The diagram shows a triangle PQR.
XYZR is a parallelogram where
X is the midpoint of RP,
Y is the midpoint of PQ,
and Z is the midpoint of QR.
Prove that triangle PYX is congruent
to triangle YQZ.
Total marks: 4
Answers
Answer:
Triangle ΔPYX is congruent to triangle ΔYQZ by Angle-Angle-Side condition of congruency
Step-by-step explanation:
The given
Statement [tex]{}[/tex] Reason
PQR is a triangle [tex]{}[/tex] Given
XYZR is a parallelogram [tex]{}[/tex] Given
X is the midpoint of RP [tex]{}[/tex] Given
Y is the midpoint of PQ [tex]{}[/tex] Given
Z is the midpoint of QR [tex]{}[/tex] Given
Therefore;
QY = YP, Definition of midpoint
XY is parallel to QR, and YZ is parallel to RP Midpoint theorem
Therefore, ∠PYX ≅ ∠PQR and ∠QZY ≅ ∠YXP Corresponding angles of parallel lines
From which we have;
Triangle ΔPYX is congruent to triangle ΔYQZ by Angle-Angle-Side condition of congruency.
Related Questions
⚠️⚠️please answer⚠️⚠️
Answers
Answer:
The slope is -3/4 and the y-intercept is 1.
Step-by-step explanation:
B is the point where the line cross the y-axis, or vertical axis. Slope is the steepness of the line. Determined by rise over run. When the slope goes down 3 units, the slope goes to the right 4 units.
Answer:
slope is -3/2 and y intercepts the line at (0,1)
A new four way intersection is being constructed in New York Hyde park through point P(-3,-15) an equation of the line representing one road is y = -3/4x + 7 create an equation of the line representing the new road that will run perpendicular to the first road
Answers
Given:
A new four way intersection is being constructed in New York Hyde park through point P(-3,-15).
Equation of line of one road : [tex]y=-\dfrac{3}{4}x+7[/tex].
New road that will run perpendicular to the first road
To find:
The equation of line for the new road.
Solution:
The slope intercept form of a line is
[tex]y=mx+b[/tex]
where, m is slope and b is y-intercept.
We have,
[tex]y=-\dfrac{3}{4}x+7[/tex]
Slope of this line is [tex]-\dfrac{3}{4}[/tex] and y-intercept is 7.
Product of slopes of two perpendicular line is -1.
[tex]m_1\times m_2=-1[/tex]
[tex]-\dfrac{3}{4}\times m_2=-1[/tex]
[tex]m_2=\dfrac{4}{3}[/tex]
The point slope form of a line is
[tex]y-y_1=m(x-x_1)[/tex]
where, m is slope.
The slope of new line is [tex]\dfrac{4}{3}[/tex] and it passes through P(-3,-15). So, the equation of line of new road is
[tex]y-(-15)=\dfrac{4}{3}(x-(-3))[/tex]
[tex]y+15=\dfrac{4}{3}(x+3)[/tex]
[tex]y+15=\dfrac{4}{3}x+4[/tex]
Subtract 15 from both sides.
[tex]y=\dfrac{4}{3}x+4-15[/tex]
[tex]y=\dfrac{4}{3}x-11[/tex]
Therefore, the equation of the line representing the new road is [tex]y=\dfrac{4}{3}x-11[/tex].
A bakery sells 5 bagels for 7.50.There is a proportion relationship between the cost and the number of bagels,Which equation represents the cost in dollars, c, for b bagels?
Answers
Answer:
$1.5b
Step-by-step explanation:
If a bakery sells 5 bagels for $7.50, we are to find the equation that will represent the cost of b bagels. This can be gotten using the equality postulate as shown;
5 bagels = $7.50
b bagel = $c
Cross multiply
5*c = 7.50b
Divide both sides by 5
5c/5 = 7.50b/5
c = 1.5b
Hence the cost of b bagel c is $1.5b
Answer:
Step-by-step explanation:Taylor works on an art project that uses only rectangular pieces of paper the first rectangle has length 3/8 in and width 3 in
A covered bridge is 8 yards long. In a painting for sale at a gallery, the bridge in the painting to the actual length of the bridge. One salesperson says the ratio in simplest form is 5/8. Another salesperson says the ratio in simplest form is 5/24. Which ratio is correct? What error leads to the incorrect ratio?
