Consider the diagram and the paragraph proof below.
Given: Right △ABC as shown where CD is an altitude of the triangle
Prove: a2 + b2 = c2
Because △ABC and △CBD both have a right angle, and the same angle B is in both triangles, the triangles must be similar by AA. Likewise, △ABC and △ACD both have a right angle, and the same angle A is in both triangles, so they also must be similar by AA. The proportions and are true because they are ratios of corresponding parts of similar triangles. The two proportions can be rewritten as a2 = cf and b2 = ce. Adding b2 to both sides of first equation, a2 = cf, results in the equation a2 + b2 = cf + b2. Because b2 and ce are equal, ce can be substituted into the right side of the equation for b2, resulting in the equation a2 + b2 = cf + ce. Applying the converse of the distributive property results in the equation a2 + b2 = c(f + e).
Which is the last sentence of the proof?
A. Because f + e = 1, a2 + b2 = c2.
B. Because f + e = c, a2 + b2 = c2.
C. Because a2 + b2 = c2, f + e = c.
D. Because a2 + b2 = c2, f + e = 1.
Answers
This is because since f + e = c,
then a² + b² = c(f + e)
a² + b² = c(c)
a² + b² = c²
In the right angle triangle ABC [tex]\rm a^2+b^2=c^2[/tex] because (e + f = c) and this can be determined by using the Pythagorean theorem.
Given :
Right △ABC is shown where CD is an altitude of the triangle.
The following steps can be used in order to prove that [tex]a^2+b^2=c^2[/tex]:
Step 1 - According to the Pythagorean theorem, the sum of the square of the shorter side is equal to the square of the longer side.
Step 2 - The Pythagorean theorem is given below:
[tex]\rm H^2=B^2+P^2[/tex] --- (1)
where H is the hypotenuse, B is the base, and P is the perpendicular.
Step 3 - So, according to the given diagram:
H = e + f
B = a
P = b
Step 4 - Substitute the values of the known terms in the expression (1).
[tex]\rm a^2+b^2=(e+f)^2[/tex]
Step 5 - According to the diagram, (e + f = c). So, the above expression becomes:
[tex]\rm a^2+b^2=c^2[/tex]
Therefore, the correct option is C).
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Related Questions
Shen needs to memorize words on a vocabulary list for german class. he has memorized 12 of the words, which is two-thirds of the list. how many words are on the list?
Answers
2/3x = 12
x = 12 / (2/3)
x = 12 * 3/2
x = 36/2
x = 18 <=== there are 18 words on the list
Give an example of a cubic function
Answers
Final answer:
A cubic function example is f(x) = x^3, which shows a curve with odd function symmetry that decreases with negative x values and increases with positive ones.
Explanation:
An example of a cubic function would be the function f(x) = x3. This function represents a basic cubic equation where the variable x is raised to the third power, or cubed. The graph of this function is a curve that demonstrates symmetry about the origin, with the curve decreasing for negative values of x and increasing for positive values. As x is cubed, it indicates that the function has an odd function symmetry.
q+5/9=1/6
what is q?
Answers
q = 1/6 - 5/9 . in order to subtract you need to find lcd
q = -7/17
hope this helps . give brainliest thanks
q+5/9=1/6
Step 1: Subtract 5/9 from both sides
q+59−59=16−59
q=−7/18 =
Answer:q=−7/18
Please help me with math question
Answers
MQ would be CQ-CM
21-17 = 4
MQ = 4
21-17 = 4
MQ = 4
Write the slope intercept equation of a line that passes through points (-3,4) and (2, -6)
Answers
-6-4 / 2-(-3)
-10/5
-2
Then plug one set of coordinates and the slope in to find the b value
-6= -2(2)+b
-6=-4+b
-2=b
Final answer: y=-2x-2
Michael is three times as old as Margaret, and in 6 years he will be twice as old as her. How old was Michael when Margaret was born?
Answers
Answer:
12 years old
Step-by-step explanation:
m = Michael
a = Margaret
m = 3a
m+6 = 2(a+6)
m+6 = 2a+12
Two equations, two unknowns, so we can use substitution.
3a+6 = 2a+12
a+6 = 12
a = 6
Plug it back in.
m = 3(6)
m = 18
When Michael was 18, Margaret was 6. So when she was born (basically when she was 0) Michael was 18-6 = 12.
Answer:
Michael was 12 years old when Margaret was born.
