(-3, 0) is a solution to given equation
(-6, -1) is a solution to given equation
<em><u>Solution:</u></em>
<em><u>Given that equation is:</u></em>
![y = \frac{1}{3}x + 1](https://tex.z-dn.net/?f=y%20%3D%20%5Cfrac%7B1%7D%7B3%7Dx%20%2B%201)
<h3><em><u>
Option 1</u></em></h3>
(-3, 0)
Substitute x = -3 and y = 0 in given equation
![0 = \frac{1}{3} \times -3 + 1\\\\0 = -1 + 1\\\\0 = 0](https://tex.z-dn.net/?f=0%20%3D%20%5Cfrac%7B1%7D%7B3%7D%20%5Ctimes%20-3%20%2B%201%5C%5C%5C%5C0%20%3D%20-1%20%2B%201%5C%5C%5C%5C0%20%3D%200)
Thus (-3, 0) is a solution to given equation
<h3><em><u>
Option 2</u></em></h3>
(-9, -1)
Substitute x = -9 and y = -1 in given equation
![-1 = \frac{1}{3} \times -9 + 1\\\\-1 = -3 + 1\\\\-1 \neq -2](https://tex.z-dn.net/?f=-1%20%3D%20%5Cfrac%7B1%7D%7B3%7D%20%5Ctimes%20-9%20%2B%201%5C%5C%5C%5C-1%20%3D%20-3%20%2B%201%5C%5C%5C%5C-1%20%5Cneq%20%20-2)
Thus (-9, -1) is not a solution to given equation
<h3><em><u>
Option 3</u></em></h3>
(-6, -1)
Substitute x = -6 and y = -1 in given equation
![-1 = \frac{1}{3} \times - 6 + 1\\\\-1 = -2 + 1\\\\-1 = -1](https://tex.z-dn.net/?f=-1%20%3D%20%5Cfrac%7B1%7D%7B3%7D%20%5Ctimes%20-%206%20%2B%201%5C%5C%5C%5C-1%20%3D%20-2%20%2B%201%5C%5C%5C%5C-1%20%3D%20-1)
Thus (-6, -1) is a solution to given equation
Answer:
Step-by-step explanation:
What we have is a general equation that says this in words:
Laura's hours + Doug's hours = 250 total hours
Since we don't know either person's number of hours, AND since we can only have 1 unknown in a single equation, we need to write Laura's hours in terms of Doug's, or Doug's hours in terms of Laura's. We are told that Doug spent Laura's hours plus another 40 in the lab, so let's call Laura's hours "x". That makes Doug's hours "x + 40". Now we can write our general equation in terms of x:
x + x + 40 = 250 and
2x = 210 so
x = 105
Since Laura is x, she worked 105 hours in the lab and Doug worked 40 hours beyond what Laura worked. Doug worked 145. As long as those 2 numbers add up to 250, we did the job correctly. 105 + 145 = 250? I believe it does!!
We have that x = 3, LM = 14 and LN = 2. options A, C and E
<h3>How to determine the value</h3>
We known that the three sides are on a straight line
LM + MN = LN
Let's substitute the values, we have
3x + 5 + 4x = 11x - 7
Collect like terms
3x + 4x - 11x = -7 -5
-4x = -12
x = -12/ -4
x = 3
LM = 3x + 5 = 3(3) + 5 = 14
LN = 11x - 7 = 11(3) -7 = 33 -7 = 26
Thus, we have that x = 3, LM = 14 and LN = 2. options A, C and E
Learn more about geometry here:
brainly.com/question/20303542
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The value of the function is -20
-3 = x^2 + 4x + 1
0 = x^2 + 4x + 1 + 3
0 = x^2 + 4x + 4
Discriminant is b^2 - 4ac.
4^2 - 4(1)(4)
16 - 4(4)
16 - 16 = 0
Discriminant Rules:
1. If b²-4ac is negative, there are no real answers.
2. If b²-4ac is zero, there is one real answer.
3. If b²-4ac is positive, there are two real answers.
Based on rule 2, the answer is ONE REAL ROOT.