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°.
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Related Questions
3
3. Your boss has you on the schedule working 35 hours per week. If you make $9.50 per hour, what is your
gross income every two weeks?
A) $332.50
B) $665
C) $191.58
D) $334.50
Answers
Answer: B
Step-by-step explanation:
35 x 2 = 70 (since there are 2 weeks)
70 x 9.50 = 665
Please please help find height and volume of pyramid!!!
Answers
Answer:
Height of the pyramid:
h = [tex]\sqrt{22.1^2 - (28/2)^2}[/tex] = [tex]\sqrt{292.41}[/tex] = 17.1 mVolume:
V = 1/3BhV = 1/3*28²*17.1 = 4468.8 m³Irene is going to read a 216-page book.
If she reads at a rate of 18 pages per day, how many days will it take her to read 1/
3 of the book
Answers
Answer:
4 days
Step-by-step explanation:
216/3 = 72
72/18 = 4
Determine the point that lies on the equation y = -5x - 3.
Answers
Answer:
it would start on the y-interecpt of -3 because if x is 0 then y would just be -3
Step-by-step explanation:
Liam has 478 gummy sharks.He has 278 more gummies than Lee.How many gummy sharks do they have altogether
Answers
Answer:
756
Step-by-step explanation:
478 + 278 = 756
Answer:678 Gummies
Step-by-step explanation:
You do 478-278 which equals 200 so you add 200+478 which equals 678
Which of the following equations describes the line shown below? Check all
that apply.
(-4, 4)
(2, 1)
Answers
Answer:
y = -1/2 x + 2
Step-by-step explanation:
Which of the following equations describes the line shown below? Check all
that apply.
(-4, 4)
(2, 1)
The standard equation of a line is y = mx,+b
m is the slope
b is he y-inttercept
Get the slope
Slope m = y2-y1/x2-x1
Substitute the coordinate
M = 1-4/2-(-4)
M = -3/6
M = -1/2
Substitute m= -1/2 and (2,1) into y = mx+b
1 = -1/2(2)+b
1 = -1+b
b = 1+1
b=2
Get the equation
Recall y =mx+b
y = -1/2 x + 2
A pen, a marker and pencil have a total length of 48cm. The pen is 1cm shorter than the marker which is 1cm shorter than the pencil. Calculate the length of each
Answers
We know that the sum of these lengths is 48 cm so:
P + Pn + M = 48 (Equation 1)
Now we need to use the relationships of the lengths to find 2 more equations:
Pn = M - 1 (Equation 2)
M = P - 1 (Equation 3)
Now, sub Equations 2 and 3 into the first equation and solve for the value of P, which is 17.
Next, use the value of P to find your M value and then finally use that M value to get your Pn value.
The final answer is: pencil length = 17cm, marker length = 16cm and pen length = 15cm.
NO LINKS!! Someone pls help me pls What is the measure of B in degrees?
Answers
Answer:
B = 60°
Since the measure of all sides of the given triangle are equal, it is an equilateral triangle.
An equilateral triangle have all sides and angles equal.
Therefore, each angle measures 60°.
Can someone pleas Help me with this I don't get it. And Thank you o much if you helped me.
Answers
Answer: 20=96 40=192 60=288
Step-by-step explanation:
Answer:
20 shirts cost 96.00
40 shirts cost 192.00
60 shirts cost 288.00
Step-by-step explanation:
Multiply 4.80( per shirt) with the amount of shirts you have
Plz brainly
what is 50 ÷ 5 × 6 + 70
no cheating
Answers
Answer:
130
Step-by-step explanation:
Answer:
130
Step-by-step explanation:
50 / 5 = 10 x 6 = 60 + 70 = 130
find the solution of given expression
[tex] \sqrt{9 \times 36} [/tex]
Answers
Answer:
solution given:
[tex] \sqrt{9 \times 36} [/tex]=[tex] \sqrt{3² \times 6²} [/tex]=±(3×6)=±18 is your answer
Classify this angle. I need this urgently please! Thank you!
Answers
The Answer Is Acute
The angle hasn't reached the point of a right angle (90°), which makes it a acute angle.
