Answers
Answer: The triangles are congruent by the HL theorem
HL = hypotenuse leg
======================================================
Explanation:
Through the segment addition postulate, we can say:
WZ = WT+TZ
YT = TZ+ZY
Notice how both WZ and YT have TZ as part of their segments.
Since WZ and YT are the same length, we can then say,
WZ = YT
WT+TZ = TZ+ZY
WT = ZY
I used substitution for the second step.
The last step is where I subtracted TZ from both sides, and they canceled out.
---------------------
We have the following info:
WT = ZY (just found)AT = UZ (given)angle AWT = angle UYZ (given)Normally, the conclusion from here would be "not enough info" because this is a SSA case. Note how the angles are not between the congruent sides. So we wouldn't use SAS.
However, despite us having SSA, it doesn't mean we can't keep going. The reason why is because we have two right triangles. So we can use the HL theorem instead. Statement 1 above refers to the L of HL, while statement 2 is the H.
HL = hypotenuse leg
Again, HL only works for right triangles. It's the only time we can use SSA to prove right triangles are congruent; otherwise, SSA is not a valid congruence theorem.
Related Questions
Two Boys are building a skateboard ramp. They want the ramp to be 3 feet tall and 5 feet long. One of them thinks that they can use a piece of plywood that is 4 feet long to cover the top of the frame.
This is one of theirs work.
a2 + b2 = c2
32 + b2 = 52
9 + b2 = 25
b2 = 16
b = 16−−√
b = 4
Why is his reasoning incorrect? Explain.
How long does the piece of plywood have to be to cover the top of the frame of the skateboard ramp? Round your answer to the nearest tenth of a foot. Show your work.
Another boys parents bought a 10 foot piece of plywood for him and his friend to use to cover the top of the frame. Draw and label a ramp they could create. Justify your work using the Pythagorean Theorem.
Draw
Answers
Answer:
The answer is below
Step-by-step explanation:
A triangle is a polygon with three sides and three angles. Types of triangles are acute, obtuse, scalene, isosceles, equilateral and right angled triangle.
Pythagoras theorem states that for a right angled triangle, the square of the hypotenuse is equal to the sum of the square of the remaining two sides.
The ramp has the form of a triangle. The height of the ramp is the vertical side of a triangle, the top of the frame is the hypotenuse while the length of the ramp is the base side of the triangle.
Let the hypotenuse be b Hence:
b² = 3² + 5²
b² = 9 + 25
b² = 34
b = 5.83 feet
Answer:C
Step-by-step explanation:
Test question........................
Answers
You Have Passed Thy Test!!! BADAAAA (\•o•/)
Need honest and urgent help thank you
Answers
Answer:
(Top to bottom) The third and the fifth.
Step-by-step explanation:
I feel lazy typing this so I'll just take a pic if you're curious about the process.
a pack of ice cream bars costs $5.11. What is the unit price?
Answers
Answer:
how much is in each pack?
Step-by-step explanation:
Find the length of each arc
Answers
Answer:
27 pi/4 or 6 3/4 pi
Step-by-step explanation:
First find the circumference
C = 2*pi*r
C = 2 * pi *9
C = 18 pi
The find the fraction of the arc
A circle is 360 degree
135/360 =3/8
Multiply the circumference by the fraction
18 pi * 3/8 =
27 pi/4
6 3/4 pi
4^2-2 X 3 + 6 = ?
SOLVE with PEMDAS
my son has had problems with algebra and tbh I don't know how to do it either i was hoping someone on here can help!
Answers
4^2 -2×3+6=16 is your answer
Answer:
Step-by-step explanation:
P means parenthesis, of which we have none. So we move to E, which is exponents, which we do have. So we start there:
[tex]4^2-2*3+6[/tex] becomes
16 - 2 * 3 + 6. Now we have to do multiplication/division in the order we come to it in the problem. That means multiplying 2*4 first:
16 - 6 + 6. Now we do addition/subtraction in the order we come to it in the problem:
16- 6 + 6 = 10 + 6 = 16
Please help??? An explanation would help too and the answers
Answers
the first, (f+g)(x) is f(x) + g(x)
calculating it like:
x² + 7x + (8 -x²)
= x² + 7x + 8 -x²
= 7x + 8
you just writ it down as a calculation and calculate it. i hope that helps understanding the concept/basic idea. please let me know wich ones you need more help with.
edit1: the domain is the range of possibilities wich x we can plug into the new equation
Find the geometric mean of 16 and 36. Write your answer in the simplest form.
