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Answer: 140?
I am not really sure but I think 140......
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If (x1, y1) and (x2, y2) are distinct solutions to the system of equations shown above, what is the sum of the y1 and y2?
Answers
Solving the system we can see that the sum of the y-values of the two solutions is 139.
How to get the sum of y₁ and y₂?
Let's solve the system of equations.
y = 10 + 16x − x²
y = 3x + 50
We can write this as a single quadratic equation:
10 + 16x - x² = 3x + 50
10 + 16x - x² - 3x - 50 = 0
-x² + 13x - 40 = 0
Using the quadratic formula we will get the two solutions for x:
So the two solutions are:
x = (-13 + 3)/-2 = 5
x = (-13 - 3)/-2 = 8
Evaluating the linear equation in these two values we will get y1 and y2.
if x = 5
y₁ = 3*5 + 50 = 65
if x= 8
y₂ = 3*8 + 50 = 74
The sum is:
65 + 74 =139
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Final answer:
The distinct solutions to the system of equations are (5, 65) and (8, 74), and the sum of the y-values is 139.
Explanation:
To find the sum of y-values of the distinct solutions to this system of equations, first, you need to set the two equations equal to each other to find the x-values of the solutions:
10 + 16x − x^2 = 3x + 50.
Then, solve the resulting equation for x:
x^2 - 13x + 40 = 0.
This is a quadratic equation, and it can be solved either by factoring or using the quadratic formula. The solutions for x result in:
x = 5 and x = 8.
These are the two distinct x-values for the intersections of the graphs of the two equations. To find the corresponding y-values, plug these x-values into either of the original equations. We'll use the simpler equation, y = 3x + 50:
For x = 5, y = 65 and for x = 8, y = 74.
Therefore, the distinct solutions to the system of equations are (5, 65) and (8, 74). Finally, the sum of y1 and y2 is 65 + 74 = 139.
Learn more about System of Equations here:
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6(f+4) + 2(f+4)
Use the distributive property:
6f+24 + 2f + 8
Now combine like terms:
8f +32
The answer is 8f + 32
Answer:
8 f + 32
Step-by-step explanation:
6 ( f + 4 ) + 2 ( f + 4 )
Distribute
6 × f + 6 × 4 + 2 × f + 2 × 8
6 f + 24 + 2f + 8
Collect like terms
6 f + 2 f + 24 + 8
Add the numbers
8 f + 32
Answers
(7b - 2b) = 5b
3 - 1 = 2
Thus:
5b + 2 = 0
5b = -2
b = -2/5 = -0.4
5b+2=0
5b=-2
b=-2/5
Answers
Answer:
t=10
Step-by-step explanation:
3t + 15 = 45
3t = 30
t = 10
Answer:
t = 10
Step-by-step explanation:
if you want detailed explanation then ask in comments
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Answer : LCM = 1020
Hope this helps. - M
(10x+20y+10z)
Answers
Answer:
I think the answer is 40.
Step-by-step explanation: