An inequality can be formed by simply translating the problem statement to numerical expressions.
From the problem we know that
added with
hours should be equal or greater than
(helpful insight from the keyword "at least"). Therefore, it's inequality would look like:
(>= is used instead of ≥ for constraints in formatting)
The inequality above best models the situation.
Answer:
a) not proportional
b) proportional; k = 
Step-by-step explanation:
a) for any proportional equation, the line must pass through the origin. The equation in a) is y = 4x + 1, and the '+1' is the y-intercept. This means that the line does not pass through the origin, so x and y cannot increase by the same amount (i.e. they are not proportional).
Another way to determine this is is to use the y = kx base. If you have an equation that fits that it's likely proportional.
Here, if the equation was only y = 4x then it'd be proportional because u can see that k = 4. This is not the equation though, and the 4x + 1 doesn't fit to the y = kx formula so it can't be proportional.
b) straight away you can see that there's no 'c' term (y = mx + c) which means the y-intercept is 0, so the line passes through the origin. While this does not immediately mean the line is proportional, you can make sure that it is by checking it fits with the y = kx equation.
y = -(3/5)x fits with y = kx, with k being -3/5
Answer:
x < 33.84
Step-by-step explanation:
we have
13.48x-200 < 256.12
Solve for x
Adds 200 both sides
13.48x-200 +200 < 256.12+200
13.48x < 456.12
Divide by 13.48 both sides
13.48x/13.48 < 456.12/13.48
x < 33.84
The solution is the interval ----> (-∞, 33.84)
All real numbers less than 33.84
9x - 2 = 67
67 + 2 = 69
69 × 9 = 621
621 = x
Answer:
A, B, C, and D, all options are correct.
A is correct because,
∠2 and ∠3 are corresponding angles.
B is correct because,
∠5 and ∠7 are corresponding angles.
C is correct because,
∠2 and ∠4 are corresponding angles.
D is correct because,
∠5 and ∠6 are alternate interior angles.
Note,
If two lines parallel, then
- Corresponding angles are equal.
- Alternate interior angles are equal.
