The solutions to the system of equations are given as follows: (1, -3) and (-4,2).
<h3>What is a system of equations?</h3>
A system of equations is when two or more variables are related, and equations are built to find the values of each variable.
The equations are given as follows:
- (x + 3)² + (y + 2)² = 17.
From the second equation:
y = -2 - x.
Replacing in the first:
(x + 3)² + (y + 2)² = 17.
(x + 3)² + (-2 - x + 2)² = 17
x² + 6x + 9 + x² = 17
2x² + 6x - 8 = 0
2(x² + 3x - 4) = 0
2(x + 4)(x - 1) = 0.
Then the solutions for x are:
The solutions for y are:
- When x = 1, y = -2 - 1 = -3.
- When x = -4, y = -2 -(-4) = 2.
Hence the solutions are:
(1, -3) and (-4,2).
More can be learned about a system of equations at brainly.com/question/24342899
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Two water balloons were launched into the air at different moments and collided. the water balloons were modeled by the quadratic functions: y = −7x2 26x 3 and y = −6x2 23x 5, where y represents the height in meters and x represents the time in seconds after the launch. 2.0 seconds is the time, in seconds, that the balloons collided at the highest point
The time in seconds that the balloons collided at the highest point is; B: 2.0 seconds
We are told that the water balloons were modeled by the quadratic functions:
y = -7x² + 26x + 6 and y = -6x² + 25x + 4
where;
y = the height in meters
x = the time in seconds after the launch
The time at which they will collide has to be at the same height.
Thus;
-7x² + 26x + 6 = -6x² + 25x + 4
Rearranging this gives;
x² - x - 2 = 0.
Using an online quadratic equation solver gives us x = 2 or -1. We will take the positive one as x = 2.0 seconds
Learn more about quadratic equations at
brainly.com/question/1214333
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Answer:
360 ft
Step-by-step explanation:
<h3>Given</h3>
- Area = 57600 ft²
- Length = x
- Width = 4/9x
<h3>Solution</h3>
- A = lw
- x*4/9x = 57600
- 4/9x²= 57600
- x² = 57600*9/4
- x² = 129600
- x = √129600
- x = 360 ft
Step-by-step explanation:
let us attend to each cases one after the other. each relationship is in bold in parenthesis
1. The cost of hiring a mover is based on the distance traveled and the total weight of the objects moved. (positive or direct proportional relationship)
2. The amount of time needed to paint a house decreases as the number of painters increases.(Negative or inverse relationships)
3. The income of a worker who gets paid an hourly wage depends on the number of hours worked positive or direct proportional relationship)
The awnser is 6(4t-3) I hope this helps u