Answers
Answer:
The ratio that is correct is 5/24.
The error that leads to the incorrect ratio is working with the different units of length.
Step-by-step explanation:
Here is the complete question:
A covered bridge is 8 yards long. In a painting for sale at a gallery, the bridge is 5 feet long. A customer wants to know the ratio of the length of the bridge in the painting to the actual length of the bridge. One salesperson says the ratio in simplest form is 5/8 Another salesperson says the ratio in simplest form is 5/24 Which ratio is correct? What error leads to the incorrect ratio?
Step-by-step explanation:
From the question,
A covered bridge is 8 yards long and in a painting at the gallery, the bridge is 5 feet long.
To determine the ratio of the length of the bridge in the painting to the actual length of the bridge,
First, we will convert both lengths to the same unit and then divide the length of the bridge in the painting by the actual length of the bridge.
Convert 8 yards to feet
1 yard = 3 feet
∴ 8 yards = (8 × 3) feet = 24 feet
The actual length of the bridge is 24 feet
The length of the bridge in the painting is 5 feet
Hence, the ratio of the length of the bridge in the painting to the actual length of the bridge is 5 feet ÷ 24 feet = 5/24
Hence, the ratio that is correct is 5/24.
The error that leads to the incorrect ratio is working with the different units of length (that is, not converting both length to the same unit before determining the ratio).
Find the distance between (8,0) and (4,-4)
Answers
Answer:5.656854
Step-by-step explanation:
Write as an expression or an equation: Two times a number plus six equals 16.
help please
Answers
Answer:
2x10+6=16
that's the equation
the expression doesn't have an answer so it would look like this:
2x10+6
Jane decided she would spend the
of her money on Sweet Tarts. About how
many pounds of Sweet Tarts did Jane
purchase?
. Between the gum balls, Pixie Sticks, and
that she would spend the rest
Sour Patch Kids, how much money will
Nicholas have left of his allowance?
Answers
Answer:
can you comment the real question because this is just gibrish
Step-by-step explanation:
If x= -2 what is the value of -5x + 8x/4 + 7
Answers
Answer:
13
Step-by-step explanation:
Hope This Helps!
Plz Mark Brainliest!
10 - 16/4 + 7
10 - 4 + 7
13
Need help ASAP please ‼️‼️
Naomi is planning a holiday. The hotel costs $80 every night she stays and the flight costs $250,
She has a budget of $700 for her hotel and flight. How many nights will she be able to stay at
the hotel without going over her budget?
Answers
Answer:
5 nights
Step-by-step explanation:
# of nights= budget - flight {divided by} price per night
= 700$ - 250$ {divided by} 80$
= 450$ {divided by} 80$
= 5.6
=5 (round down)
Answer:
she will be able to stay 5 nights at the hotel
the second awnser and the third awnser.
Step-by-step explanation:
if the flight costs $250 and a night at the hotel costs $80 then 5 nights would equal $400 and then you would add the flight costs and it would equal $650. it can't be 6 nights cause she would go over her budget.
A hockey player strikes a hockey puck. The height of the puck increases until it reaches a maximum height of 3 feet, 55 feet away from the player. The height $y$ (in feet) of a second hockey puck is modeled by $y=x\left(0.15-0.001x\right)$ , where $x$ is the horizontal distance (in feet). Compare the distances traveled by the hockey pucks before hitting the ground.
Answers
Answer:
Second puck travels farther
Step-by-step explanation:
Maximum height of first puck = 3 feet
The height of a second hockey puck is modeled by:
[tex]y=x\left(0.15-0.001x\right)[/tex]
[tex]y=0.15x-0.001x^2[/tex]
To find maximum height of second puck
[tex]y'=0.15-0.002x[/tex]
Equate the derivative equals to 0
0.15-0.002x=0
[tex]\frac{0.15}{0.002}=x[/tex]
75 = x
At x = 75
[tex]y=0.15(75)-0.001(75)^2=5.625[/tex]
So, The maximum height of second puck is greater than first puck
So, Second puck travels farther
Only answer if you know for sure you’re right! :)
Answers
Answer:
14x+14=14(x+1)
Mr. Turner employer pays 100% of his medical insurance. He has rent of $800 and $600 for car payment, $100 light bill, and $300 car insurance. His payroll and income taxes are estimated to be $287.What is his necessary monthly salary to have a gross income to meet his total expenses including the payroll and income taxes? The monthly salary is
Answers
Given :
Mr. Turner employer pays 100% of his medical insurance. He has rent of $800 and $600 for car payment, $100 light bill, and $300 car insurance. His payroll and income taxes are estimated to be $287.
