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.
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).
For more information, refer to the link given below:
https://brainly.com/question/22568405
How many different combinations of a 4-member debating team can be formed from a group of 10 qualified students?
The area of this parallelogram is 24 square units the base is 8 units what is the height of the figure
Peter wants to put 2 coats of paint on both the inside and outside of the walls. There are 5 walls, each side having 45 ft2 of paintable surface. A gallon of paint covers x ft2. Explain how to write an expression to represent the number of gallons of paint Peter needs.
To calculate the number of gallons Peter needs, multiply the surface area of one side of the wall (225 ft2) by 2 for both sides, and then by 2 again for two coats, totaling 900 ft2. Then divide 900 ft2 by the coverage per gallon x to get the expression 900 / x.
To determine the number of gallons of paint Peter needs, we must first calculate the total paintable surface for both the inside and outside of the walls and then factor in the two coats of paint. Peter has 5 walls, with each side having 45 ft2 of paintable surface, so the total paintable surface for one side is 5 walls imes 45 ft2/wall = 225 ft2. Since he wants to paint both sides, we double this to get 450 ft2. For two coats, we need to double this again, resulting in 900 ft2. Now, if a gallon of paint covers x ft2, the number of gallons needed is total square footage divided by coverage per gallon, which is 900 ft2 / x ft2/gallon.
Therefore, the expression to represent the number of gallons Peter needs is 900 / x.
Which correctly applies the distributive property to show an equivalent expression to (–2.1)(3.4)?
Answer:
(–2.1)(3) + (–2.1)(0.4)
Step-by-step explanation
It's D
The measure of a supplement of angle is 12 more than three times the measure of a complement. find the measure of the angle.
Please help :)))) ( attachment )
Sophia used the digits 6, 3, and 8 to write a number less than 6 and greater than 5. Her number has three digits, and the digit in the tenths place is odd. She used each digit only once in the number. What is Sophia's number?
Which property justifies that 4.37.25=4.25.37?
Simply x squared over Y plus Y squared over X all over Y squared minus XY plus X squared
A movie theater sold a total of 390 adult and child tickets on a certain day. The theater sold 2.25 times as many adult tickets as child tickets. Each adult ticket cost $7 and each child ticket cost $3. How much revenue did the theater generate in ticket sales that day?
The Revenue generated by theater is $2,250.
What is simplification?Simply put, to simplify is to make something simpler. Simplifying an equation, fraction, or issue in mathematics entails taking something complex and making it simpler. The issue is made simpler by calculations and problem-solving strategies. We can simplify fractions by removing all common elements from the numerator and denominator and putting the fraction in its simplest/lowest form.
It is possible to simplify mathematical formulas by merging and grouping related terms. This makes it easy to understand and decipher the puzzle.
Given total ticket sold = 390
adult ticket + child ticket = 390
and 2.25 times as many adult tickets as child tickets
so adult ticket = 2.25 child tickets
Let child ticket be x
adult ticket = 2.25x
equation will be
2.25x + x = 390
3.25x = 390
x = 120
adult ticket = 390 - 120 = 270
cost of 1 adult ticket = $7
cost of 270 adult ticket = 7 x 270 = $1890
cost of 1 child ticket = $3
cost of 120 child ticket = 3 x 120 = $360
Total revenue = $1890 + $360
Total revenue = $2,250
Hence the total collection of theater is $2,250.
Learn more about simplification;
https://brainly.com/question/28996879
#SPJ5
A=12h(a+b)
Solve for h.
A. h=2Aa+b
B.h=a+b2A
C.h=A2(a+b)
D.h=2(a+b)A
Answer:
h = 2A/a+b
or 1st answer
Step-by-step explanation:
Determine if the statement is always, sometimes, or never true:
An equilateral triangle is a right triangle.
always
sometimes
never
Answer:
never
Step-by-step explanation:
To Find :An equilateral triangle is a right triangle.
1. always
2.sometimes
3.never
Solution :
Definition of equilateral triangles: a triangle having all sides equal in length
Since all sides are equal so by property of triangle (angle opposite to equal sides are equal ) so, all angles are equal .
If equilateral triangle is right angle then one of its angle is of 90°
And in equilatera triangle all angles are equal so all angles must be of 90°
We know that triangle sum property is : Sum of all angles of triangle is equal to 180°
So, 90°+90°+ 90° =180°
⇒270°≠180°
since this violates the angle sum property of triangle .
Thus an equilateral triangle can never be a right triangle
Answer:
NEVER
Step-by-step explanation:
What is the equation of the line that passes through (5, -2) and (-3, 4)?