Step-by-step explanation:
Let Michael be x and Margaret be y.
x=3y
x+6 (years) = 2(6+y) --> x+6=12+2y --> x=6+2y
Now that we have x, substitute x=3y:
6+2y=3y --> y=6
Now we have y, substitute again with x=3(6) --> x=18
So, Michael, x, is 18 years old. Margaret, y, is 6 years old. But, to find how old Michael was when Margaret was born, do 18 (Michael's age)-6 (Margaret's age) to get 12. So, Michael was 12 years old when Margaret was born. Hope that helped, sorry if I missed something... :D
A regular 18-sided polygon is rotated with the center of rotation at its center.
What is the smallest degree of rotation needed to map the polygon back on to itself?
Is it 180 degrees or 20 degrees? Or are both my answers wrong? :(
Answers
360 degrees / 18 sides = 20 degrees
the answer is 20 degrees
A rectangle is cut in half along the diagonal to form a triangle. if the area of the triangle is (2x + 10) cm^2, what is the area of the rectangle? Please provide steps and reason for your answer too!
Answers
the triangle's area (a)=(1/2)*(b) (the rectangle's area) we can multiply 2 to both sides to get 2*a=b. Since a is (2x+10), we can plug it in and use the distributive property (since we just can't add up variables and integers) to get
2*(2x+10)=4x+20=b
Trina and Jessie went on a vacation. Trina went scuba diving with an elevation of -85.6. Jessie went hand gliding with an altitude of 87.9 meters . Which is above sea level
Answers
so anything above sea level is positive and anything below sea level is negative. So Jessie, who is at an altitude of 87.9 meters, is above sea level
Joann works in a publicity office at the state university. she is paid $ 13.00 $13.00 an hour for the first 35 35 hours she works each week and $ 19.50 $19.50 an hour for every hour after that. if she makes $ 650.00 $650.00 one week, how many hours did she work?
Answers
Point Z on a coordinate grid is at (-1,3). If the point is reflected across the line y=-x, what are the coordinates of its image?
Answers
x,y > -y,-x
Therefore (-1,3) is (-3,1)
A company manufactured a 16-oz box of cereal. Boxes are randomly weighted to ensure the correct amount. If the discrepancy in weight is more than 0.15 oz, the production is stopped. What is the range of acceptable values for production to continue?
Answers
Answer:
The acceptable range will be : 15.85 oz to 16.15 oz
Step-by-step explanation:
Let the weight of the box be = x
As given,
If the discrepancy in weight is more than 0.15 oz, the production is stopped.
And if the discrepancy in weight is less than 0.15 oz then the production will continue.
We can express this as : If [tex]|x-16| \leq 0.15[/tex] ; the production continues
[tex]|z| \leq a[/tex] or we can say
[tex]-a\leq z\leq a[/tex]
Now, z = x-16, and a=0.15, then the value becomes,
[tex]-0.15 \leq x-16 \leq 0.15[/tex]
Solving for x:
We get the final range as :
[tex]-0.15+16 \leq x-16+16 \leq 0.15+16[/tex]
[tex]15.85\leq x \leq 16.15[/tex]
Therefore, the answer is : [tex]15.85\leq x \leq 16.15[/tex]
It should be noted that the range that's acceptable will be 15.85 oz and 16.15 oz.
How to calculate the range.From the information, the discrepancy in weight is about 0.15 oz. The lowest weight will be:
= 16 - 0.15 = 15.85 oz
The highest weight will be:
= 16 + 0.15 = 16.15 oz.
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A club decides to sell t-shirts for $15 as a fundraiser. It cost $20 plus $9 per t-shirt to make the t-shirts. Write and solve an equation to find how many t-shirts the club needs to make and sell in order to profit at least $152?
A. 15x - (9x+20) greater than or equal to 150; x greater than or equal to 28.33
B. 15x-9x + 20 greater than or equal to 150; x greater than or equal to 20
C. (8x+20) -15x greater than or equal to 150; x greater than or equal to 20
D. 15x -9 (x+20) greater than or equal to 150;x greater than or equal to 20
Answers
Profit = Revenue - Total Cost
Revenue is the total sales you get while total cost includes the capital and other variable costs.
Letting x be the number of t-shirts, the revenue would be 15x, while the total cost is (20 + 9x). So, the profit equation becomes:
150 ≤ 15x - (20 +9x)
The ≤ symbol means that the right side of the equation must be equal or greater than 150 so that you can reach your goal profit.
