Answer:
10 < 6n -2 ≤ 34
n= {3, 4, 5, 6}
Step-by-step explanation:
number
⇒ n
two less than six times the number
⇒ 6n -2
it is between ten and thirty-four (inclusive)
⇒ 10 < 6n -2 ≤ 34
we can solve it as:
- 10 < 6n -2 ≤ 34 ⇒ add 2 to all sides
- 12 < 6n ≤ 36 ⇒ divide by 6 all sides
- 2 < n ≤ 6
- n= (2, 6]
or
9514 1404 393
Answer:
2 1/2 feet
Step-by-step explanation:
The Pythagorean theorem is not useful in this problem.
__
If you reflect the triangle over the vertical line, you find that line to be the altitude of an equilateral triangle. That is, all of the vertex angles are 60°.
The base of that equilateral triangle is necessarily twice the length of the base of the triangle shown. All sides of the equilateral triangle are the same length, so all are 5 ft. The base of the triangle shown is half that.
The base (short leg) of the triangle shown is 2 1/2 feet.
_____
Since angles are given, this can be solved using trigonometry. The short leg will be (5 ft)·cos(60°) = (5 ft)(0.5) = 2.5 ft. (The cosine of 60° is one of the few exact rational values of trig functions of exact angles measured in degrees.)
Answer:
John and Pam are paid $8.5 for each hour worked. John's share of the money is $29.75.
Step-by-step explanation:
Let x = the hourly salary. John worked for 3.5 hrs, and Pam for two. We can represent this using the equation:
3.5x + 2x = 46.75, where the coefficients equals the amount of hours.
Let's solve for x!
5.5x=46.75
x = 46.75/5.5 = 17/2 = 8.5
John and Pam are paid 8.5 dollars per each hour worked.
To figure out John's share of the money, we will multiply the wage by the hours he worked.
8.5 x 3.5 = 29.75
Answer:
5
Step-by-step explanation:
The initial value is when x=0
When x=0, y =5
The initial value is 5
Answer:
8x-4
Step-by-step explanation:
(3x-5)+(5x+1)
=3x-5+5x+1
=8x-4
