In the diagram below, BC = QR = x, AC = PR = y, and triangle PQR is a right
triangle. Use the drop-down menus to complete the proof that if the equation
22 + y2 = z2 is true of the side lengths in triangle ABC, then triangle ABC must be a right
triangle.
P
y у
y
B
R
х
Q
x2 + y2 = 22
Triangle PQR is a right triangle
Click the arrows to cho
from each menu.
Triangle PQR is given to be a right triangle, so the Pythagorean theorem can be used to
Answers
Applying the Pythagorean theorem, we have ΔPQR ≅ ΔABC. then we would have: ∠ACB = ∠PRQ = 90°
What is the Pythagroean Theorem?The pythagorean theorem states that the square of the longest side (hypotenuse) of a right triangle is always equal to the sum of the squares of the other two sides (legs) of the right triangle.
Since we know that ΔPQR is a right triangle, then:
x² + y² = PQ²
We are also given that x² + y² = z², so by substitution, we have:
z² = PQ², which makes both triangles have corresponding congruent sides. Therefore, ΔPQR ≅ ΔABC.
Using the corresponding parts of the congruent triangles, we can conclude that: ∠ACB = ∠PRQ = 90°.
Learn more about the Pythagorean theorem on:
https://brainly.com/question/343682
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Related Questions
Someone help me please-
Answers
Answer:
Rectangle 11.59 sqft
Rectangle 36 sqft
Polygon 47.59 sqft
Step-by-step explanation:
Jay took a number n and increased it by 25%. Then, he doubled the resulting product.
Which of the following is equivalent to these two steps and would result in the same final number?
A. doubling the number and then decreasing the result by 25%
B. increasing the number by 50%
C. multiplying the number by 1.25
D. multiplying the number by 2.5
Answers
Answer: multiplying the number by 2.5
Your answer
Step-by-step explanation:
Jay took a number n and increased it by 25%. This will be:
= n + (25% × n)
= n + (0.25 × n)
= n + 0.25n
= 1.25n
Then, he doubled the resulting product. This will now be:
= 2 × 1.25n
= 2.50n
Therefore, the equivalent will be option D "multiplying the number by 2.5".
Simplify:............
Answers
[tex] - \frac{4 {m}^{2} }{1 + {m}^{4} + {m}^{8} } [/tex]
is your answer
Answer:
jshdgdhdhdhdhdhdhd English project work
A grocery store sells a bag of 5 oranges for $3.10. If Ishaque spent $2.48 on oranges, how many did he buy?
Answers
what is the problem??
Answers
Answer:
there is none
Step-by-step explanation:
A sphere has a surface area of 196 pi. What is the radius of the sphere?
r = 7
r = 14
r = 65.33
r = 12.12
Answers
Please help. I will give brainliest.
Answers
Answer:
e
Step-by-step explanation:
Someone please help me I’ll give out brainliest please dont answer if you don’t know
Answers
Answer:
see explanation
Step-by-step explanation:
j - 4 ≤ 0 ( add 4 to both sides )
j ≤ 4
The graph has a closed circle at 4 on the number line with the arrow pointing left
If a1=10 and an An-1 + 4 then find the value of
05.
Answers
Answer:
26
Step-by-step explanation:
Just put n = 5 and substitute
Then a5 = a4 + 4 = a3 + 8 = a2 + 12 = a1 + 16 = 26
Tapanga drew triangle XYZ on her paper the measure of angle X was 80 degrees angle y was congruent to angle Z what was measure of angle Z
Answers
Answer:
50degrees
Step-by-step explanation:
The sum of angle in the triangle XYZ is 180degrees, hence;
<X + <Y + <Z = 180
Given
m<X = 80degree
m<Y = m<Z
Required
m<Z
Substitute the given angle
80 + m<Z + m<Z = 180
80 + 2m<Z = 180
2m<Z = 180 - 80
2m<Z = 100
m<Z = 100/2
m<Z = 50degrees
Hence the measure of angle Z is 50degrees
Calculate the curved surface area of a cylindrical container 10cm diameter, length 18cm take the value of pie to 3.14
Answers
Answer:
56.52 cm^2
Step-by-step explanation:
curved surface area = 2πrh
the diameter is the straight line that passes through the centre of a circle and touches the two edges of the circle.
