Answer:
<u>The system has two solutions:</u>
<u>x₁ = 5 ⇒ y₁ = -10</u>
<u>x₂ = -2 ⇒ y₂ = 11</u>
Step-by-step explanation:
Let's solve the system of equations, this way:
y = -3x + 5
y = x ² - 6x - 5
Replacing y in the 2nd equation:
y = x ² - 6x - 5
-3x + 5 = x ² - 6x - 5
x ² - 3x - 10 = 0
Solving for x, using the quadratic formula:
(3 +/- √(9 -4 * 1 * -10))/2 * 1
(3 +/- √9 + 40)/2
(3 +/- √49)/2
(3 +/- 7)/2
x₁ = 10/2 = 5
x₂ = -4/2 = -2
x₁ = 5 ⇒ y₁ = -10
x₂ = -2 ⇒ y₂ = 11
<u>As we can see the system has two different solutions</u>
The answer is..........
A. 9
Answer:D The number of tickets is increasing by 97% each year
Step-by-step explanation:
The rate of change is (0.97). You change that decimal into a percent To get your percentage rate / increase rate...I think
Like all problems that involve images within the question, we should definitely try to draw this out. In the picture above, I have done this.
Now, we can see that this is just a simple proportion problem. For every 2.5 cm of height of the flower, we are 2 cm from the opening, or aperture. For every 20 cm of height, how far are we? We can set up the problem like this:
20 ............2.5
-------- = ---------
...x ............. 2
where x is the unknown distance to the aperture from the flower. Now, we just need to get x by itself. A typical way of solving something like this is by doing "butterfly multiplication" which is really just a shortcut haha. Anyway, I can rewrite that equation ^ as:
20×2 = 2.5 × x
Then, to solve for x, we would divide both sides by 2.5. (If you don't know why that is, please let me know and I'll elaborate).
We would then have:
20×2
------- = x
2.5
Which then simplifies to:
x = 16
Try using the same logic for your second question, and if you get stuck, I'd be happy to help! please let me know if any of this doesn't make sense. :)
You are counting by 10s so the answer is 40,50,60,70,80
the complete sequence: 10,20,30,40,50,60,70,80,90,100