/tex]
where P is the pricipal amount of money, R is the rate of interest and T is the time period.
So, putting the given values into the formula, we have
[tex]\frac{(5000)(4.5)(2)}{100}\\\\=\frac{45000}{100}\\\\=450[/tex]
Thus, $450 is the total simple interest accumulated in the checking account after 2 years.
The sum of two numbers is 25 one number is twice the second number plus sevenwhat are the two numbers
Answer:
The two numbers are 6 and 19.
Step-by-step explanation:
To find these, we must first set the first number as x. Then we can set the second one in terms of x as 2x + 7.
Now that we have these values, we can add them together and set equal to 25.
x + 2x + 7 = 25
3x + 7 = 25
3x = 18
x = 6
With the first value being 6, we can solve for the second by using the equation built.
2x + 7
2(6) + 7
12 + 7
19
The Lisbon’s new heat pump cost $4,500.
They bought it to replace their old furnace and air
conditioner which cost about $2,800 a year to
run. The heat pump will save them approximately
39% a year. In how many years will the heat
pump pay for itself? Round to the nearest tenth.
Answer:
4.1 years.
Step-by-step explanation:
We have been given that The Lisbon’s new heat pump cost $4,500. They bought it to replace their old furnace and air conditioner which cost about $2,800 a year to run. The heat pump will save them approximately 39% a year.
Yearly cost was 2800 at first and the pump will save 39% of 2800. So annual saving with new heat pump will be:
[tex]\frac{39}{100}*2800=0.39*2800[/tex]
Let x be the number of years in which heat pump will pay for itself, so saving in x years will be:
[tex]0.39*2800*x[/tex]
Now let us equate the savings by new heat pump with cost of heat pump to find the number of years (x).
[tex]0.39*2800*x=4500[/tex]
[tex]1092*x=4500[/tex]
[tex]x=\frac{4500}{1092}[/tex]
[tex]x=4.1208791208791209\approx 4.1[/tex]
Therefore, the heat pump will pay for itself in 4.1 years.
The heat pump will pay for itself in approximately 4.1 years.
To determine the number of years it will take for the heat pump to pay for itself, we need to calculate the annual savings from using the heat pump instead of the old furnace and air conditioner, and then divide the initial cost of the heat pump by these annual savings.
First, we calculate the annual savings by applying the 39% savings rate to the old cost of running the furnace and air conditioner:
Annual savings = 39% of $2,800
= 0.39 * $2,800
= $1,092
Now, we divide the initial cost of the heat pump by the annual savings to find out how many years it will take to recoup the cost:
Number of years to pay for itself = Initial cost of heat pump / Annual savings
= $4,500 / $1,092
= 4.12 years
Rounded to the nearest tenth, the heat pump will pay for itself in approximately 4.1 years.
What is the solution to the system of equations?
-3x-4y+z=-1
2x+y-z=-8
x+8y-z=23
A. (-3,4,6)
B. (4,-3,-1)
C. (-3,4,8)
D. (3,-4,-6)
Answer:
The answer is A (-3,4,6).
Step-by-step explanation:
1 Solve for z in -3x-4y+z=-1
z=3x-1+4y
2 Substitute z=3x-1+4y into 2x+y-z=-8
-x-3y+1=-8
3 Substitute z=3x-1+4y into x+8y-z=23
-2x+4y+1=23
4 Solve for x in -x-3y+1=-8
x=-3y+9
5 Substitute x=-3y+9 into z=3x-1+4y
z=-5y+26
6 Substitute x=-3y+9 into -2x+4y+1=23
10y-17=23
7 Solve for y in 10y-17=23
y=4
8 Substitute y=4 into z=-5y+26
z=6
9 Substitute y=4 into x=-3y+9
x=-3
10 Therefore,
x=-3
y=4
z=6
What is the distance between the points (-1, 5) and (3, 7)? Round your answer to the nearest hundredth. A. 3.46 B. 4.47 C. 10.77 D. 12.65
Answer:
B.4.47
Step-by-step explanation:
The equation to calculate the distance between two points is
D=[tex]\sqrt{(x_{1}-y_{1} )^{2}+(x_{2}-y_{2} )^{2 }[/tex]
here
[tex](x_{1},y_{1})=(-1,5)\\(x_{2},y_{2})=(3,7)[/tex]
substituting the values
[tex]\sqrt{(-1-3)^{2}+(5-7)^{2} }[/tex]
[tex]\sqrt{(-4)^{2}+(-2)^{2} }[/tex]
[tex]\sqrt{20}[/tex]
[tex]\sqrt{20}=4.47[/tex]
If lisa has 2,134 buttons that needed to be sorted equally into 12 jars.How many buttons will be in each jar.
You sell pies at a farmers' market for $7.50 each. Five people want to share a pie by splitting the cost equally. How much will each of them need to pay to buy a whole pie together?
