We will use substitution to solve this system of linear equations, as the first equation has x and y with no coefficients, which makes it easier to find one in terms of the other. We can then substitute that value in the other equation and find the values of x and y.
x = y + 5 ---> equation 1
3x + 2y = 5 ---> equation 2
From equation 1, we get the value of x as y + 5. Using the substitution method, we can find the value of y by substituting (y+5) for x in the 2nd equation.
3(y+5) + 2y = 5
3y + 15 + 2y = 5
5y = 5 - 15
5y = -10
y = -2
Subsituting this value of y in (y+5), we can find x.
x = y + 5
x = -2 + 5
x = 3
Therefore, x = 3 and y = -2.
I will also solve this using elimination method.
Let us multiply equation 1 by 2, so that we get 2y in both equations.
2x = 2y + 10
3x + 2y = 5
Let us add both the equations.
2x + 3x + 2y = 5 + 2y + 10
5x = 15 + 2y - 2y
5x = 15
x = 3
Substituting this value of x in equation 1, we get
x = y + 5
3 = y + 5
y = 3 - 5
y = -2
Therefore, x = 3 and y = -2.
Answer:
0.0492
Step-by-step explanation:
Based on the tree diagram we need to tell the the probability that the test for lice returns a false positive. False positive means that the student has no lice but still the test shows a positive result.
So for this we have to first look for the branch, from the starting node, which shows that student has no lice. From the starting point, the upper branch represents the students that have lice and lower branch represents the students who have no lice. So, we will consider the lower branch with probability mentioned as 0.82
Now, the lower branch is divided into two branches further. We have to look for the branch which shows positive test result. This would be the upper branch with probability mentioned as 0.06.
The overall probability of this event is mentioned at the end of the branch which is 0.0492
This is the probability of the combined event: Student has no lice but tests shows positive result which is the False positive.
Thus, the probability that the test for lice returns a false positive is 0.0492
Answer: it would be 5
Step-by-step explanation: i hope this helps
Answer:
<u>The length of GI is 90.06 units</u>
Step-by-step explanation:
1. Let's review the information given to us to answer the question correctly:
GH = 60 units
HI = 42 units
∠H = 123°
2. Using the Law of Cosines, we can find the length of GI, this way:
GI² = GH² + HI² - 2 * GH * HI * cos ∠H
Replacing with the real values:
GI² = 60² + 42² - 2 * 60 * 42 * cos ∠123°
GI² = 3,600 + 1,764 - 2 * 60 * 42 * -0.545
GI² = 3,600 + 1,764 - 2 * 60 * 42 * -0.545
GI² = 3,600 + 1,764 + 2,746.8
GI² = 8,110.8
<u>GI = √ 8,110.8 = 90.06 units</u>
Answer:
-195 degrees
Step-by-step explanation:
we can subtract 360 from 165 to find the negative coterminal angle.
165-360=-195
