Inequalities and equations use similar steps to solve, but inequalities give a range of numbers that can represent the variable while an equation will give a direct answer.
Example:
4+5x=24
First you would subtract 4 or add the opposite of 4 from 24.
4+5x=24
+(-4) +(-4)
—————
5x=20
Then divide each side by 5 or multiply each side by the reciprocal of 5 to isolate the variable.
1/5*5x=20*1/5 (reciprocal)
X= 4
You would use the same steps in an inequality but end up with a different sign.
Answer: the height in inches, of the pile after 3 weeks is 34 11/12 inches
Step-by-step explanation:
Each consecutive week for the next 5 weeks the height of pile increase by 8 7/12 inches. Converting 8 7/12 inches to improper fraction, it becomes 103/12 inches. The height is increasing in an arithmetic progression. The formula for determining the nth term of an arithmetic sequence is expressed as
Tn = a + (n - 1)d
Where
a represents the first term of the sequence.
d represents the common difference.
n represents the number of terms in the sequence.
From the information given,
a = 17 3/4= 71/4 inches
d = 103/12 inches
n = 3 weeks
the height in inches, of the pile after 3 weeks, T3. Therefore,
T3 = 71/4 + (3 - 1)103/12
T3 = 71/4 + 2 × 103/12 = 71/4 + 103/6
T3 = 419/12 inches = 34 11/12 inches
Answer:
y = -1/2x + 2
Step-by-step explanation:
y = 2x - 3. The slope here is 2. A perpendicular line will have a negative reciprocal slope. To find the negative reciprocal, just flip the slope and change the sign.
slope = 2 or 2/1.....flip it.....1/2....change the sign...-1/2. So our perpendicular line will have a slope of -1/2.
y = mx + b
slope(m) = - 1/2
(2,1)....x = 2 and y = 1
now we sub and find b, the y intercept
1 = -1/2(2) + b
1 = -1 + b
1 + 1 = b
2 = b
so ur equation is : y = -1/2x + 2 <===
and u can check it with ur points....(2,1)
y = 2x - 3
1 = 2(2) - 3
1 = 4 - 3
1 = 1 (yep...it checks out)
Step-by-step explanation:
Consider a function
f
(
x
)
which is twice differentiable. The graph of such a function will be concave upwards in the intervals where the second derivative is positive and the graph will be concave downwards in the intervals where the second derivative is negative. To find these intervals we need to find the inflection points i.e. the x-values where the second derivative is 0.
Answer:
The inequality 2.50x>40.00 represents the number of lunches needed to be purchased for the monthly lunch pass to be a better deal.
Step-by-step explanation:
Given that:
Cost of each lunch = $2.50
Cost of monthly lunch pass = $40.00
Number of lunches = x
For making the monthly pass a better deal, the cost of lunches should be greater than the cost of monthly lunches, therefore
Cost of lunch * Number of lunches > Cost of monthly lunch pass
2.50x > 40.00
Hence,
The inequality 2.50x>40.00 represents the number of lunches needed to be purchased for the monthly lunch pass to be a better deal.
