Mathematics College

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

Triangle A B C is shown. Angle A C B is a right angle. An altitude is drawn from point C to point D on side A B to form a right angle. The length of C B is a, the length of A C is b, the length of A B is c, the length of A D is e, the length of D B is f, and the length of C D is h.

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 StartFraction c Over a EndFraction = StartFraction a Over f EndFraction and StartFraction c Over b EndFraction = StartFraction b Over e EndFraction 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?

Because f + e = 1, a2 + b2 = c2.
Because f + e = c, a2 + b2 = c2.
Because a2 + b2 = c2, f + e = c.
Because a2 + b2 = c2, f + e = 1.

Answers

Answer 1

Answer:

I don't know how I can help you but I found this from another person. Hope this helps!

Consider The Diagram And The Paragraph Proof Below.Given: Right ABC As Shown Where CD Is An Altitude
Answer 2

Answer:

The answer is b

Step-by-step explanation:

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

 Triangle A B C is shown. Angle A C B is a right angle. An altitude is drawn from point C to point D on side A B to form a right angle. The length of C B is a, the length of A C is b, the length of A B is c, the length of A D is e, the length of D B is f, and the length of C D is h.

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 StartFraction c Over a EndFraction = StartFraction a Over f EndFraction and StartFraction c Over b EndFraction = StartFraction b Over e EndFraction 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?

Because f + e = 1, a2 + b2 = c2.

Because f + e = c, a2 + b2 = c2.

Because  a2 + b2 = c2, f + e = c.

Because  a2 + b2 = c2, f + e = 1.

Related Questions

What is the slope of the equation y- 5 = -3x?

Answers

Answer:

-3/1

Step-by-step explanation:

It's always the x value over the y value, so whatever's in the x

Answer:

-3

Step-by-step explanation:

the equation is y=-3x+5, so m=-3

Alex ate 1/3 of a pizza. Katelyn ate 2/7 of the same pizza. How much larger of a portion did Alex eat than Katelyn?

Answers

Answer:

1/21

Step-by-step explanation:

1/3 - 2/7 = 7/21 - 6/21 = 1/21

Hope I helped!

Help please i am stuck

Answers

Answer:

it is because so you can evenly add it

Step-by-step explanation:

because it is easyer to add 5/10 + 2/10

than    5/10 + 1/5 isnt it?

Johnson has recently opened his workshop at the main street of a major city in the North East. Johnson estimates about 20 cars arriving at his workshop for repairs every day. Based on industry data, he estimates that 40% of the arrivals will agree to have the work repaired at his workshop. His average daily cost at the workshop is $1200. He expects to make a revenue of $200 for each car that is repaired. Johnson would like to know the following information:____________
a) The probability that no car will arrive at his workshop for repair on a given day.
b) The probability that he will have at least 4 cars to repair on a given day.
c) The expected daily profit assuming that he is able to repair all the arriving cars in a day.
d) Develop a probability distribution for this problem.

Answers

The answer to that is a I hope this helps

What is the distance between the points (2, 1) and (14, 6) on a coordinate
plane?

Answers

Answer:

the answer is 13 units

Step-by-step explanation:

I would appreciate it if someone could help me

Answers

First box on top should be 729


i need help asappppp

Answers

13/39 ....................

Answer:

he ran (7/8)

Step-by-step explanation:

first, you add the two fractions ( i did mine with a calculator) 1.125 or 9/8

then you subtract 2 from the sum that you got

then boom there your answer

Solve for X.
Х
3 ft.
6 ft.
9 ft.

Answers

I’m pretty sure the answer is 4,232

HELP PLEASE!!!
14 + 3x = 8x − 3(x − 4)
Also show work

Answers

Answer:

x=1

Step-by-step explanation:

14+3x=8x-3(x-4)


How can you rewrite a^7 using exponent rules?

Answers

a+a+a+a+a+a+a is the answer I believe

Solve for the value of n.