Solving for x,
150 + 20 ≤ 15x - 9x
x ≥ 28.33
Hence, the answer is A.
A meteorologist was accurate 90% of the time, reporting accurately on 45 days. how many days of weather did he report? 50
Answers
4/5 - 2/7 find difference
Answers
hope this is what u r looking for
Which angles are corresponding angles?
a. ∠7 and ∠3
b. ∠8 and ∠3
c. ∠3 and ∠11
d. none of this
Answers
Angles 7 and 3 are vertical angles.
The answer is C, angles 3 and 11 are corresponding angles.
Find the mean of the integers -16,-27,21,-19,14,-3
Answers
= -65+14
= -51
=> -51/6
=> -8.5
The mean of the integers -16, -27, 21, -19, 14, -3 is found by adding together all the numbers to get -30, and then dividing by the total number of values, which in this case is 6. This results in a mean of -5.
Explanation:The solution to this problem falls under the branch of Mathematics known as Statistics, which is the study of collecting, analyzing, interpreting, presenting, and organizing data. The term mean is frequently used in statistics, and it refers to the average of a set of numbers. In this case, you are required to find the mean of the set of integers -16, -27, 21, -19, 14, -3.
To compute the mean, you need to follow a simple two-step process: Add together all the numbers in the set, and then divide the total by the number of items in the set. For the numbers given in your case (-16, -27, 21, -19, 14, -3), you add these together which gives you a total of -30. There are 6 numbers in the set, so the mean would be -30 divided by 6, which equals -5.
Therefore, the mean of the integers -16, -27, 21, -19, 14, -3 is -5.
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Mathematically, what is the correct way to write a speed of 100 meters per second?
Answers
Also note that a negative power in the numerator is equivalent to a positive in the denominator.
Example:
1/s = s^-1
1/(s^2) = s^-2
Based on this:
100 meters per seconds can be written as:
100 m/s , or
100 ms^-1
An airplane over the Pacific Ocean sights an atoll at an 7° angle of depression. If the plane is 663 m above the water, how many kilometers is it from a point 663 m directly above the atoll
Answers
distance = 663 / tan (7)
distance = 663 / 0.12278
distance = 5,400 meters = 5.4 kilometers
After reviewing her driving record for the past 3 years, Cindy’s insurance company offers her a good driver discount of 4.5%. Her original policy was based on the premiums listed below. What is her new annual premium including the discount?
Answers
Cindy's new annual premium including the discount would be given by: Option A: $504.24
What is a percentage?A ratio or value that may be stated as a fraction of 100 is called a percentage. And it is represented by the symbol '%'.
The table given is:
Type of Insurance Coverage= {Coverage Limits} and {Annual Premiums}
Bodily Injury $50/100,000 $31. 75
Property Damage $25,000 $120. 50
Collision $500 deductible $275. 75
Comprehensive $100 deductible $100. 00
Her total annual premium = 31.75 + 120.50 + 275.75 + 100 = $528
Discount offered to her = 4.5% of $528 = (in dollars)
The new premium that she needs to pay after discount = Old premium - discount = $528 - $23.76 = $504.24
Therefore, Cindy's new annual premium including the discount would be given by: Option A: $504.24
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The complete question is ;
After reviewing her driving record for the past 3 years, Cindy’s insurance company offers her a good driver discount of 4. 5%. Her original policy was based on the premiums listed below. What is her new annual premium including the discount? Cindy's Auto Insurance Policy Type of Insurance Coverage Coverage Limits Annual Premiums Bodily Injury $50/100,000 $31. 75 Property Damage $25,000 $120. 50 Collision $500 deductible $275. 75 Comprehensive $100 deductible $100. 00 a. $504. 24 b. $523. 50 c. $528. 00 d. $551. 76.
To pay for a swimming pass, Cameron earned $65 by mowing lawns. Cameron plans to go swimming for 10 weeks this summer. He can buy a pass for $60, pay the regular price of $1.25 each time, or buy a permit for $25 plus 50 cents each time he swims. Cameron estimates that he will go swimming 5 times per week. Which is the best deal?
Answers
that is the answer
‼️correct answer will get brainliest‼️
Each week, Alfonso earns $85 for every shift he works at the theater and $15 for every dog-walking job. He uses the expression 85x + 15y to keep track of his earnings.
