Seth is using the figure shown below to prove Pythagorean Theorem using triangle similarity:
In the given triangle ABC, angle A is 90° and segment AD is perpendicular to segment BC.
The figure shows triangle ABC with right angle at A and segment AD. Point D is on side BC.
Which of these could be a step to prove that BC2 = AB2 + AC2?
possible answers -
By the cross product property, AB2 = BC multiplied by BD.
By the cross product property, AC2 = BC multiplied by BD.
By the cross product property, AC2 = BC multiplied by AD.
By the cross product property, AB2 = BC multiplied by AD.
Answers
The correct step to prove that [tex]BC^2 = AB^2 + AC^2[/tex] is:
By the cross product property, [tex]AC^2 = BC \cdot AD[/tex].
To prove that [tex]BC^2 = AB^2 + AC^2[/tex], we can use the triangle similarity and the Pythagorean theorem. Here's a step-by-step explanation:
Given triangle ABC with right angle at A and segment AD perpendicular to segment BC.
By triangle similarity, triangle ABD is similar to triangle ABC. This is because angle A is common, and angle BDA is a right angle (as AD is perpendicular to BC).
Using the proportionality of similar triangles, we can write the following ratio:
[tex]$\frac{AB}{BC} = \frac{AD}{AB}$[/tex]
Cross-multiplying, we get:
[tex]$AB^2 = BC \cdot AD$[/tex]
Similarly, using triangle similarity, triangle ACD is also similar to triangle ABC. This gives us:
[tex]$\frac{AC}{BC} = \frac{AD}{AC}$[/tex]
Cross-multiplying, we have:
[tex]$AC^2 = BC \cdot AD$[/tex]
Now, we can substitute the derived expressions into the original equation:
[tex]$BC^2 = AB^2 + AC^2$\\$BC^2 = (BC \cdot AD) + (BC \cdot AD)$\\$BC^2 = 2 \cdot BC \cdot AD$[/tex]
It was made possible by cross-product property.
Therefore, the correct step to prove that [tex]BC^2 = AB^2 + AC^2[/tex] is:
By the cross product property, [tex]AC^2 = BC \cdot AD[/tex].
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Two number cubes are tossed. Find P(1, then 2 or 3).
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Answer:
1/2
Step-by-step explanation:
Answer:
1/6 × 2/6 × 3/6 = 1/36
Step-by-step explanation:
Consider C = {vowels in the word "clinic"}. Find n (C)
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Answer:
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Answer:
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Step-by-step explanation:
Given the linear system:
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Answers
Answer:
13.95 metre square
Step-by-step explanation:
The measurements you gave are different. Hence it concludes that the floor is rectangular in shape.
Sooo,
Area of rectangle = length x breadth
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Answer:
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Step-by-step explanation:
F the total number of fees is how much 250 + 15g equals
Nicole is choosing an outfit from the following. Pants: denim, black Shirts: green, yellow Shoes: sandals, tennis shoes She starts a tree diagram: A tree diagram. D branches to G and Y. B branches to G and Y. How many possible combinations are there? There are possible combinations.
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Step-by-step explanation:
Answer:
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Step-by-step explanation:
the length of the rectangle is 3 times the width. The perimeter is 65.6cm. find the width
Answers
Answer:
Step-by-step explanation:
L = 3W
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8W = 65.6 cm
W = 8.2 cm
4x + 5y = 48
Y=3x + 2
Answers
4x + 15x + 10 = 48
19x + 10 = 48
19x = 38
x = 2
y = 3x + 2
y = 3(2) + 2
y = 6 + 2
y = 8
The solution of the given equation is x = 2 and y = 8.
What is an expression?The mathematical expression combines numerical variables and operations denoted by addition, subtraction, multiplication, and division signs.
Mathematical symbols can be used to represent numbers (constants), variables, operations, functions, brackets, punctuation, and grouping. They can also denote the logical syntax's operation order and other properties.
The value of x and y will be calculated as,
4x + 5(3x+2) = 48
4x + 15x + 10 = 48
19x + 10 = 48
19x = 38
x = 2
Calculate the value of y,
y = 3x + 2
y = 3(2) + 2
y = 6 + 2
y = 8
Therefore, the solution of the given equation is x = 2 and y = 8.
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A car travels 136 miles using 7 gallons of gas. At that rate, how far can the car travel using 42 gallons of gas?
Answers
Answer:
in 136 miles=7 gallons
?=42 gallon
= 136=7
?=42
cross multiply
136×42=5,712
=5,712÷7=816
Answer:
816 miles
Step-by-step explanation:
136miles/7 g =19.43
19.43 x 42 ≅ 816.06
or
136/7 = X/42
solve for X
42/7 =6, then 136 x6= 816
x = 816 miles
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Answers
Answer:
1/45 = 0.02
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Step-by-step explanation:
The expression of 1.45 to 4.35 as a fraction in its simplified form is 1/3.
