Answer:
15y +6
Step-by-step explanation:
3(5y+2)
Distribute
3*5y +3*2
15y +6
Answer:
- first shift: 13,750 bulbs
- second shift: 2500 bulbs
Step-by-step explanation:
The production ratio is ...
shift 1 : shift 2 = 5.5 : 1 = 11 : 2
so, the production on shift 1 as a ratio to the total is ...
shift 1 : total = 11 : (11+2) = 11 : 13
The first shift produced ...
(11/13)(16,250 bulbs) = 13,750 bulbs . . . . first shift
and the second shift produced ...
(2/13)(16,250 bulbs) = 2,500 bulbs . . . . second shift
_____
Of course, once you have one of the numbers, you can also find the other by using the 5.5 factor or by subtracting from total production.
The preimage was shifted to the image by a translation 2 units right and 2 units up, so the answer is 
Make an equation:
6x + 12 = 268.26
6x = 256.26
X = $42.71
The monthly payment is $42.71
Answer:
c = 13
m∡A = 60°
m∡B = 30°
Step-by-step explanation:
This is a 5-12-13 triangle. However, to make sure, I will put the steps.
Allow for each sides to be denoted as a-b-c, in which c is the hypotenuse (longest side). Set the equation:
a² + b² = c²
Plug in the corresponding numbers to the corresponding variables:
5² + 12² = c²
Simplify. First, solve the exponents, and then add:
(5²) = 5 * 5 = 25
(12²) = 12 * 12 = 144
25 + 144 = c²
c² = 169
Note the equal sign, what you do to one side, you do to the other. Isolate the variable, c, by rooting both sides:
√c² = √169
c = √169 = √(13 * 13) = 13
c = 13
13 is your answer for c.
Note the measurements of the angles. We know that this is a 30-60-90 triangle, and so it will be easy to figure it out. Note that the corresponding angles will depend on that of the opposite side's measurement lengths. The hypotenuse will always be on the opposite side of the largest angle (as given), as c, the longest side, is opposite of ∡C, which is the largest angle (90°). Based on this information, it means that ∡A would be 60° (as it is opposite of the middle number, 12), and ∡B would be 30° (opposite of the smallest number, 5).