Answers

Answer:

3n-4= 44

3n=40

no u can solve

Answer:

17°

Step-by-step explanation:

3n - 5° + 90° + 44° = 180° { being linear pair }

3n + 129° = 180°

3n = 180° - 129°

3n = 51°

n = 51° / 3

n = 17°

Hope it will help :)

What is 1 + 1 :)))))) EZ 100

Answers

Answer:

2

Step-by-step explanation:

You add i guess? Umm, seems pretty hard to explain such a simple question, lol

Answer:

2

Step-by-step explanation:

Evaluate the expression [2³ ×(140 ÷ 7)] - 32

Answers

Answer:

128

Step-by-step explanation:

(2³) (140/7)-32 =128

Answer:

128

Step-by-step explanation:

[2³ ×(140 ÷ 7)] - 32

[2³ ×( 20)] - 32

[8×(20)] - 32

[160] - 32

128

what is the image point of (0,8) after a translation right 3 units and down 5 units​

Answers

Answer:

(3,3)

Step-by-step explanation:

(0+3,8-5)

(3,3)

What is 7x - 62 > 1 ?

Answers

Answer:

X>9

Step-by-step explanation:

Move all terms not containing x to the right side

7x>63

divide each term by 7 and simplify

7x/7 >63/7

cancel the common factor of 7

x>63/7

divide 63 by 7 x>9

x>9

2+5x+1/2x^3dx
Answer

Answers

Answer:

[tex]2x+\frac{5x^2}{2}+\frac{x^4}{8}+C[/tex]

Step-by-step explanation:

I notice you have a dx at the end of the equation, this leads me to believe this is an integral. With no bounds of integration, I will solve for the indefinite integral. I will also interpret your equation as follows:

[tex]\int \:2+5x+\frac{1}{2}x^3dx[/tex]

Sum rule tells us:

[tex]\int \:2dx+\int \:5xdx+\int \frac{1}{2}x^3dx[/tex]

From this we get:

[tex]2x+\frac{5x^2}{2}+\frac{x^4}{8}[/tex]

Don't forget to add the constant!

[tex]2x+\frac{5x^2}{2}+\frac{x^4}{8}+C[/tex]

What is the solution for the equation shown below?
x^2+4=0

Answers

X^2+4=0
X^2=-4

X does not belong to a large R

NEED HELP ASAP!!! for geometry class

Answers

Answer:

B) AAS

Step-by-step explanation:

B) AAS

The answered to the problem is... B) AAS

The difference of the square of a number and 10 is equal to 3 times that number. Find the negative solution.

Answers

Answer:

-2

Step-by-step explanation:

Let's call the number x. The statement tells us that

x^2 - 10 = 3x, or

x^2-3x-10 = 0

Factoring:

(x-5)(x+2) = 0. Here, we see that there are two solutions: x = 5 and x = -2. So, the negative solution is x = -2.

Emily is three years older than Carla and five years younger than Dante. if Carla is c years old, how old is Dante in terms of c?

A. c + 6
B. c + 8
C. c + 10
D. 2c + 3
E. 2c + 5

Answers

Answer:

I think that Dante is

D. 2c +3

hope this helps

Answer:

B

Step-by-step explanation:

Emily is three years older than Carla so

Emily = C + 3

Emily is 5 years older than Dante so

Dante is (C + 3) +5

which is C + 8

After Halloween, pumpkins were 25% off. Amy bought 2 big
pumpkins that were originally $7 each. How much did she
spend (before tax)?

Answers

Yes that’s true. You got that correct everyone listen to them.

