Answer: The inequality solves to x ≥ 42
The graph is shown below
==================================================
Explanation:
We have some unknown number x, and we're dividing by 6 to form the fraction x/6. That result is 7 or larger which means we write x/6 ≥ 7
To solve for x, we undo the division. We'll multiply both sides by 6. That's how we get to x ≥ 42
The graph will involve a number line. Plot a closed filled in circle at 42 on the number line. Shade to the right. This visually represents any number that is 42 or larger. The endpoint 42 itself is included in the solution set.
Side note: We would use an open circle if we didn't have the "or equal to" portion for the inequality sign.
Hey there!
y = -2x + 19
y = x + 7
We gonna solve this system of equation by using the substitution method.
We wanna solve y = -2x + 19 for y
Let start by substitute -2x + 19 for y in y = x + 7
y = x + 7
-2x + 19 = x + 7
Subtract x from both sides
-2x + 19 - x = x + 7 - x
-3x + 19 = 7
Now subtract 19 on both sides
-3x + 19 - 19 = 7 - 19
-3x = -12
Then divide both sides by -3
-3x/-3 = -12/-3
x = 4
We have the value of x. Now we gonna use that same value to find the value for y.
We gonna do that by substitute 4 for x in y = -2x + 19
y = -2x + 19
y = -2(4) + 19
y = -8 + 19
y = 11
Thus,
The answer is: x = 4 and y = 11
Let me know if you have questions about the answer. As always, it is my pleasure to help students like you!
Answer:
first one : x=−2y−5z−17
2nd one: x=
3
/2
y−z−8
3rd one: x=
−1
/3
y+
1
/3
z+1
Step-by-step explanation:
A) zeroes
P(n) = -250 n^2 + 2500n - 5250
Extract common factor:
P(n)= -250 (n^2 - 10n + 21)
Factor (find two numbers that sum -10 and its product is 21)
P(n) = -250(n - 3)(n - 7)
Zeroes ==> n - 3 = 0 or n -7 = 0
Then n = 3 and n = 7 are the zeros.
They rerpesent that if the promoter sells tickets at 3 or 7 dollars the profit is zero.
B) Maximum profit
Completion of squares
n^2 - 10n + 21 = n^2 - 10n + 25 - 4 = (n^2 - 10n+ 25) - 4 = (n - 5)^2 - 4
P(n) = - 250[(n-5)^2 -4] = -250(n-5)^2 + 1000
Maximum ==> - 250 (n - 5)^2 = 0 ==> n = 5 and P(5) = 1000
Maximum profit =1000 at n = 5
C) Axis of symmetry
Vertex = (h,k) when the equation is in the form A(n-h)^2 + k
Comparing A(n-h)^2 + k with - 250(n - 5)^2 + 1000
Vertex = (5, 1000) and the symmetry axis is n = 5.
Answer:
B.
Step-by-step explanation:
y intercept: 3
Slope: rise 2 run 1 so -2/1 or -2