A radius is half of the diameter
10 / 2 = 5
2 x 3.14 x5 x 18 = 56.52 cm^2
the area of a square is 144 square centimeters. What is the length of one side of the square? pls help its on khan
Answers
12cm
have an amazing day <3
Help needed for some geometry
Answers
Answer:
hope this help you. look it once.
suppose 70% of the 500 orders at a fast food restaurant include a drink what is the percentage as a part to whole ratio as well as a part to part ratio simplify each ratio
Answers
Answer:
140
Step-by-step explanation:
Solve the inequality 4x -5 greater than or equal to 7
Answers
to 3.
Explanation: Add 5 on both sides and then after divide 4 on both sides. The sign stays the same.
Dont answer this question if you dont know the answer
Answers
Answer:
C
Step-by-step explanation:
sin = 5/13
cos = 12/13
tan = 5/12
solve for the x value of the x intercept of the line 5x-y=-5
Answers
y intercept: (0,-5)
hope this helped
Cindy feeds her dog 1/3 pound of food each day after 6 day,how many pounds of food has she given to her dog?
Answers
Answer: 2 pounds
Step-by-step explanation: if each day the dog gets 1/3 pounds, then after two days the dog would get 2/3 pounds. 3 days would be 1 pound, so after 6 days that would be 2 pounds.
A group of children bought 3 presents that cost $W each and a card that cost $200. The children shared the total cost equally. Express the amount of money each student paid in terms of W
Answers
Answer:
Amount of money paid by each student is equal to [tex]\$3W+\$200[/tex]
Step-by-step explanation:
Given: A group of children bought [tex]3[/tex] presents that cost [tex]\$W[/tex] each and a card that cost [tex]\$200[/tex].
To find: amount of money each student paid in terms of [tex]W[/tex]
Solution:
Cost of each present [tex]=\$W[/tex]
Cost of [tex]3[/tex] presents [tex]=\$3W[/tex]
Cost of a card [tex]=\$200[/tex]
Therefore,
Amount of money paid by each student in terms of [tex]W[/tex] = Cost of [tex]3[/tex] presents + Cost of a card
[tex]=\$3W+\$200[/tex]
How do you know if something is congruent? (scale Factors)
Answers
example: Two polygons are congruent if they are the same size and shape - that is, if their corresponding angles and sides are equal.
Answer:
Two polygons are congruent if they are the same size and shape - that is, if their corresponding angles and sides are equal. Move your mouse cursor over the parts of each figure on the left to see the corresponding parts of the congruent figure on the right.
Step-by-step explanation:
answer this question for 30 points and brainilest
Answers
Answer:
Volume of left side cylinder will be less than the volume of right side cylinder.
Step-by-step explanation:
Volume of a cylinder is given by the formula,
Volume = πr²h
Here, r = radius of the circular base
h = Height of the cylinder
Volume of the left hand cylinder = π(b)²a
Volume of the right hand cylinder = π(a)²b
It's given in the question that a > b
Let the value of a = 3 and b = 2
Then the volume of left hand cylinder = π(2)²(3)
= 12π
Similarly, volume of right hand cylinder = π(3)²(2)
= 18π
Therefore, volume of left side cylinder will be less than the volume of right side cylinder.
given 2x - 9y - 12 = 0, express 5x - 4y + 7 = 0 in terms of x only
Answers
Answer:
[tex]4 \frac{1}{9}x[/tex] + [tex]12\frac{1}{3}[/tex] = 0
Step-by-step explanation:
Based on 2x - 9y - 12 = 0
-9y = 12 - 2x
9y = -12 + 2x
y = [tex]-1\frac{1}{3} + \frac{2}{9} x[/tex]
Therefore...
5x - 4y + 7 = 0
5x - 4([tex]-1\frac{1}{3} + \frac{2}{9} x[/tex]) + 7 = 0
5x + [tex]5\frac{1}{3}[/tex] - [tex]\frac{8}{9} x[/tex] + 7 = 0
[tex]4 \frac{1}{9}x[/tex] + [tex]12\frac{1}{3}[/tex] = 0
can someone help me asap
Answers
Answer:
a) hundreds
b) tens
c) hundreds
d) hundreds
Answer:
This is easy!!
Step-by-step explanation:
1. hundreds
2. tens
3. hundreds
4. hundreds
Hope this Helps!!
