First translate the English phrase "Four times the sum of a number and 15 is at least 120" into a mathematical inequality.
"Four times..." means we're multiplying something by 4.
"... the sum of a number and 15..." means we're adding an unknown and 15 and then multiplying the result by 4.
"... is at least 120" means when we substitute the unknown for a value, in order for that value to be in the solution set, it can only be less than or equal to 120.
So, the resulting inequality is 4(x + 15) ≤ 120.
Simplify the inequality.
4(x + 15) ≤ 120
4x + 60 ≤ 120 <-- Using the distributive property
4x ≤ 60 <-- Subtract both sides by 60
x ≤ 15 <-- Divide both sides by 4
Now that we have the inequality in a simplified form, we can easily see that in order to be in the solution set, the variable x can be no bigger than 15.
In interval notation it would look something like this:
[15, ∞)
In set builder notation it would look something like this:
{x | x ∈ R, x ≤ 15}
It is read as "the set of all x, such that x is a member of the real numbers and x is less than or equal to 15".
Use the unit circle to find the inverse function value in degrees.tan^-1 sqrt 3
The correct answer would be 60 degrees. Since you are asked to find an angle that the tangent is equal to sqrt 3. The only angle that is equal to that given the interval is 60 degrees. So that is the correct answer. I hope this answer helped you.
Step-by-step explanation:
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6 years
A parent increases a child’s monthly allowance by 20% each year. If the allowance is $8 per month now. This is an exponential function, An exponential function is given by:
Let x be the number of years and y be the allowance. The initial allowance is $8, this means at x = 0, y = 8
Since it increases by 20% each year, i.e 100% + 20% = 1 + 0.2 = 1.2. This means that b = 1.2
Therefore:
To find the number of years will it take to reach $20 per month, we substitute y = 20 and find x
x = 6 years to the nearest year
