Answer:
t = 36
Step-by-step explanation:
If one of the roots is "a", the equation can be factored as ...
(5x -a)(x -a) = 0
5x^2 -6ax +a^2 = 0
Comparing terms to the given equation, we see that ...
-6ax = -36x
a = 6 . . . . . . . . divide by -6
Then ...
a^2 = t
36 = t . . . . . . . substitute 6 for a
_____
The roots are 6 and 6/5.
Answer:
Below!
Step-by-step explanation:
Using Pythagoras theorem, I will solve all of the problems.
<h3>________________________________________________</h3>
<u>Question 9:</u>
- 10² = 6² + x²
- => 100 = 36 + x²
- => 100 - 36 = x²
- => 64 = x²
- => x = 8
<h3>________________________________________________</h3>
<u>Question 10:</u>
- 26² = 24² + x²
- => 676 = 576 + x²
- => 676 - 576 = x²
- => 100 = x²
- => x = 10
<h3>________________________________________________</h3>
<u>Question 11:</u>
- 15² = 12² + x²
- => 225 = 144 + x²
- => 225 - 144 = x²
- => 81 = x²
- => x = 9
<h3>________________________________________________</h3>
<u>Question 12:</u>
- x² = 8² + 12²
- => x² = 64 + 144
- => x² = 208
- => x = √208
- => x = 14.2 (Rounded)
<h3>________________________________________________</h3>
<u>Question 13:</u>
- 7² = 2² + x²
- => 49 = 4 + x²
- => 49 - 4 = x²
- => 45 = x²
- => x = √45
- => x = 6.7 (Rounded)
<h3>________________________________________________</h3>
<u>Question 14</u>
First, let's solve for the variable x using Pythagoras theorem.
- => 5² = 3² + x²
- => 25 = 9 + x²
- => 16 = x²
- => x = 4 units
Now, let's solve for the variable y using Pythagoras theorem.
- (3 + 6)² = 5² + y²
- => (9)² = 25 + y²
- => 81 = 25 + y²
- => y² = 56
- => y = √56
- => y = 7.5 (Rounded) units
Answers (Nearest tenth):
<h3>________________________________________________</h3>
<u>Question 15:</u>
First, let's find the value of the variable y using Pythagoras theorem.
- 8² = 6² + y²
- => 64 = 36 + y²
- => 28 = y²
- => y = √28
- => y = 5.3 (Rounded) units
Now, let's find the value of the variable x using multiplication.
- x = 2y
- => x = 2(5.3)
- => x = 10.6 units
Answer (Nearest tenth)
- x = 10.6 units
- y = 5.3 units
<h3>________________________________________________</h3>
Answer:
3 meters
Step-by-step explanation:
We assume the storage room is a rectangle, like most rooms, no indication it is otherwise.
We know it's a rectangle and not a square because it is longer than wide.
We have the perimeter measurement (16 meters).
So, we can make the following equation:
2x + 2y = 16
x being the width of the room, y being it's length. A perimeter is the sum of all sides.
We also know the room is 2 meters longer than wide... so:
y = x + 2
If we replace y in the first equation by its value relative to x, we get:
2x + 2(x + 2) = 16 which becomes
2x + 2x + 4 = 16
4x =12
thus x = 3
Width: 3 meters
Length: 5 meters.
Confirms the 16 meters perimeter.