Answer:
Each of them need to pay to buy a whole pie together = $1.50
Step-by-step explanation:
Unit rates defined as the rates are expressed as a quantity of 1, such as 7 feet per second or 9 miles per hour, they are called unit rates.
As per the statement: You sell pies at a farmers' market for $7.50 each.
⇒ Cost of each pie = $7.50
Also, five people want to share a pie by splitting the cost equally.
Number of people = 5
then, by definition of unit rate;
unit rate per people = [tex]\frac{Cost of whole pie}{Number of people} = \frac{7.50}{5} = \$1.50[/tex]
Therefore, $1.50 will each of them need to pay to buy a whole pie together.
Each person needs to pay $1.50.
Calculating Individual Payments for a Shared Pie
If five people want to share a pie by splitting the cost of $7.50 equally, we need to divide the total cost by the number of people to find out how much each person will pay. To do this, we take $7.50 and divide it by 5. This calculation gives us:
$7.50 / 5 = $1.50
Therefore, each of the five people will need to pay $1.50 to buy the whole pie together. This allows them to split the cost equally and purchase the pie at the farmers' market.
Spencer owns horses, and the nearest horse vet is 8 centimeters away from Spencers stable on a map. If the scale of the map is 1 centimeter = 7 kilometers, then what is the actual distance between Spencers stable and the vet?
Answer:
The actual distance is 56 km
Step-by-step explanation:
We can use ratio's to solve this problem
1 cm 8cm
---------- = -----------------
7 km x km
Using cross products
1 * x = 8 * 7
x = 56
x = 56 km
The perimeter of a rectangular field is 340 yards. If the length of the field is 91 yards, what is its width?
PLEASE SOMEONE HELP ME THANK YOU!!
Answer:
79
Step-by-step explanation:
91 x 2 is 182. 340-182 is 158 divide by 2 and you get 79
Answer:
The width is 79 yards
Step-by-step explanation
Okay, so the perimeter of a shape is the sum of all the side-lengths of said shape. Because the shape is a rectangle, there are 4 sides (2 sides being the length, 2 sides being the width). This being said, the equation that can be used to find the perimeter is Perimeter = Length + Length + Width + Width or Perimeter = 2Length + 2Width. You would then plug in your given variables and solve for width. I have shown my work in the image below, I hope this is helpful :)
An elephant needs to drink at least 40 gallons of water each day. A drinking tank contains 4 gallons of water. The elephant has already consumed 24 gallons of water. How many more tanks x of water does the elephant need to drink? Write your answer as an inequality.
Answer:
x≥4
Step-by-step explanation
24+4x≥40. Subtract 24 from both sides to get 4x≥16. Divide both sides by 4 to get x≥4.
Answer:
it requires more than or equal to 4 tanks
Step-by-step explanation:
An elephant needs to drink at least 40 gallons of water each day. A drinking tank contains 4 gallons of water. The elephant has already consumed 24 gallons of water. How many more tanks x of water does the elephant need to drink? Write your answer as an inequality.
An elephant drinks 40 gallons of water
a tank contains 4 gallon of water
lets convert the 40 gallons of water to tanks,t
40/4=10t
the elephant has consumed 24 gallons already
it means it has consumed 24/4=6t
x=more tanks need to drink
xt+6t≥10t..................1
xt≥10t-6t
x≥4
it requires more than or equal to 4 tanks
Look at the picture below
John states that by ASA.
Mary states that by AAS.
Phillip states that the triangles are not congruent.
Which student is correct? why?
MY ANSWER:
Phillip is correct. XY=/ AC. (But i have another guess/answer)
No student is right, These triangles arent congruent but these triangles are to different triangles. We can see this with XY/AC. (But doesnt that just mean phillip is correct?) HELP!
Answer: Phillip is correct. The triangles are not congruent.
How do we know this? Because triangle ABC has the 15 inch side between the two angles 50 and 60 degrees. The other triangle must have the same set up (just with different letters XYZ). This isn't the case. The 15 inch side for triangle XYZ is between the 50 and 70 degree angle.
This mismatch means we cannot use the "S" in the ASA or AAS simply because we don't have a proper corresponding pair of sides. If we knew AB, BC, XZ or YZ, then we might be able to use ASA or AAS.
At this point, there isn't enough information. So that means John and Mary are incorrect, leaving Phillip to be correct by default.
Note: Phillip may be wrong and the triangles could be congruent, but again, we don't have enough info. If there was an answer choice simply saying "there isn't enough info to say either if the triangles are congruent or not", then this would be the best answer. Unfortunately, it looks like this answer is missing. So what I bolded above is the next best thing.
Answer:
Phillip states that the triangles are not congruent.
Step-by-step explanation:
Assume for a second the triangles are congruent.
Then the angles are equal
<A =< X
<B= <Y
<C = <Z
Then
Triangle ABC = Triangle XYZ
from this information
AB = XY
and BC = YZ
and CA = ZX
but the only other piece of information we have is CA = 15 and XY = 15
If this is true then CA = ZX = 15 and AB = XY = 15
That would make this an isosceles triangle (AB = AC)
so angles B and C would have to be equal, but they are not.