To Find :
What is his necessary monthly salary to have a gross income to meet his total expenses including the payroll and income taxes.
Solution :
Minimum salary to bear all expenses is :
S = Basic expenses + Payroll and taxes
S = $( 800 + 600 + 100 + 300 + 287)
S = $2087.00
Therefore, monthly salary is $2087.00 .
Hence, this is the required solution.
Can someone please help me with this problem? Will mark brainliest
Answers
I will send you on comment section the statics and it's correct answer. Please mark me as a brainist.
On a famous episode of Star Trek, Captain Kirk and the gang played a card game called Phisbin. This problem is about another game, called Frisbin. The object of Frisbin is to throw three Frisbees at three different-sized bins that are set up on the ground about 20 feet away from the player. If a Frisbee lands in the largest bin, the player scores 1 point. If a Frisbee lands in the medium-sized bin, the player scores 5 points. If a Frisbee lands in the smallest bin, the player scores 10 points. Kirk McCoy is playing the game. If all three of his Frisbees land in bins, how many different total scores can he make?
Answers
Answer:
10 different possible scores
Step-by-step explanation:
the total possible scoring combinations are:
large bin (1) medium bin (5) small bin (10) score
3 0 0 3
2 1 0 7
2 0 1 12
1 2 0 11
1 0 2 21
1 1 1 16
0 3 0 15
0 2 1 20
0 1 2 25
0 0 3 30
Using the principle of combination, the number of different total scores that can be made is 10.
Using the combination relation which includes repetition :
[tex] \binom{n + k - 1}{k} [/tex]n = number of Frisbee = 3 k = number of bins = 3Substituting the values into the formula :
[tex] \binom{3 + 3 - 1}{3} = \binom{5}{3} [/tex]
Using the combination formula :
[tex]nCk = \frac{n!}{(n-k)!k!}[/tex]
[tex]5C3 = \frac{5!}{(5-3)!3!}[/tex]
[tex]5C3 = \frac{5!}{2!3!}[/tex]
[tex]5C3 = \frac{5 \times 4}{2} = \frac{20}{2} = 10[/tex]
The number of different total scores that he can make is 10.
Learn more :https://brainly.com/question/19299862
-6 - 13
I don’t get it can someone explain?
Answers
Answer:
-19
Step-by-step explanation:
So, you can also write this equation as:
-6 + -13 = -19
For example:
You owe your friend $6.
You borrow 13 more dollars from him.
Now you owe him $19.
You have $-19 because you are in debt.
Hope I helped :)
Please consider Brainliest :)
Bernie helped design a magician costume for a school play. He used 5.75 feet of ribbon for the magician's wand. He used 11.75 feet of the same ribbon to decorate the magician's robe. If Bernie used $10.50 of ribbon in all, how much did the ribbon cost per foot?
Answers
Answer:
The ribbon cost per foot $0.6 per foot
Step-by-step explanation:
Total number of ribbon used = (5.75 + 11.75) = 17.50 feet
17.50 feet of ribbon cost = $10.50
1 foot of ribbon cost = x
Cross Multiply
17.50 × x = 1 foot × $10.50
x = 1 foot × 10.50/17.50
x = $0.6
The ribbon cost per foot $0.6 per foot
Answer: $0.75
Step-by-step explanation:
Total amount used for the ribbons = $1.50
Total feet of ribbons used = 5.75 feet + 11.75 feet = 17.5 feet
The cost of ribbon per foot will now be:
= $10.50/17.5
= $0.6 per foot
Please help i dont understand
Answers
Answer:
5
Step-by-step explanation:
find the measure
Xy = 6
M of x = 55°
M of s = 50°
Because the triangles are congruent the corresponding angles are also going to have congruent measures but I’m not sure if 6 is the right answer for the measure of XY because I took geo last year so it might not be right
On a coordinate plane, a line is drawn between points (negative 4, negative 3) and (negative 1, 4).
