Solve each equation by graphing the related function. If the equation has no real-number solution, write no solution.
1 .x^2-9=0
2. x^+7=0
3. 3x^2=0
4. 1/4x^2-4=0
5. 4g^2=25
6. 64b^2=16
7.144-p^2=0
8. 5z^2-45=0
9. h^2=49
10.s^2-35=-35
please help me out :)
1A
2d
3C
4B
5C
6B
7C
8A
9C
10A
Sure, I can help you solve these equations by graphing the related functions. Let's start with the first equation:
1. x^2 - 9 = 0
To solve this equation graphically, we need to graph the function y = x^2 - 9 and find the x-values where the graph intersects the x-axis (where y = 0).
Plotting the graph of y = x^2 - 9, we get a parabolic shape opening upwards. To find the x-intercepts, we look for the values of x where the graph crosses the x-axis. In this case, the graph crosses the x-axis at x = -3 and x = 3.
Therefore, the solutions to the equation x^2 - 9 = 0 are x = -3 and x = 3.
Now, let's move on to the second equation:
2. x^2 + 7 = 0
Similarly, we graph the function y = x^2 + 7 and find the x-intercepts.
However, when graphing y = x^2 + 7, we observe that the graph does not intersect or touch the x-axis. This means there are no solutions (no real-number solution) to the equation x^2 + 7 = 0.
Therefore, the equation x^2 + 7 = 0 has no solution.
For the rest of the equations, we can follow the same process:
3. 3x^2 = 0
The function y = 3x^2 is a parabola opening upwards. The graph intersects the x-axis at x = 0.
Therefore, the solution to the equation 3x^2 = 0 is x = 0.
4. (1/4)x^2 - 4 = 0
The function y = (1/4)x^2 - 4 is also a parabola opening upwards. The graph intersects the x-axis at x = -4 and x = 4.
Therefore, the solutions to the equation (1/4)x^2 - 4 = 0 are x = -4 and x = 4.
5. 4g^2 = 25
The function y = 4g^2 is a parabola opening upwards. The graph intersects the x-axis at g = -5/2 and g = 5/2.
Therefore, the solutions to the equation 4g^2 = 25 are g = -5/2 and g = 5/2.
6. 64b^2 = 16
The function y = 64b^2 is also a parabola opening upwards. The graph intersects the x-axis at b = -1/4 and b = 1/4.
Therefore, the solutions to the equation 64b^2 = 16 are b = -1/4 and b = 1/4.
7. 144 - p^2 = 0
The function y = 144 - p^2 is a downward-opening parabola. The graph intersects the x-axis at p = -12 and p = 12.
Therefore, the solutions to the equation 144 - p^2 = 0 are p = -12 and p = 12.
8. 5z^2 - 45 = 0
The function y = 5z^2 - 45 is a parabola that opens upwards. The graph intersects the x-axis at z = -3 and z = 3.
Therefore, the solutions to the equation 5z^2 - 45 = 0 are z = -3 and z = 3.
9. h^2 = 49
The function y = h^2 is a parabola opening upwards. The graph intersects the x-axis at h = -7 and h = 7.
Therefore, the solutions to the equation h^2 = 49 are h = -7 and h = 7.
10. s^2 - 35 = -35
To graph the function y = s^2 - 35, we simplify the equation to y = 0. This means the graph intersects the x-axis at s = ±√35.
Therefore, the solutions to the equation s^2 - 35 = -35 are s = ±√35.
I hope this helps! Let me know if you have any further questions.
Sure, I can help you solve these equations by graphing the related functions. To do this, we need to graph the functions and find the x-intercepts, which represent the solutions to the equations.
1. x^2 - 9 = 0:
The related function is y = x^2 - 9. To graph it, plot points for different values of x and y. The x-intercepts are the points where y = 0.
By graphing the function, the x-intercepts are at x = -3 and x = 3. So, the solutions to the equation are x = -3 and x = 3.
2. x^2 + 7 = 0:
The related function is y = x^2 + 7. By graphing it, we can see that the graph does not intersect the x-axis. Therefore, there are no real-number solutions to this equation. We can write it as "no solution".
3. 3x^2 = 0:
The related function is y = 3x^2. By graphing it, we see that the graph intersects the x-axis at x = 0. Therefore, the solution to the equation is x = 0.
4. (1/4)x^2 - 4 = 0:
The related function is y = (1/4)x^2 - 4. By graphing it, we can see that the graph intersects the x-axis at x = -4 and x = 4. So, the solutions to the equation are x = -4 and x = 4.
5. 4g^2 = 25:
The related function is y = 4g^2 - 25. By graphing it, we see that the graph intersects the x-axis at g = -5/2 and g = 5/2. Thus, the solutions to the equation are g = -5/2 and g = 5/2.
6. 64b^2 = 16:
The related function is y = 64b^2 - 16. By graphing it, we can see that the graph intersects the x-axis at b = -1/4 and b = 1/4. So, the solutions to the equation are b = -1/4 and b = 1/4.
7. 144 - p^2 = 0:
The related function is y = 144 - p^2. By graphing it, we see that the graph intersects the x-axis at p = -12 and p = 12. Therefore, the solutions to the equation are p = -12 and p = 12.
8. 5z^2 - 45 = 0:
The related function is y = 5z^2 - 45. By graphing it, we can see that the graph intersects the x-axis at z = -3 and z = 3. Hence, the solutions to the equation are z = -3 and z = 3.
9. h^2 = 49:
The related function is y = h^2 - 49. By graphing it, we see that the graph intersects the x-axis at h = -7 and h = 7. Thus, the solutions to the equation are h = -7 and h = 7.
10. s^2 - 35 = -35:
The related function is y = s^2 - 35 + 35. Simplifying, we get y = s^2. By graphing it, we see that the graph intersects the x-axis at s = 0. So, the solution to the equation is s = 0.
I hope this helps you solve the equations!