Given the coordinates, determine whether PQR & XYZ are congruent
P(5,-4), Q(-3, 7), R(0, 2), X(-2,-1), Y(9, 7), Z(3, 2)
PQ=
XY=
QR=
YZ=
PR=
XZ=
Are the triangles congruent? If yes, explain your reasoning and write a congruence statement.
Answer:
The triangles are congruent
Step-by-step explanation:
Given
[tex]P(5,-4), Q(-3, 7), R(0, 2), X(-2,-1), Y(9, 7), Z(3, 2)[/tex]
Required
Determine if PQR = XYZ
To do this, we make use of distance formula.
[tex]D = \sqrt{(x_2-x_1)^2+(y_2-y_1)^2}[/tex]
For PQ:
[tex](x_1,y_1) = (5,-4)[/tex] and [tex](x_2,y_2) = (-3,7)[/tex]
So:
[tex]PQ = \sqrt{(-3-5)^2+(7-(-4))^2}[/tex]
[tex]PQ = \sqrt{(-8)^2+(7+4)^2}[/tex]
[tex]PQ = \sqrt{(-8)^2+(11)^2}[/tex]
[tex]PQ = \sqrt{64+121}[/tex]
[tex]PQ = \sqrt{185}[/tex]
For XY:
[tex](x_1,y_1) = (-2,-1)[/tex]
[tex](x_2,y_2) = (9,7)[/tex]
So:
[tex]XY = \sqrt{(9-(-2))^2+(7-(-1))^2}[/tex]
[tex]XY = \sqrt{(9+2)^2+(7+1)^2}[/tex]
[tex]XY = \sqrt{(11)^2+(8)^2}[/tex]
[tex]XY = \sqrt{121+64}[/tex]
[tex]XY = \sqrt{185}[/tex]
For QR:
[tex](x_1,y_1) = (-3,7)[/tex] and [tex](x_2,y_2) = (0,2)[/tex]
So:
[tex]QR = \sqrt{(0-(-3))^2 + (2-7)^2}[/tex]
[tex]QR = \sqrt{(0+3)^2 + (-5)^2}[/tex]
[tex]QR = \sqrt{(3)^2 + 25}[/tex]
[tex]QR = \sqrt{9 + 25}[/tex]
[tex]QR = \sqrt{34}[/tex]
For YZ:
[tex](x_1,y_1) = (9,7)[/tex] and [tex](x_2,y_2) = (3,2)[/tex]
So:
[tex]YZ = \sqrt{(3-9)^2+(2-7)^2}[/tex]
[tex]YZ = \sqrt{(-6)^2+(-5)^2}[/tex]
[tex]YZ = \sqrt{36+25}[/tex]
[tex]YZ = \sqrt{61}[/tex]
For PR:
[tex](x_1,y_1) = (5,-4)[/tex] and [tex](x_2,y_2) = (0,2)[/tex]
So:
[tex]PR = \sqrt{(0-5)^2+(2-(-4))^2}[/tex]
[tex]PR = \sqrt{(-5)^2+(2+4)^2}[/tex]
[tex]PR = \sqrt{(-5)^2+(6)^2}[/tex]
[tex]PR = \sqrt{25+36}[/tex]
[tex]PR = \sqrt{61}[/tex]
For XZ:
[tex](x_1,y_1) = (-2,-1)[/tex] and [tex](x_2,y_2) = (3,2)[/tex]
So:
[tex]XZ = \sqrt{(3-(-2))^2+(2-(-1))^2}[/tex]
[tex]XZ = \sqrt{(3+2)^2+(2+1)^2}[/tex]
[tex]XZ = \sqrt{5^2+3^2}[/tex]
[tex]XZ = \sqrt{34}[/tex]
From the calculations above:
[tex]PQ = XY = \sqrt{185[/tex]
[tex]QR = XZ = \sqrt{34[/tex]
[tex]PR = YZ = \sqrt{61[/tex]
Hence, the triangles are congruent base on SSS (Sides- Sides-Sides)
ASAP HELP!! sorry the photo is bad it’s the lighting but please help
Answer:
3
Step-by-step explanation:
How can you rewrite -8 -− 10 as an addition problem?
A:-8- -10
B -8+10
C-8+18
D-8+ -18
Answer:
B. -8+10
Step-by-step explanation: keep the -8 change - sign to +sign then change -10 to 10 .
Hope it helps :)
........................
Answer:
Step-by-step explanation:
Figure (1)
x° = 107° [Vertically opposite angles]
Since, vertical angles are equal in measure.
Figure (2)
x + 71° = 90° [Given, complementary angles]
x = 90° - 71°
x = 19°
Figure (3)
x + 21° = 180° [Given as supplementary angles]
x = 180° - 21°
x = 159°
Figure (4)
x = 129° [Vertical angles]
Figure (5)
x° = 90° [Given]
z° + 34° = 90°
z° = 90° - 34°
z° = 56°
Since, x° + y° + z° = 180° [Linear angles]
90° + y° + 56° = 180°
y° + 146° = 180°
y° = 180° - 146°
y° = 34°
6.) Which is the best description of the equation
below?
