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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Related Questions
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).
Farmer brown uses super dip to ensure his cattles are free of parasites. What is the independent variable when cattles are devided into three groups?
Answers
Answer:
what are there any numbers
Step-by-step explanation:
(111)-8,5
3.
Write the following integers in ascending order (smallest to biggest).
Do you
(i) -5,2,1,-8
(ii) -4,-3, -5,2
(iii) -10,-15,-7
Answers
Answer:
(I) -8, -5, 1, 2
(ii) -5, -4, -3, 2
(iii) -15, -10, -7
Step-by-step explanation:
You can think about what a number line looks like to solve problems like this, for example a number line that goes from -10 to 10 would look something like this, with smaller numbers on the left and bigger on the right
-10, -9, -8, -7, -6, -5, -4, -3, -2, -1, 0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10
9(5x) need help asap
Answers
Answer:
45x happy to help ya :)
Step-by-step explanation:
Help its due in 20 minutes please
Answers
Answer:
The answer is A
Step-by-step explanation:
F the total number of fees is how much 250 + 15g equals
1.45 to 4.35 as a simplified fraction
Answers
Answer:
1/45 = 0.02
4/35 =0.1 142857
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.
= 1.45 as a ratio of 4.35
= 1.45/ 4.35
= 1/3
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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
I NEED HELP NOWWWWW pls
Answers
12x=(6)(8)
Solve for x
X=4
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.
10+9= 19+5=24
16
24/16
Answer:
[tex]\frac{3}{5}[/tex]
Step-by-step explanation:
Timothy worked 9 hours and earned $7425. How much does he make per
nour at his job?
Answers
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
A piece of paper has an area of 93.5 square inches. How many times does it need to be folded in half before the area is less than 1 square inch? Explain how you know.
Answers
Answer:
7 times.
Step-by-step explanation:
Keep dividing 93.5 by 2 until it becomes less than 1.
The sheet needs to be folded in half 7 times.
Since the area of the piece of paper is 93.5 square inches, and we need to fold the sheet in half it 'n' times to get an area less than 1 square inch. This is written mathematically as 93.5(1/2)ⁿ ≤ 1.
So, dividing through by 93.5, we have
(1/2)ⁿ ≤ 1/93.5
(1/2)ⁿ ≤ 0.0107
taking natural logarithm of both sides, we have
㏑(1/2)ⁿ ≤ ㏑0.0107
n㏑(1/2) ≤ ㏑(0.0107)
n ≤ ㏑(0.0107)/㏑(1/2)
n ≤ -4.538/-0.693
n ≤ 6.55
Rounding up to the nearest whole number,
n ≅ 7
So, the sheet needs to be folded in half 7 times.
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how to get the answer for 2 3/4 gallons and 5/8 to equal 1 23/32
Answers
Answer:
jhwgehebf
Step-by-step explanation:
bwjsfehoal topu
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)
with y(c)=0
a. Determine the solution y_i(t) to the equation for nonzero, finite values of a and c, and for b = 0.
b. Determine the solution y_u(t) of the equation for nonzero, finite values of a and b, and for c = 0.
Answers
Answer:
A) [tex]y_{i}(t) = C.e^{-at}[/tex]
B) [tex]y_{u}(t) = - \frac{b}{a} e^{-at} + \frac{b}{a}[/tex] t > s
Step-by-step explanation:
Attached below is a detailed solution of the given problem
Given equation:
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]
[tex]y_{u}(t) = - \frac{b}{a} e^{-at} + \frac{b}{a}[/tex]
All changes saved
Shane invested $3,500 in a savings account that pays 4% interest semiannually (every 6 months). How much
money will he have in his account in 5 years?
Answers
Answer:
$4,266.48
Step-by-step explanation:
Hope this helps.
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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Cranberry juice is made with a 16:3:1 ratio of water:sugar:cranberries. How much water,
in gallons, how much water is needed in order to make three gallons of cranberry juice? Express your answer as a
common fraction.
Answers
Answer:
2 2/5
Step-by-step explanation:
We need to find out how many gallons of water so,
16/20 = water
3 gallons * 16/20 = 48/20 = 2 8/20 = 2 2/5
this works because then cranberries would be:
2 2/5/16 = 15/100
and for sugar that means
15/100 * 3 = 45/100
so in total
2 40/100 + 45/100 + 15/100 = 3 gallons
and if we simpilfy 2 40/200 we get 2 2/5
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!
Your uncle is 2 years older than 3 times your age! You are 12 years old so how old is your uncle?
Answers
Answer:
18
cuz 2×3=6 so 6 ×3 equals 18
Answer:
38 hrs old
Step-by-step explanation:
3 *12 = 36 + 2 years = 38 years old
A company has net working capital of $843. Long-term debt is $4,402, total assets are $6,633, and fixed assets are $4,272. What is the amount of total liabilities?
Answers
Answer:
Step-by-step explanation:
6633-4272-843+4402=5920
btw,wrong subject
Given the linear system:
5x + 3y = 17
-8x - 3y = 9
What is the correct formula for the solution to the linear system?
Answers
Answer:
Step-by-step explanation:
For this question, it's C
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.
Answers
Answer:
8 possible outcomes
Step-by-step explanation:
Answer:
8 is correct!!
Step-by-step explanation:
a2+3b−12
a=6
and b=2
answer plsss
Answers
(6×2)+(3×2)-12
the answer is 6
hope that helps:)
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
Perimeter = 2L + 2W = 2(3W) + 2W = 8W
8W = 65.6 cm
W = 8.2 cm
açıl hızlı cevap verin lütven
Answers
Answer:12
Step-by-step explanation:
The floor in the room is 4.5m long and 3.1m wide. Calculate the area of the floor
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
= 4.5×3.1 = 13.95 m^2
Hope it helped!!!
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.
Two number cubes are tossed. Find P(1, then 2 or 3).
Answers
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)
A. 6
B. 4
C. 2
D. 12
Answers
Answer:
D galiba ama emin değilim
Answer:
C. 2
Step-by-step explanation:
As you know
Vowels are a , e , i , o , u
"Cl 'i' n 'i' c" so that's 2
submit in simplest radical form :(
Answers
Answer:
x=5√3=8.6......
y=5
.....