What is a simplified fraction?A simplified fraction is an improper fraction that can no longer be further divided by a divisor. An improper fraction is a fraction with both the numerator and the denominator.
From the information given, we are to express 1.45 to 4.35 as a simplified fraction.
i.e.
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Timothy worked 9 hours and earned $7425. How much does he make per
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at a school there are 10 students taking only chemistry, 9 students taking only physics 5 students taking both, and 16 students not taking either. if a student is randomly selected from the other school, what is the probability that they are taking chemistry or physics?
Answers
Answer:
24/16 (not simplified nor teacher checked)
Step-by-step explanation:
What you would need to do is add up all of the students that are taking chemistry, physics, or both. Then place that number in a divsion form.
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16
24/16
Answer:
[tex]\frac{3}{5}[/tex]
Step-by-step explanation:
(111)-8,5
3.
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Do you
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Answers
Answer:
(I) -8, -5, 1, 2
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Step-by-step explanation:
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Answers
Answer:
7 times.
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Keep dividing 93.5 by 2 until it becomes less than 1.
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n㏑(1/2) ≤ ㏑(0.0107)
n ≤ ㏑(0.0107)/㏑(1/2)
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Answer:
x=5√3=8.6......
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Answer:
Step-by-step explanation:
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Answers
Answer:
2 2/5
Step-by-step explanation:
We need to find out how many gallons of water so,
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this works because then cranberries would be:
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15/100 * 3 = 45/100
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Answer:
18
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Answer:
38 hrs old
Step-by-step explanation:
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The principle of superposition is a useful technique in developing solutions to differential equations after an initial solution is derived. In developing such solutions it is often convenient to consider separately the response of a system to initial conditions with all forcing function inputs equal to zero, and, secondly, the response to the forcing function with all initial conditions equal to zero. Consider the following differential equation:
dy/dt + ay= bus(t)
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Answers
Answer:
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Step-by-step explanation:
Attached below is a detailed solution of the given problem
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dy/dt + ay = [tex]bu_{s}(t)[/tex] with Y(c) = 0
A) Determine the solution [tex]Y_{i}(t)[/tex]
[tex]y_{i}(t) = C.e^{-at}[/tex]
B) Determine the solution [tex]Y_{u} (t)[/tex]
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All changes saved
Shane invested $3,500 in a savings account that pays 4% interest semiannually (every 6 months). How much
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Answers
Answer:
$4,266.48
Step-by-step explanation:
Hope this helps.
State weather ABC and AED are congruent. Justify your answer
Answers
I think the answer is c. I hope this helps. Be safe out there!
SOMEONE PLEASE HELP ME ASAP THIS IS ALMOST DUE ILL MARK BRAINLIEST!!!!
Answers
Answer:
64.5°
25
Step-by-step explanation:
64.5° (If they are similar, they have the same angle measurements).
You can figure out z by using ratios.
6/10=15/z
cross multiply
150=6z
150÷6=z
z=25 (Although, there is a problem with this. If you use the Pythagorean theorem to find z, you get 28.8).
please answer it’s urgent!!
Answers
Perimeter = 16
Perimeter = 32
Area = length x width so 8 x 8 = 64
Perimeter = ALL sides ADDED up together so 8 + 8 + 8 + 8 = 32
how to get the answer for 2 3/4 gallons and 5/8 to equal 1 23/32
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Answer:
jhwgehebf
Step-by-step explanation:
bwjsfehoal topu
5. Cuando abrió sus puertas, una tienda de café ofrecía 6 tipos diferentes de
bocadillos. Desde entonces, agregó dos nuevos bocadillos cada semana.
Si la tienda ofrece ahora 28 bocadillos diferentes, ¿cuántas semanas (s) han
transcurrido desde su inauguración?
?
Answers
Answer:
11 weeks have passed.
Step-by-step explanation:
We can create a linear function that represents the number of bocadillos offered as a function of the number of weeks (s) that went by since the beginning (when the number of bocadillos was 6):
f(s) = 6 + 2 * s
Since now the number of bocadillos is 28, we can solve for s in the equation
28 = 6 + 2 * s
subtract 6 from both sides
28 - 6 = 2 * s
22 = 2 * s
divide both sides by 2
11 = s
Therefore, 11 weeks have passed.
a2+3b−12
a=6
and b=2
answer plsss
Answers
(6×2)+(3×2)-12
the answer is 6
hope that helps:)