Any obvious wrong answers will be reported.
Answers
Answer:
Step-by-step explanation:
Find the geometric mean of 16 and 36. Write your answer in the simplest form.
Any obvious wrong answers will be reported.
Nigel has 2 dogs one eats 21/2 pounds of food each week. The other eats 1 3/8 pounds a week together how much food do the dogs eat in a week?
Answers
Answer:The dogs eat 3 7/8 pounds of food together each week.
Step-by-step explanation:
First dog eats eats 21/2 pounds of food each week
The second eats eats 1 3/8 pounds of food each week
In total the two dogs eat
2 1/2 + 1 3/8 = 3 (4+3)/8
=3 7/8
The dogs eat 3 7/8 pounds of food together each week.
Ahmed needs to fill a fish tank with water. He uses three cups of water to fill 1/4 of the tank. How many cups of water will he need to completely fill the tank.
-1
-3
-4
-12
Answers
===========================
Work Shown:
3 cups = 1/4 tank
4*(3 cups) = 4*(1/4 tank)
12 cups = 1 tank
Have a nice day :DD
What are solutions to the equation x^2-34=864
Answers
Answer:
x=29.9
Step-by-step explanation:
x=29.9
Hellpp please and thank……………
Answers
Answer:
a1 = 2
a2 = 6 = 2.3 = a1.3
a3 = 18 = a1.3²
a4 = 54 = a1.3³
=> this is a geometric sequence with a1 = 2
q = 3
=> a11 = 2.3¹⁰ = 118098
More help with cylinder math?
Answers
2(15) (3.14) (4)
-multiply them together
Then you will need to find the base.
-3.14x15x4
Then find the surface area
-answer from lateral area and 2(-answer from base-)
Add that and that is ur answer
Answer:
[tex]V=706.5[/tex] [tex]ft^3[/tex]
Step-by-step explanation:
Since it's saying, "how much water does your neighbor need to completely fill his pool", it's asking for us to find the volume of the pool because the volume is the amount of space inside the pool which will be filled with water.
The volume formula for a cylinder: [tex]V=\pi r^2h[/tex]
In the text, since they gave the diameter and not the radius, we need to find the radius by dividing the diameter by two: [tex]\frac{15}{2}=7.5[/tex]
Now, we can start solving.
[tex]V=(3.14)(7.5^2)(4)[/tex]
[tex]V=(3.14)(56.25)(4)[/tex]
[tex]V=(3.14)(225)[/tex]
[tex]V=706.5[/tex]
Hope this helps
if f(x) = 3x+2 what is f(5)?
Answers
Answer:
just put 5 on the place of x
Step-by-step explanation:
3(5)+2
15+2
17
hope it helps
Answer:
lets say f equals 1
x-2 = 3x
-2 = 2x
x=-1
1(-1)
-1
!!!!someone help please??????
Answers
Answer:
The image you provided doesnt work
Step-by-step explanation:
Answer:
The answer is 8, take away 8.25 from 210 and then divide it by 23
Find the product of (2x-3)(x-1)
Answers
Answer:
Step-by-step explanation:
[tex](2x -3)(x-1) = 2x(x-1) -3(x-1)[/tex]
[tex]=2x^2 -2x -3x +3\\= 2x^2 - 5x + 3[/tex]
72. Linear Speed. A wheel with a 30-cm radius is rotat- ing at a rate of 3 radians / sec. What is the linear speed of a point on its rim, in meters per minute?
Answers
========================================================
Explanation:
Let's find the circumference
C = 2*pi*r
C = 2*pi*30
C = 60pi
This is the exact circumference in terms of pi.
In one revolution, the point on the wheel moves forward exactly 60pi cm.
In a sense, it's "speed" is 60pi cm per revolution.
----------------
Let's convert that speed to meters per minute as shown in the diagram below (I'm using the railroad tracks method to convert).