I will Mark the brainliest pls help
Answers
Answer:
Bella do you know the distance formula? that's the "tool" you need for these questions. :) Answers are bolded below :)
Step-by-step explanation:
dist = sqrt[ x2-x1)^2 +(y2-y1)^2]
Robins house is at Point P1 = (-9,10) in the form (x1,y1)
Sarah's house is at Point P2=(3,5) in the form (x2,y2)
dist from Robin's to Sarah's is
dist_RS = sqrt[ (3-(-9))^2 +(5-10)^2]
dist_RS = sqrt[ (3+9)^2 + (-5)^2]
dist_RS = sqrt[ 12^2 + 25 ]
dist_RS = sqrt [ 144+25]
dist_RS = sqrt [ 169]
dist_RS = 13
distance from Robin's to Jada's
where Jada's house is at Point P3 =(-3,2) in the form (x3,y3) (we can think of this as P2 in the form (x2,y2) in our formula)
dist_R J= sqrt [ (-3-(-9))^2 + (2-10)^2 ]
dist_R J= sqrt [ (-3+9)^2 + (-8)^2 ]
dist_R J= sqrt [ (6)^2 + 64 ]
dist_R J= sqrt [ 36 + 64]
dist_R J= sqrt [ 100 ]
dist_R J= 10
distance to Madison's house
where Madison's house is at Point P4 = (-1,-5) in the form (x2,y2)
dist_RM = sqrt [ (-1-(-9))^2 + (-5-10)^2 ]
dist_RM = sqrt [ (-1+9)^2 + (-15)^2 ]
dist_RM = sqrt [8^2 + 225 ]
dist_RM = sqrt [ 64 + 225 ]
dist_RM = sqrt [289 ]
dist_RM = 17
Jada's house is 10 , Madison's is 17 so it's 7 miles farther to Madison's than to Jada's
Find the equation for the
following parabola.
Vertex (2, 3)
Focus (7,3)
Answers
Answer:
b
Step-by-step explanation:
formula
(y-k)^2 = 4a(x-h) horizontal parabol
a = 7 - 2 =5
(y-k)^2 = 4*5*(x-h)
(y-k)^2 = 20(x-h)
k=3 , h=2
(y-3)^2 = 4a(x-2)
Select the correct answer.
Consider this equation.
cos(0) = 41
if & is an angle in quadrant IV, what is the value of sin(O)?
OA SVA
5741
OB.
541
41
oc.
5
OD.
5-4
Answers
Answer:
- 5 41 /41
it is A
Step-by-step explanation:
This is the answer for plato users, I took the test btw
The value of sin(θ) is -5√41/41 because sin is negative in the fourth quadrant option (A) -5√41/41 is correct.
What is trigonometry?Trigonometry is a branch of mathematics that deals with the relationship between sides and angles of a right-angle triangle.
We have:
cos(θ) = 4√41/41
As we know cos is the ratio of the side adjacent to the angle to the hypotenuse.
cos(θ) = adjacent/hypotenuse
From the Pythagoras theorem:
hypotenuse² = opposite² + adjacent²
41² = opposite² + (4√41)²
After calculating:
opposite = √1025
opposite = -5√41 (because sin is negative in the fourth quadrant)
sin is the ratio of the opposite to hypotenuse:
sin(θ) = -5√41/41
Thus, the value of sin(θ) is -5√41/41 because sin is negative in the fourth quadrant option (A) -5√41/41 is correct.
Learn more about trigonometry here:
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<1 and <2 are complementary angles given m<1 = 12 find m<2 =
Answers
Answer:
m∠2=78°
Step-by-step explanation:
∡2=90°-∡1=90°-12°=78°, therefore ∡2=78°
The measure of ∠2 is 78°.
We have two angles ∠1 and ∠2 which are complementary angles such that ∠1 = 12°.
We have to find the measure of ∠2.
What are Complementary angles ?When the sum of two angles is equal to 90 degrees, they are called complementary angles.
∠X + ∠Y = 90
According to the question, we have -
The measure of angle ∠1 = 12°.
Assume that the magnitude of ∠2 is x.
Then -
∠ 1 + x = 90°
x = 90° - ∠1
x = 90° - 12°
x = 78°
Hence, the measure of ∠2 is 78°.
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Help me pls, math is my weak point TwT
Answers
Answer:
I hope this helps
does anyone know how to do 1 and 2? i suck at trigonometry.
Answers
Answer:
Step-by-step explanation:
Here's the answers I got. Sorry super busy at school ahh
The 5th graders decided to have a bake sale to raise money for graduation! They had 332 people volunteer to bake. Each volunteer baked 15 brownies. They then separated the brownies into twenty bags to sell. How many brownies are being sold in each bag?
Answers
Answer:
249 brownies in each bag.