2x-2y=6
A Cause I'm big brain and we learned that
PLEASE HELP ME IN SUPER CONFUSED!
Represent the following sentence as an algebraic expression, where "a
number" is the letter x. You do not need to simplify.
Twice the difference of a number and 3.
Answer:
x-3*2
Step-by-step explanation:
I WILL BRAINLIEST PLS HELP ME I NEED HELP PLS ,
If 2 cm = 5 ft, what is the area of the playground?
Answer:
Step-by-step explanation:
Ok so
2 cm is 5 feet and there are 24
2 = 5
4 = 10
6 = 15
8 = 20
10 = 25
11 = 30
So for this one there are about . 10 feet at the top and 8 feet for the other
Answer:
The scale of the drawing is
Step-by-step explanation:
we know that
If two figures are similar, then the ratio of its areas is equal to the scale factor squared
Let
z-----> the scale drawing
x-----> the area of the playground in the scale drawing
y----> the area of the actual playground
we have
substitute
simplify
or
Divide by 4 both numerator and denominator
Help me please thanks
Answer:
y=x+4
Step-by-step explanation:
Slope intercept is y= mx+b
The slope is rise/run or change in y/change in x. Here the slope is 1 since when y goes up1, x goes to the right 1 (1/1=1).
The y intercept is 4 since it hits the y axis at 4.
so it would be y= 1x+4 which is y=x+4
please help if u can! :)))
Work out the area of the trapezium ABDE.
Answer:
(half * base 1 * base 2)/height
base 1 is 6 and base 2 is 9
get the height from similarity
6/9 = 8/CE
therefore CE = 72/6
Answer:
30cm²
Step-by-step explanation:
AE/BD = CE/CD
9/6 = CE/8
CE = 9/6 x 8
CE = 12cm
DE = CE - CD
DE = 12 - 8 = 4 cm
½(6 + 9)4 = 30cm²
The sum of four times a number and eight is between zero and twelve. Find the range of numbers.
2<x<3 or Anything between negative 2 and 3
Step-by-step explanation:
0<4x+8<12
-8<4x<12
-2<x<3
can some one please help me please
Answer:
x = 65.4
Step-by-step explanation:
I solved this question already. My explanation is here: https://brainly.com/question/20456072
Hope this helped! <3
Select all of the equations where x = 3 is a solution.
A.7x - 2 = 19
B.5x = 15
C.5x + 6 = 21
D.2x=5
E.3x = 33
F.3x = 1
Answer:
x=3 in equation ;5x=15 and in equation C.
Need done ASAP 25 points!!!!!!!!
Answer:
Step-by-step explanation:
A
10p - 3p-2/4+5 when p = 10
*I'm in 5th grade pls help*
Answer:
10(10)-3(10)-2/4+5=149/2 (decimal 74.5)
Find the value of each.
4 boxes of pasta at $1.25 each
Answer:
The total of all the boxes would be $5.00.
There are 8 bones in a large snake for 3 bones in a small snake. The small snake has 150 bones. How many bones does the large snake have?
Answer:
400!
Step-by-step explanation:
150/3= 50
50*8=400
Answer:
XD lol
Step-by-step explanation:
50 POINTS PLEASE HELP!!!!!!!!!!!!!
On average, Carter can get ready in 25 minutes but, depending on the day, his time can vary from the average by 15 minutes. Which absolute value equation can be used to calculate Carter's maximum and minimum time to get ready? Let x represent the maximum and minimum time.
|x−15|=25
|x+15|=25
|x+25|=15
|x−25|=15
Answer:
i thinking a or d
Step-by-step explanation:
The absolute value equation is |x+15|=25. Therefore, option B is the correct answer.
What is a absolute value equation?To solve an equation containing absolute value, isolate the absolute value on one side of the equation. Then set its contents equal to both the positive and negative value of the number on the other side of the equation and solve both equations.
Given that, on average, Carter can get ready in 25 minutes but, depending on the day, his time can vary from the average by 15 minutes.
Let x represent the maximum and minimum time.
So, the absolute value equation is |x+15|=25
Therefore, option B is the correct answer.
To learn more about a absolute value equation visit:
https://brainly.com/question/2166748.
#SPJ2
What’s 2*4 equal to in a Meath knowledge
Answer: 8
Step-by-step explanation:
I think the answer is 8
hey please help
just tell me all the ones that work
Answer:
D and A and B i think
Step-by-step explanation:
John paid $50 for renting a cycle for 5 hours. Which graph shows the relationship between the cost of renting a cycle for different hours? (1 point)
A graph is shown. The title of the graph is Cycle Renting. The horizontal axis label is Number of Hours. The horizontal axis values are 0, 1, 2, 3, 4, 5, 6. The vertical axis label is Cost in dollars. The vertical axis values are 0, 10, 20, 30, 40, 50, 60. Points are plotted on the ordered pairs 1,10 and 2,20 and 3,30.