Part A: Identify the coefficients and variables in the expression. (3 points)
Part B: How many terms are in the expression, what are they, and how do you know? (4 points)
Part C: Which term in the expression shows the total earned from the dog-walking jobs? (3 points)
Answers
There are two terms in the expression: 85x and 15y
Since you are earning 15 dollars for each dog walking session, it is 15y.
2. A term is both a coefficient and a variable together. So there are two terms in this equation.
3. 85 dollars is earned for every shift for theater and 15 for every dog walking shift. So the 15y is the total earned for dog walking, where y is how many shifts Alfonso worked for.
Walt is mixing friut punch for a party. He combies 1 gallon 2 quarts 3 pints of ornge juice , 1 gallon 3 quarts 7 pints of pineapple juice, and 1 gallon 3 quarts 3 pints of ginger ale. What is the total liquid measure of the punch?
A. 6 gal. 2 qt. 1 pt.
B. 6 gal. 2 qt. 2 pt.
C. 5 gal. 3 qt. 1 pt.
D. 6 gal. 3 qt. 1 pt.
Answers
If the correlation between variables is .60, what is the coefficient of alienation?
Answers
We can calculate the coefficient of alienation by using the following formula;
1 - r²
where r is the correlation between variables.
Coefficient of alienation = 1 - (0.60)²
= 1- 0.36
= 0.64
So, 0.64 is the coefficient of alienation when the correlation between variables is 0.60.
Y = 1/2x - 6
Is this a function?
Answers
When you graph it, it creates a straight line since it is linear. It has a slope that is not undefined so therefore each x value has a unique y value, thus making it a function.
Hope this helps!
Answer:
what about y=(x - 5 to the 2nd power is it linear
Which number is prime?
27
14
91
59
Which trinomial is a perfect square trinomial?
a2 – 8a + 64
a2 – 4a + 64
a2 – 4a + 16
a2 – 8a + 16
Answers
I believe it is the first one
Final answer:
The number 59 is prime, and the trinomial a^2 - 4a + 4 is a perfect square trinomial.
Explanation:
Prime number: The number 59 is prime because it is only divisible by 1 and itself, while the other numbers have factors other than 1 and themselves.
Perfect square trinomial: The trinomial a2 - 4a + 4 is a perfect square trinomial because it can be factored to (a - 2)(a - 2), making it a square of a binomial.
round the number to the given place value
24.617 hundredths
A.24.61
B 24.62
C.24.65
D.24.67
Answers
the order is
< -etc. hundred thousands, ten thousands, thousands, hundreds, tens, ones, tenths, hundredths, thousandths, ten thousands, etc ->
hope this helps :D
The average gas mileage m in miles per gallon for a compact car is modeled by m(s) = -0.015(s - 47)^2 + 33, where s is the car's speed in miles per hour. The average gas mileage for an SUV is modeled by m(s) = -0.015(s - 47)^2 + 15. What kind of transformation describes this change, and what does this transformation mean?
Answers
That means that the SUV does 18 miles per gallon less than the compact car.
A line passes through the point (4, –2) and has a slope of mc010-1.jpg.
What is the value of a if the point (–4, a) is also on the line?
–6
–5
5
6
Answers
The value of a if the point (–4, a) is also on the line is -6
What is the value of a if the point (–4, a) is also on the line?If a line passes through the point (4, –2) and has a slope of 1/2, its equation can be written in point-slope form as:
y - (-2) = 1/2(x - 4)
Simplifying the equation gives:
y + 2 = 1/2x - 2
To find the value of a, substitute x = -4 and y = a into the equation:
a + 2 = 1/2(-4) - 2
a + 2 = -4
a = -6
Hence, the value of a is -6
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Question
A line passes through the point (4, –2) and has a slope of 1/2 What is the value of a if the point (–4, a) is also on the line?
The sum of three consecutive even integers is 378. what is the largest of the three integers
Answers
The largest of the three integers is 127.
It is required to find the largest of the three integers.
What is integer?An integer is a whole number (not a fractional number) that can be positive, negative, or zero.
Given that:
Let's assume, that first number is "x", than second number will be "x + 1" and third one is "x + 2".
x + (x + 1) + (x + 2) = 378
x + x + 1 + x + 2 = 378
3x + 3 = 378
3(x + 1) = 378
Divide by 3
x + 1 = 126
x = 125
The first number is 125, second number is 126 and third number is 127.
So, the largest of the three integers is 127.
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