Step-by-step explanation:
I know this because 332x15=4,980
And 4,980 divided by 20 equals 249
Hope this helps :)
Links and anything not helpful will be reported
Answers
Answer: C
Step-by-step explanation: Hope this help :D
An inequality is shown 1 < -18% 8 Which value of x makes the inequality true??
Answers
Answer:0.02
Step-by-step explanation:
How many turning points are in the graph of the polynomial function?
a.) 4 turning points
b.) 5 turning points
c.) 6 turning points
d.) 7 turning points
Answers
5 turning points are in the graph of the polynomial function.
What are Turning point in graph?Turning points occur when a graph shifts from rising to dropping (rising to falling) or from decreasing to increasing (falling to rising). A polynomial of degree n can turn at most once, or n1.
The point on a parabola where the graph shifts from increasing to decreasing, or from decreasing to increasing, is known as the turning point of a parabola and is also known as the vertex. We refer to a graph as growing when it is rising from left to right.
Turning points are places on a graph where the direction of the line switches from upward to downward.
And from below to above.
We can see that graph is changing its direction at 5 different points and the points are
(-5,6) ,(-3,-3) ,(0.5,0.5) ,(3,2.5) ,(5,5)
Thus, there are 5 turning points.
Learn more about Turning point here:
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Will give brainliest if your answer is correct.
Answers
Answer:
B
Step-by-step explanation:
One hour would cost $30 and every hour after is $5 more so B is the correct answer.
8. This model of the backboard of a basketball goal is made of a semicircle. Use the ruler provided to measure the dimensions of the model to the nearest half inch. Which measurement is closest to the area of the model of the backboard in square inches? Use 3 for π.
Answers
It is c i did it oh khan
(pls branliest)
can you say a triangle with equal angles of 60 is equilateral
Answers
Answer:
Not really
Step-by-step explanation:
NOT NECESSARILY would a triangle be equilateral if one of its angles is 60 degrees. To be an equilateral triangle (a triangle in which all 3 sides have the same length), all 3 angles of the triangle would have to be 60°-angles; however, the triangle could be a 30°-60°-90° right triangle in which the side opposite the 30 degree angle is one-half as long as the hypotenuse, and the length of the side opposite the 60 degree angle is √3/2 as long as the hypotenuse. Another of possibly many examples would be a triangle with angles of 60°, 40°, and 80° which has opposite sides of lengths 2, 1.4845 (rounded to 4 decimal places), and 2.2743 (rounded to 4 decimal places), respectively, the last two of which were determined by using the Law of Sines: "In any triangle ABC, having sides of length a, b, and c, the following relationships are true: a/sin A = b/sin B = c/sin C."¹
Step-by-step explanation:
A triangle with three equal interior angles is called an equiangular triangle. In an equiangular triangle has three. equal sides, and it is the same as an equilateral triangle.
Two wires are attached 6 feet up a tree and 3 feet from the base of the tree. About how much TOTAL wire was used?
Answers
Answer:
9 cm²
Step-by-step explanation:
Two wires are attached 6 feet up a tree and 3 feet from the base of the tree. About how much TOTAL wire was used?
We solve the above question, using the Area of a Triangle
Area = 1/2 × Base × Height
Area = 1/2 × 3 × 6
Area = 9 cm²
Therefore, the total wore that was used was 9cm² of wire
WILL REWARD BRAINLIEST! Is segment AB tangent to circle O shown in the diagram, for AB = 8, OB = 3.75, and AO = 10.25. Explain your reasoning and show all work in your own words.
Answers
Answer: look at the picture, it going to take my long to write so I give you a picture. In the picture it my work done for you.
Step-by-step explanation: Hope this help :D
solve for x. The segments labeled in the picture are the tangets.
Answers
Hope it helps u!!!!
The work of a student to solve the equation 3(2x − 4) = 8 + 2x + 6 is shown below: Step 1: 3(2x − 4) = 8 + 2x + 6 Step 2: 5x − 7 = 14 + 2x Step 3: 5x − 2x = 14 + 7 Step 4: 3x = 21 Step 5: x = 7 In which step did the student first make an error and what is the correct step? (5 points) a Step 2; 6x − 12 = 14 + 2x b Step 2; 6x − 7 = 2(6 + x + 4) c Step 3; 5x − 2x = 14 − 7 d Step 3; 5x + 2x = 14 + 7
Answers
Step-by-step explanation:
The answer is 7x= 21
divide both sides by 7
to get 3
therefore the answer is X =3
2 1/3 + 5 5/16 + 2/7 = __ + __ + __ = __
Answers
Answer:
12 17 19 =48
Step-by-step explanation: