Answer:
Option D. (x + 4)(x + 1)
Step-by-step explanation:
From the question given above, the following data were obtained:
C = (6x + 2) L
D = (3x² + 6x + 9) L
Also, we were told that half of container C is full and one third of container D is full. Thus the volume of liquid in each container can be obtained as follow:
Volume in C = ½C
Volume in C = ½(6x + 2)
Volume in C = (3x + 1) L
Volume in D = ⅓D
Volume in D = ⅓(3x² + 6x + 9)
Volume in D = (x² + 2x + 3) L
Finally, we shall determine the total volume of liquid in the two containers. This can be obtained as follow:
Volume in C = (3x + 1) L
Volume in D = (x² + 2x + 3) L
Total volume =?
Total volume = Volume in C + Volume in D
Total volume = (3x + 1) + (x² + 2x + 3)
= 3x + 1 + x² + 2x + 3
= x² + 5x + 4
Factorise
x² + 5x + 4
x² + x + 4x + 4
x(x + 1) + 4(x + 1)
(x + 4)(x + 1)
Thus, the total volume of liquid in the two containers is (x + 4)(x + 1) L.
original price = $113
MArkup = 45% = 45/100 = 0.45 ( decimal form)
Sell price = 113 (1 + 0.45) = 113 * 1.45 = $163.85
Answer:
The correct answer is t < 60.
Step-by-step explanation:
Lauren wants to keep her cell phone bill below $60 per month.
Lauren's current cellphone plan charges her a fixed price of $30 and per text price for one text is $0.50.
Let Lauren sends t texts in a complete month.
Total money spent on texts in a month is given by $ (0.50 × t)
Therefore Lauren's total spent in a month is given by $ (30 + (0.50 × t)).
But this amount should be under $60 as per as the given problem.
∴ 30 + (0.50 × t) < 60
⇒ (0.50 × t) < 30
⇒ t < 
⇒ t < 60.
So in order to keep her phone monthly bill under $60, Lauren should keep her number of texts below 60.
Answer:
13 inches
Step-by-step explanation:
Let P(t) and P(s) be the perimeters of the equilateral triangle and square respectively. Similarly, t and s be the side lengths of equilateral triangle and square respectively.
According to the first condition :
(Perimeter of an equilateral triangle is 11 inches more than the perimeter of a square)
According to the second condition :
(The side of the triangle is 6 inches longer than the side of the square)
From equations (1) & (2)
3(s + 6) = 4s + 11
3s + 18 = 4s + 11
3s - 4s = 11 - 18
-s = - 7
s = 7 inches
Thus the side of the triangle is 13 inches long.
Answer:
Explanation:
opposite angles in a quadrilateral sum up to 180°
total interior angles in a quadrilateral is 360°
solve for x:
x - 2 + x + 2 = 180°
2x = 180°
x = 90°
solve for each angle:
1st
x + 2
90° + 2 = 92°
2nd
x - 2
90° - 2 = 88°
3rd
x - 10
90° - 10° = 80°
4th
360° - 80° - 88° - 92° = 100°