So these two triangles cannot be congruent.
Given the following system, what variable will eliminate?
Can someone please help me with this question? Thanks if you!
Answer: D) 93
The red arc that spans from point X to point Z is 186 degrees, half of which is 186/2 = 93 and this is equal to the inscribed angle XYZ. I'm using the inscribed angle theorem which says that the arc measure is two times the inscribed angle that cuts off the arc.
Answer:
Faulty question in my opinion. See below.
Step-by-step explanation:
The central angle = the arc angle in degrees. So the central angle is 186 degrees.
The angle XYZ is 1/2 174 87 because it is 1/2 the measurement of the minor arc which is 174. That answer is not there unfortunately. The central angle must be on the same side as the arc measurement. The arc angle is on the opposite side of XZ. I would ask your instructor about this one.
There are 22456 pine trees in the park the park workers are going to plant 6478 more trees this year how many trees will there be when they are done
Answer:28934
Step-by-step explanation:
You add 22456 and 6478
After the park workers plant 6478 more trees in the park which currently has 22456 trees, the total number of trees would be 28934.
Explanation:This is a question of simple addition in mathematics. Currently, the park consists of 22456 pine trees. The park workers are planning to plant another 6478 trees. Therefore, to find out the total number of trees after they plant the new ones, we add together the current number of trees and the number of trees to be planted.
22456 (Current number of trees) + 6478 (Additional number of trees to be planted) = 28934
So, after planting the additional trees, there will be a total of 28934 trees in the park.
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Cindy has 2 boxes of pencils. Patrice has 5 boxes of pencils. Each box has the same number of pencils in it.
Answer:
hey mate..
plzz add more to ur question soo that we can answer it...!
;)
The expression which represents the total number of pencils will be 7x where x is the number of pencils.
What is an expression?An expression is a combination of some mathematical symbol such that an arithmetic operator and variable such that all are constrained and create an equation.
In other meaning, expression is very useful to determine the end or root value of constraint.
As per the given,
Cindy has 2 boxes of pencils. Patrice has 5 boxes of pencils.
Suppose the number of pencils in each box is "x" as it is the same.
Total pencils in Cindy boxes = 2x
Total pencils in Patrice boxes = 5x
Total pencils = 2x + 5x = 7x
Hence "The expression which represents the total number of pencils will be 7x where x is the number of pencils".
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The complete question is below,
Which expression helps you find the length x of a side of a rectangle that has a diagonal of 17 units and a width of 8 units?
To find the length of a rectangle given the diagonal and width, one can utilize the Pythagorean theorem. By treating the diagonal as the hypotenuse of a right triangle formed within the rectangle, we solve for 'x' (length) and get our desired result.
Explanation:To find the length (x) of the side of a rectangle given the diagonal (17 units) and the width (8 units), you can use the Pythagorean theorem, which states that in a right triangle, the square of the length of the hypotenuse is equal to the sum of the squares of the lengths of the other two sides. In the rectangle, the diagonal forms a right triangle with two sides.
In the context of this question, our hypotenuse is the diagonal, which is 17 units long. Let's denote the width as 'w' and the length we're trying to find as 'x'. With 'w' being 8 units, our scenario can be represented by the Pythagorean theorem like this: (17²) = (8²) + (x²)
In determining 'x', we can rearrange the equation to solve for 'x': x = sqrt[(17²) - (8²)]. So, when we subtract the square of 8 from the square of 17 then take the square root, we get the length of 'x'.
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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:
Correct answer is option C.
Step-by-step explanation:
Trapezoid ABCD ≅ trapezoid A'B'C'D'
You can reflect trapezoid ABCD across the x-axis and then rotating it 90°clockwise.
Answer:
C. Trapezoid ABCD ≅ trapezoid A'B'C'D'
You can reflect trapezoid ABCD across the x-axis and then rotating it 90°clockwise.
Step-by-step explanation:
Given : 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).
To find : Which statement correctly describes the relationship between trapezoid ABCD and trapezoid A'B'C'D'.
Solution : We have given that trapezoid ABCD.
Parent coordinates of A (2,6), B (5,6), C (7,1), and D (-1,1)
Translated coordinates A' (-6, -2),B' (-6, -5), C' (-1, -7), and D' (-1, 1).
By reflection rule : Reflection across x axis (x , y) →→( x , -y) and rotating it 90°clockwise (x , y) →→( -y, x).
Therefore, C. Trapezoid ABCD ≅ trapezoid A'B'C'D'
You can reflect trapezoid ABCD across the x-axis and then rotating it 90°clockwise.
please include all steps
This is a pretty simple proof, actually.
A parallelogram's diagonal always bisects each other.
The given proves that both diagonals bisect each other at point N. So if they bisect each other, it is a parallelogram.