A graph is shown. The title of the graph is Cycle Renting. The horizontal axis label is Number of Hours. The horizontal axis values are 0, 1, 2, 3, 4, 5, 6. The vertical axis label is Cost in dollars. The vertical axis values are 0, 10, 20, 30, 40, 50, 60. Points are plotted on the ordered pairs 1, 50 and 2,50 and 3,50.
A graph is shown. The title of the graph is Cycle Renting. The horizontal axis label is Number of Hours. The horizontal axis values are 0, 1, 2, 3, 4, 5, 6. The vertical axis label is Cost in dollars. The vertical axis values are 0, 10, 20, 30, 40, 50, 60. Points are plotted on the ordered pairs 1, 5 and 2,10 and 3,15.
A graph is shown. The title of the graph is Cycle Renting. The horizontal axis label is Number of Hours. The horizontal axis values are 0, 1, 2, 3, 4, 5, 6. The vertical axis label is Cost in dollars. The vertical axis values are 0, 10, 20, 30, 40, 50, 60. Points are plotted on the ordered pairs 1,20 and 2,40 and 3,60.
Answer:
Graph A <==
Step-by-step explanation:
$ 50 for 5 hours......50/5 = 10...thats $ 10 per hr
so the equation would be : y = 10x...with x being the number of hrs and y being the total cost.
So ur x axis will be the hours and your y axis will be the total cost.
so ur answer is :the title of the graph is cycle renting. the x axis (the horizontal axis)...since it is the hours, will be labeled 0,1,2,3,4,5,6
the y axis (the vertical axis)...since it is the total cost, will be labeled
0,10,20,30,40,50,60. points are plotted on (1,10),(2,20), and (3,30)
Which expression is equivalent to 4x4x4x4x4
Answer:
Step-by-step explanation:
4x4x4x4x4=4^5=1024
A manager of a clothing store always orders 2 small T-shirts and 3 large T-shirts for
every 4 medium T-shirts. The manager plans to order 24 medium T-shirts. How
many small T-shirts and large T-shirts should the manager order? Show your work.
Answer:
12 small, 18 large
Step-by-step explanation:
x - small
y - large
z- medium
4z=2x=3y then she orders 24
24/4=6 times more than usually, so we should *6 for every x and z
24z=6*2x=6*3y
12 - x - small tshirt
18 - y - large
How do I do this?
My son school just gave him this and he doesn’t know how to do it and I don’t know.
Answer:
I would just search online what are corresponding angles and then base it off of angles like angle number 4 is corresponding because corresponding angles are just angles with the same size and same line
Question 1 (3 points)
(6.03)
Which expression shows a sum of three terms? (3 points)
O a
x3
3 + x + 3
Ob
ос
3x
Od
3(x + 3)
Answer:
more context please:)
Step-by-step explanation:
Answer:
3 + x + 3
Step-by-step explanation:
Hope it helps!
2y-x=8 and y-2x=-5. Solve the system of equations
Answer:
y = 7 x = 9
Step-by-step explanation:
2y-x=8
2(2y-x=8)
4y-2x=16
-(y-2x= -5)
3y +0x= 21
3y=21
y=7
2(7)-x=8
14-x=8
9=x
what is 4 1/2-3 5/6 from page 393 GO Math book
Answer:
The answer is 1/6
Step-by-step explanation:
This is the answer because it is.
The corporate team building ecent will cost $6 if it has 3 attendees. if there are 8 attendees how much will the corporate team building event cost?
Answer:
The team building event will cost $24 for 4 attendees.
Step-by-step explanation:
Given,
Cost charged corporate team building = $6 for every attendee
Number of attendees = 4
We will multiply the amount of one ticket with number of attendees in order to find the total cost.
Cost charged for 4 attendees = 6*4
Cost charged for 4 attendees = $24
ons: Practice
Question 5 of 5
Type the correct answer in the box. Use numerals instead
What value of x makes this equation true?
X/6 - 7 = -4
Answer:
[tex]x = 18[/tex]
Step-by-step explanation:
Given
[tex]\frac{x}{6} - 7 = -4[/tex]
Required
Solve for x
[tex]\frac{x}{6} - 7 = -4[/tex]
Add 7 to both sides
[tex]\frac{x}{6} - 7+7 = -4+7[/tex]
[tex]\frac{x}{6} = -4+7[/tex]
[tex]\frac{x}{6} = 3[/tex]
Multiply through by 6
[tex]6 * \frac{x}{6} = 3 * 6[/tex]
[tex]x = 3 * 6[/tex]
[tex]x = 18[/tex]
if two fair coins are tossed simultaneously, what are the chances of both coming up 'heads'?
Answer:
i think 1/4
Step-by-step explanation:
Answer:
[tex]\frac{1}{4}[/tex]
Step-by-step explanation:
We name the coins coin 1 and coin 2 for the sake of simplicity.
There are four possible situations:
coin 1 head, coin 2 head
coin 1 head, coin 2 tails
coin 1 tails, coin 2 head
coin 1 tails, coin 2 tails
Only case 1 results in both 'heads'. So the probability is 1/4.