Answer: [tex]4y=-3x-7[/tex]
Step-by-step explanation:
The equation of a line passing through (a,b) and (c,d) is given by :-
[tex](y-b)=\dfrac{d-b}{c-a}(x-a)[/tex]
The equation of a line passing through (5, -2) and (-3, 4) is given by :-
[tex](y-(-2))=\dfrac{4-(-2)}{-3-5}(x-5)\\\\\Rightarrow\ y+2=\dfrac{6}{-8}(x-5)\\\\\Rightarrow\ y+2=\dfrac{-3}{4}(x-5)\\\\\Rightarrow\ 4(y+2)=-3(x-5)\\\\\Rightarrow\ 4y+8=-3x+15\\\\\Rightarrow\ 4y=-3x-7[/tex]
A class has 11 boys and 9 girls in it. what percent of the class are boys
Answer: the answer is C 55%
Hope this helps you
Allison practices her violin for at least 12 hours per week. She [practices for three fourths of an hour each session. If Allison has already practiced 3 hours this week, how many more sessions remain for her to meet or exceed her goal?
Please show the Inequality
Answer:
[tex]3+\frac{3}{4}x\geq 12[/tex]
Step-by-step explanation:
Given,
The number of hour he already practiced in this week = 3,
Also, she practices for three fourth of an hour each session,
If x be the number of remaining session,
So, the additional number of hours he practiced in this week = [tex]\frac{3x}{4}[/tex]
Thus, the total number of hours he practiced in this week = [tex]3+\frac{3x}{4}[/tex]
According to the question,
Total number of hours ≥ 12 hours
[tex]\implies 3+\frac{3x}{4}\geq 12[/tex]
Which is the required inequality.
Et f(x) = 9x − 2 and g(x) = −x + 3. find f(g(x)). −9x − 2 −9x + 5 −9x + 25 −9x + 27
Answer:
its a on edg
Step-by-step explanation:
im 100%
If AB is parallel to CD and the slope of CD is -8, what is the slope of AB
Can anybody help me with this? It's geometry
what are rational numbers
KL = 4x+7 and LM= 5x-4
Which of the following is irrational?
A. 7.51... x -4
B. root 16 + 3/4
C. root 3 + 8.486
D. 8 2/3 x 17.75
Option (C) √3 + 8.486 is an irrational number.
What is an irrational number?An irrational number is a type of real number which cannot be represented as a simple fraction. It cannot be expressed in the form of a ratio. Those real numbers that are not rational numbers are known as irrational numbers.
For the given situation,
We need to check the options, that is irrational.
Option A: 7.51... x -4
⇒ [tex](7.51 ) (-4)[/tex]
We can express this as fraction. So it is not an irrational number.
Option B: root 16 + 3/4
⇒ [tex]\sqrt{16} +\frac{3}{4}[/tex]
⇒ [tex]4+\frac{3}{4}[/tex]
We can express this as fraction. So it is not an irrational number.
Option C: root 3 + 8.486
⇒ [tex]\sqrt{3} +8.486[/tex]
⇒ [tex]\sqrt{3}[/tex] is an irrational number, so the sum is also an irrational number.
Option D: 8 2/3 × 17.75
⇒ [tex](8\frac{2}{3})(17.75)[/tex]
We can express this as fraction. So it is not an irrational number.
Hence we can conclude that option (C) √3 + 8.486 an irrational number.
Learn more about irrational number here
https://brainly.com/question/3386568
#SPJ2
Sum or difference for (6xy + 2y + 6x) + (4xy -x)
Planes X and Y are perpendicular. Points A, E, F, and G are points only in plane X. Points R and S are points in both planes X and Y. Lines EA and FG are parallel.
Based on this information, which lines could be perpendicular to RS? Check all that apply.
EA,ER,EF,FG,FS
Answer:
Step-by-step explanation:
One day a store sold 17 sweatshirts. white ones cost $10.95 and yellow ones cost $ 11.50. in all, $192.75 worth of sweatshirts were sold. how many of each color were sold?
Choose the graph that matches the following system of equations 4x +2y=-2 x-3y=24
The solutions of the above system of equations is x = 3 and y = -7 and the graph of above system of equations is as shown below.
What is system of equations?"It is a finite set of equations for which we find the solution."
For given question,
We have been given a system of equations.
4x +2y = -2 ................(i)
x - 3y = 24 ................(ii)
From equation (ii),
x = 24 + 3y .............(iii)
Substitute this value of x in equation (i)
⇒ 4(24 + 3y) +2y = -2
⇒ 96 + 12y + 2y = -2
⇒ 14y = -98
⇒ y = -7
Substitute this value of y in equation (iii)
⇒ x = 24 + 3(-7)
⇒ x = 24 - 21
⇒ x = 3
Therefore, the solutions of the above system of equations is x = 3 and y = -7 and the graph of above system of equations is as shown below.
Learn more about the system of equations here:
https://brainly.com/question/12895249
#SPJ3
Maria says that 6.25 os 1/100 the value od 625.Wriye an explanation to support Maria's statement.You can use equations or models in your explanation.
If p(x) = 2x2 – 4x and q(x) = x – 3, what is (poq)(x)
5q + 3 = 3h solve for q (literal equations)
A segment has endpoints F and H . What are two names for the segment?