Note the color coding to see how the units cancel. The goal is to get meters on top and minutes down below. Also note how the "pi" terms cancel since we have on top and one down below.
After the canceled stuff goes away, we multiply straight across.
Multiplying the values across the top gives: 60*3*1*60*1 = 10800Multiplying across the bottom gives: 1*1*2*1*100 = 200Divide the results: 10800/200 = 54
The linear speed is 54 meters per minute
This speed is exact because the 60pi figure is the exact circumference
This is the speed the point on the wheel moves, and we can say that the car itself also moves at a linear speed of 54 meters per minute.
Side note: 54 meters per minute = 2.013 mph approximately, which is a fairly slow walking speed.
Train A leaves Paris and travels at a constant speed of 75 mph toward Pisa. At the
same time. Train B leaves Pisa headed toward Paris at a constant speed of 50
mph. Let x represent time traveled in hours and let y represent miles from Paris. If
Paris and Pisa are 500 miles apart, when will the two trains pass each other?
Answers
Answer: [tex]4.016\ hr[/tex]
Step-by-step explanation:
Given
Train A has speed of [tex]v_a=75\ mph[/tex]
Train B has speed of [tex]v_b=50\ mph[/tex]
If Paris and Pisa is 500 miles apart
If they meet x hours after the start
The sum of the distances traveled by Train A and B is 500 miles
[tex]\Rightarrow 75\times x+50\times x=500\\\Rightarrow 125x=500\\\Rightarrow x=4.016\ hr[/tex]
So, after [tex]4.016\ hr[/tex] they will pass each other.
Please help me. I feel really confused and I have no clue on what to do…
Answers
Answer:
i cant understand your questions. can you reply me? i will have better answer
when 2-(7g-3) =-9 is solved, the result is:
a. 2
b. -2
c. -4
d. none of these choices are correct
Answers
The answer is A. 2
Step-by-step explanation:
First let's simplify both sides of the equation
Now using the Subtraction Property of Equality subtract 5 from both sides
[tex]-7g+5-5=-9-5-7g=-14[/tex]
Now using the Division Property of Equality divide both sides by -7
What would be the volume of the pyramid? Little help please
Answers
Answer:
36
Step-by-step explanation:
The answer is 36, I did the work
Can some please help I don’t really know.
Answers
Answer: 1%
Step-by-step explanation:
Please help will give branliest
Answers
Answer:
ok
8^7*512/262144=4096
8^4=4096
?=4
Your Welcome
BIFFY OUT!!!
The student enrollment of South High School was 1,350 students in 1995 and increased by15% per year until 2010. Approximately how many students were enrolled at South HighSchool in 2010?
Answers
Answer:
81
Step-by-step explanation:
1350 ×15 % by 100 = 81. 15 year = 1,215
Which choice is equivalent to 4 square root 3?
A. 12
B. 748
C. V12
D. 6
Answers
Answer this for me thanks
Answers
Answer:
The value of x is 15 inch.
Step-by-step explanation:
Area, A = 81 square inch
Perimeter, P = 48 inch
let the side is y.
[tex]y^2 = 81\\\\y = 9 inch[/tex]
Let the other side is d.
P = 4 d = 48
d = 12 inch
the length x is given by
[tex]x^2 = 9^2 + 12^2\\\\x^2 =81 + 144 = 225\\\\x = 15 inch[/tex]
So, x = 15 inch.
Alternate angles add up to 180 degrees.
Is it true or false?
Please give real answers with an explaination. 80 points + I will give brainliest + 5-star rated. No Docs/No Files/No Links only answer with explaination.
Answers
Area of prallelogram
Answers
Answer:
7) 96
8) 84
9) 72
Step-by-step explanation:
A = bh
7)
b = 12, h = 8
A = 12*8 = 96
8)
b = 12, h = 7
9)
b = 8, h = 9
Find the optimized volume of a rectangular prism with a surface area of 864 m^2
Answers
A
AB
ABC
which equations results from adding the equations in this system?
x+6y=9
-x+2y=-15
Answers
Answer:
8y = -6
Step-by-step explanation:
Simply add the equations as you would numbers.
The 'x's cancel each other out. The 'y's add together as normal numbers.
9 + (-15) = -6
Hope that this helps!