Use the Pythagorean theorem to find the distance on the coordinate plane.
a2 + b2 = c2
What is the distance between the two points?
StartRoot 20 EndRoot
StartRoot 40 EndRoot
StartRoot 45 EndRoot
StartRoot 58 EndRoot
Answers
Answer:
StartRoot 58 EndRoot
Step-by-step explanation:
Given the coordinates (-4, -3) and (-1, 4)
To get the distance between the two points, we will use the formula:
D =√(y2-y1)²+(x2-x1)²
From the coordinates, x1 = -4, y1 = -3, x2 = -1 and y2 = 4
Substitute
D =√(4-(-3))²+(-1-(-4))²
D = √(4+3)²+(-1+4)²
D = √7²+3²
D = √49+9
D = √58
Hence the correct option is D
StartRoot 58 EndRoot
Answer:
D. 58
Step-by-step explanation:
Suppose the average yearly salary of an individual whose final degree is a master's is $ thousand less than twice that of an individual whose final degree is a bachelor's. Combined, two people with each of these educational attainments earn $ thousand. Find the average yearly salary of an individual with each of these final degrees. The average yearly salary for an individual whose final degree is a bachelor's is $__ nothing thousand and the average yearly salary for an individual whose final degree is a master's is $__ nothing thousand.
Answers
Answer:
m = 2b - 45000
m + b = 111000
Substitute to get
2b - 45000 + b = 111000
3b = 156000
b = 52000
So m = 59000
Step-by-step explanation:
(Go Answer my question pls! Thanks!)
If f(x) = 4x - 8, then find f(2).
Answers
Answer:
what is x
Step-by-step explanation:
Turn this into numerical form -> one-half the sum of x and 12 Thank you!
Answers
Answer: 1/2(x+12)
Step-by-step explanation: Sum is adding.
Using the given angle measures, how many triangles can be formed (one unique, more than one, or none)? Explain your answer.
Answers
what are the angle measures?
If f(x)=4x−11, what is the value of f(5)?
Answers
f(5)=20-11
f(5)=9
solve for 1/3(2x-y)=z for x
Answers
Answer:
The answer is 7.
Step-by-step explanation:
Cant you math bro?
6. Daniel has $1200 in his account and he withdraws $10 each week. Jacob has $300 in his account
and he deposits $20 each week. How long will it take for Daniel and Jacob to have the same
amount of money in their accounts?
Answers
1200-10x =300+20x
20x=900-10x
30x=900
X=30
Ranny is buying presents for members of his family. He wants to spend $10 less on his brother than he spends on his sister, and six dollars more than twice the amount he spends on his sister on his mother. If Ranny has $100 to spend, how much does he intend to spend on his brother? Please answer with a numerical explanation. No other explanation required.
Answers
Answer:
8
Step-by-step explanation:
Answer:
Step-by-step explanation: ahshshhshdbd
What is the image of the point (-5,-7) after a rotation of 270 counterclockwise about the origin
Answers
Answer:
Your answer will be (-5,7).
Step-by-step explanation:
Answer:
(-7,5)
Step-by-step explanation:
A tailor uses 12 meters of fabric daily. How many centimeters of fabric will he use in two weeks?
Answers
Length of fabric a tailor uses a day = 12 meters
Length of fabric a tailor uses a day =
2 weeks = 14 days
Length of fabric a tailor will use in 14 days =
= 14 × 12
= 168 meters
Therefore , a tailor will use 168 meters of fabric in two weeks .
So, the additive inverse of -7/8 is
Answers
Answer:
Im prett sure its 7/8
Step-by-step explanation:
The additive inverse of a number is a number that, when added, goes to zero. For example, 7 is -7 because when added it equals 0 (or 7-7)
Help in this one please
Answers
Step-by-step explanation:
hope this helps, good Night
