100POINTS!!!!!!!!!!!!!!!!!!!!!!!!!!!!1
Answers
f(x) means y
g(x) means y
y intercept is where the graph crosses the y axis or when x=0 so set x=0
f(x)
x=0 when y=-7.5
y int=-7.5
g(x)
x=0
set x=0
y=3^0-7
y=1-7
y=-6
f(x) yint=-7.5
g(x) yint=-6
A. y int of f(x) is less than yint of g(x)
-7.5<-6
true
B. this is oposite of A so this is wrong
C. this says that g(x) has no yint, false
D. they yints are eqla
-7.5=-6
false
answer is A
Answer:
f(x)
x=0 when y=-7.5
y int=-7.5
g(x)
x=0
set x=0
y=3^0-7
y=1-7
y=-6
f(x) yint=-7.5
g(x) yint=-6
A. y int of f(x) is less than yint of g(x)
-7.5<-6
true
B. this is oposite of A so this is wrong
C. this says that g(x) has no yint, false
D. the yints are equal
-7.5=-6
false
answer is A
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Answers
Super is 531×42
Answers
2 * x^2 + 8 * x = x^2 - 16
2 * x^2 - x^2 + 8 * x + 16 = 0
x^2 + 8 * x + 16 = 0
(x + 4) * (x + 4) = 0
x = - 4
The correct result would be x = - 4.
Answer:
x = -4 is the only solution.
Step-by-step explanation:
The given equation is 2x² + 8x = x² - 16
We can find the value of x by solving the equation.
(2x² + 8x) - x² = (x² - 16) - x²
x² + 8x = - 16
(x² + 8x) + 16 = (-16) + 16
x² + 8x + 16 = 0
(x + 4)² = 0 [ Since a² + b² + 2ab = (a + b)²]
⇒ (x + 4) = 0
x = -4
Therefore, x = -4 is the only solution of the given equation.
Write an equation and solve.
Answers
The number is -27/2 if two times the sum of nine and a number is the opposite of 9 after applying the concept of the linear equation.
What is a linear equation?
It is defined as the relation between two variables, if we plot the graph of the linear equation we will get a straight line.
If in the linear equation, one variable is present, then the equation is known as the linear equation in one variable.
It is given that:
Two times the sum of nine and a number is the opposite of 9.
Let the number be x:
2(x + 9) = -9
2x + 18 = -9
2x = - 9 - 18
2x =- 27
x = -27/2
Thus, the number is -27/2 if two times the sum of nine and a number is the opposite of 9 after applying the concept of the linear equation.
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This is because you have "two times" which is 2*
The sum of a number = x
Opposite of 9 = -9
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.
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Answers
Answer:
the probability that a randomly selected item is non-defective is approximately 96.3%.
Step-by-step explanation:
This involves finding the probability of an item being non-defective for each machine and then combining these probabilities based on the machine's contribution to the total production.
Let's calculate it step by step:
Probability that an item from Machine A is non-defective:
The probability of a defective item from Machine A is 3%, so the probability of a non-defective item from Machine A is 100% - 3% = 97%.
Probability that an item from Machine B is non-defective:
The probability of a defective item from Machine B is 4%, so the probability of a non-defective item from Machine B is 100% - 4% = 96%.
Probability that an item from Machine C is non-defective:
The probability of a defective item from Machine C is 5%, so the probability of a non-defective item from Machine C is 100% - 5% = 95%.
Now, we need to consider the contribution of each machine to the total production:
Machine A produces 50% of the items.
Machine B produces 30% of the items.
Machine C produces 20% of the items.
To find the overall probability that a randomly selected item is non-defective, we'll use a weighted average:
Probability (Non-Defective) = (Probability from A * Fraction from A) + (Probability from B * Fraction from B) + (Probability from C * Fraction from C)
Probability (Non-Defective) = (97% * 50%) + (96% * 30%) + (95% * 20%)
Now, calculate the weighted average:
Probability (Non-Defective) = (0.97 * 0.50) + (0.96 * 0.30) + (0.95 * 0.20)
Probability (Non-Defective) = 0.485 + 0.288 + 0.19
Probability (Non-Defective) = 0.963
So, the probability that a randomly selected item is non-defective is approximately 96.3%.
The probability that an item randomly selected from the production of machines A, B, and C is non-defective is 0.963 or 96.3%.
The question is about calculating the probability of an item being non-defective in a factory production environment. Here is how you can find the solution:
- Determine the probability that an item is produced by each machine and it isn't defective.
- Machine A: Probability = 0.50 (proportion of total items) x 0.97 (proportion of non-defective items) = 0.485
- Machine B: Probability= 0.30 x 0.96 = 0.288
- Machine C: Probability = 0.20 x 0.95 = 0.19
- Add the probabilities from each machine. This is valid because the events are mutually exclusive; an item can only be produced by one machine. Therefore, the total probability that an item randomly selected is non-defective is: 0.485 + 0.288 + 0.19 = 0.963 or 96.3%.
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