Hiii, I would love it if you can help me with these! I tried my best but it's really hard and I don't understand.
Answers
Answer:
First one i think is C and the second one is A it was easy
Step-by-step explanation:
What would be the perimeter??
Answers
Answer:
19.2
Step-by-step explanation:
4.8 x-4 = 19.2 meters
Answer:
19.2
Step-by-step explanation:
4.8 x 4
I need help asap !!!!
Answers
Answer:
C
Step-by-step explanation:
Pythagorean theorem = a² + b² = c²
Answer:
C.
Step-by-step explanation:
Pythagrean Theorem is on C
A square photo has a side length of 0.17 foot. The photo is enlarged by doubling the dimensions. Then it is enlarged again by tripling the new dimensions.
Answers
Calculate the side length of the enlarged picture
Answer:
Hence, final picture will have a side length of 1.02 foot
Step-by-step explanation:
Side length of square photo, s = 0.17
Original dimension = (0.17 by 0.17)
Enlarged photo = double the original dimension:
2 * (0.17 * 0.17)
(0.34 * 0.34)
Second enlargement = Tripling the new dimension:
3 * (0.34 * 0.34)
(1.02 * 1.02)
Hence, final enlarged dimension = (1.02 * 1.02)
Hence, final picture will have a side length of 1.02 foot
Malik is solving the equation x2 – 10x – 11 = 0 using the complete the square method. Here is Malik's work: Line 1 p^2 -10p-11=0 Line 2 p^2 -10p+25=11+25 Line 3 (p-5)^2 =36 Line 4 p-5=36 or p-5=-36 Line 5 p=41 p=-31 Line 6 the solution is p=41 or p=-31 Malik checks his answer and realizes he has made a mistake. On which line did Malik make his mistake? Explain Malik's mistake using the complete the square method in 1-3 complete sentences.
Answers
Completing the square method rearranges the equation to have the
square of linear equation and constant on both sides of the equation.
Responses:
The mistake is made in line 4The mistake is in not taking the square root of both sidesWhich is the correct completing the square method?The given equation is; x² - 10·x - 11 = 0
Line 1: p² - 10·p - 11 = 0
Which gives;
p² - 10·p = 11
Adding 25 to both sides gives;
Line 2: p² - 10·p + 25 = 11 + 25
11 + 25 = 36
Factorizing p² - 10·p + 25 = (p - 5)·(p - 5) = (p - 5)²
Line 3: (p - 5)² = 36
Which gives;
p - 5 = ±√36
Line 4: p - 5 = √36 = 6 or p - 5 = -√36 = -6 (Line that has a mistake)
Line 5: p = 6 + 5 = 11, or p = -6 + 5 = -1
Line 6: p = 11 or p = -1
The line Malik made a mistake is on line 4The mistake made is that in line 4, the root of both sides of the equation, rather than only the left side of the equation is to be taken.The constant on the left and side is then subtracted from the positive
and negative value of the square root of the right hand side to give two
results.
Learn more about completing the square here:
https://brainly.com/question/3939104
pleasee help, thank you so much
Answers
Answer:
-2
Step-by-step explanation:
Use the slope formula when given two points
Slope formula = [tex]\frac{y_2-y_1}{x_2-x_1}[/tex]
( the x and y values are determined by the given points )
Given the points ( 0 , 5 ) and ( 1 , 3 )
Plug in the x and y values of the given points into the formula
( remember y values on top x values on bottom )
[tex]slope=\frac{5-3}{0-1} \\5-3=2\\0-1=-1\\slope=\frac{2}{-1} =-2[/tex]
Hence, the answer is D
A bar of soap is shaped like a right rectangular prism. The base is a rectangle that is 12 centimeters by 2 centimeters. The height is 3 centimeters. A second bar of soap is shaped like a square pyramid with the same volume as the first bar of soap. Each side of the base of the pyramid is 6 centimeters in length. What is the height of the pyramid?
Answers
Answer:
6 cm
Step-by-step explanation:
Volume of a Prism = base area x height =
Base area = length x width = 12 x 2 = 24 cm^2
Volume = 24 x 3 = 72 cm^3
Volume of a pyramid = 1/3( l x w x h)
72 = 1/3( 6x6 x h)
Multiply both sides of the equation by 3
216 = 36 x h
divide both sides by 36
h = 6