How many 1/4 cup servings are in 3 cups of pasta?​

Answers

Answer:

12

Explanation:

1/4 × 12 = 3

Answer:

12

Step-by-step explanation:

1 cup -> 4  [tex]\frac{1}{4}[/tex] cups

3 cups -> 3 x 4 [tex]\frac{1}{4}[/tex] cups

          = 12 [tex]\frac{1}{4}[/tex] cups

Given an initial quantity Q0=150 and a growth rate of 7% per unit time, give a formula for the quantity Q as a function of time t, and find the value of the quantity at t=10.
a) Assume the growth rate is not continuous. Round your answer for Q(10) to three decimal places.
Q(t)=
Q(10) =
b) Assume the growth rate is continuous. Round your answer for Q(10) to three decimal places.
Q(t)=
Q(10)=

Answers

Answer:

Step-by-step explanation:

From the given information:

(a)

Since growth quantity is not continuous

[tex]Q(t) = 150 (1.07)^t[/tex]

For t = 10

[tex]Q(10) = 150 (1.07)^{10}[/tex]

[tex]\mathbf{Q(10) = 295.073}[/tex]

(b)

Here, for a continuous growth rate, the growth quantity can be computed in terms of initial quantity and the growth rate.

i.e.

[tex]Q(t) = 150 e^{0.07t}[/tex]

At t = 10 for a continuous growth rate;

[tex]Q(10) = 150 e^{0.07 \times 10}[/tex]

[tex]Q(10) = 150 e^{0.7}[/tex]

[tex]\mathbf{Q(10) = 302.063}[/tex]

The hypotenuse of a right triangle measures 15 cm and one of its legs measures 4 cm.
Find the measure of the other leg. If necessary, round to the nearestytenth.

Answers

Answer:

14.5 cm

Step-by-step explanation:

Pythagorean theorem: a^2 + b^2 = c^2

c = hypotenuse (15)

to solve for b (other leg), the equation is  b^2 = c^2-a^2

15^2 - 4^2 = 209

[tex]\sqrt{209}[/tex] = approx. 14.5

the other leg is (rounded to the nearest 10th) 14.5 cm

You drinking soda while playing a video game. You drank 4 full drinks over 3 1/3 rounds. If you drank the same amount each round, how much did you drink each round?

Answers

The answer to your problem would be 1 1/5 of the drink per round.

hurry answer quick I need help

Answers

Answer:

Step-by-step explanation:

Can u help me too

The equation of line WX is y = −2x − 5. Write an equation of a line perpendicular to line WX in slope-intercept form that contains point (−1, −2).

Answers

Answer:

Step-by-step explanation:

y = -2x - 5.....slope here is -2. A perpendicular line will have a negative reciprocal slope. All that means is " flip " the slope and change the sign. So the slope we will need is : 1/2. See how I flipped the slope of -2/1 and changed it to -1/2.....now I change the sign making our new slope be 1/2.

y = mx + b

slope(m) = 1/2

(-1,-2).....x = -1 and y = -2

now sub and find b, the y int

-2 = 1/2(-1) + b

-2 = -1/2 + b

-2 + 1/2 = b

-4/2 + 1/2 = b

-3/2 = b

so ur perpendicular line is : y = 1/2x - 3/2

Answer:

y = -2x - 5

m = -2

Step-by-step explanation:

The perpendicular line has a negative reciprocal slope.

m = 1/2

You are also given a point, so use the point slope formula.

y - y1 = m(x - x1)

y + 2 = 1/2(x + 1)

y + 2 = 1/2x + 1/2

y = 1/2x - 3/2

So the line perpendicular to y = -2x - 5 in slope intercept form is:

y = 1/2x - 3/2

or

y = 0.5x - 1.5

Rayna has 5 pounds of ground beef to make hamburgers for a picnic. Each hamburger uses 1/4 pound of ground beef. How many hamburgers can Rayna make?

Answers

20 ; 5 divided by 1/4 is actually 5 x 4/1

What are all the factors of 142

Answers

Answer:

142 is a composite number. Factor pairs: 142 = 1 x 142 or 2 x 71. Factors of 142: 1, 2, 71, 142. Prime factorization: 142 = 2 x 71

Answer:

1, 2, 71, 142

Pairs would be (1 x 142), (2 x 71), (71 x 2), (142 x 1)

Step-by-step explanation:

What is the area of the Rhombus​

Answers

The answer is 176. The second answer choice. It’s because if you have a four below the to four you would get 8 and 11 plus 11 would give you 22 so 8x22 gives you 176!
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