Here the answer is 21 as the LCM of 14 and 6 is 42 and 42 is exactly divisible by 21.
Answer:
x=4
Step-by-step explanation:
(2x+3)^2=121
2x+3=square root of 121
2x+3=11
2x=11-3
2x=8
x=4
(in a square all sides are equal therefore area =length ×width where length and width=2x+3)
All of them use Tons, pounds or ounces so you need the conversion factors which are these.
1 Ton = 2,000 lbs
1 lb = 16 oz
2.) 6T = 12,000 lbs (6 x 2,000)
3.) 18 lbs = 288 oz (16 x 18)
4.) 3,200 oz = 200 lbs (3,200/16)
5.) 12 T = 24,000 lbs(12x2,000)
6.) 9 lbs = 144 oz (16x9)
7.) 7 lbs = 112 oz(16x7)
8.) 100 lbs = 1,600 oz (16x100)
9.) 60,000 lbs = 30 T (60,000/2,000)
10.) 40 oz < 4 lbs (4x16)
11.) 80 oz = 5 lbs (5x16)
12.) 5,000 lbs < 5 T (5x2,000)
13.) 18,000 lbs = 9 T (9x2,000)
14.) 25 lbs > 350 oz (250x16)
15.) 27 oz < 2 lbs (16x2)
16.) 3 T = 6,000 lbs (3x2,000)
17.) First you need to know how many ounces 22 pounds is, so you multiply 16 by 22 to get 352 oz. Then subtract by 112 oz, she can add 240 more oz or 15 more lbs.
Answer:
Step-by-step explanation:
The diagonals of the parallelogram are A(-5, -1), C(-1, 5) and B(-9, 6), D(3, -2).
Slope of diagonal AC = (5 - (-1)) / (-1 - (-5)) = (5 + 1) / (-1 + 5) = 6 / 4 = 3/2
Slope of diagonal BD = (-2 - 6) / (3 - (-9)) = -8 / (3 + 9) = -8 / 12 = -2/3
For the parallelogram to be a rhombus, the intersection of the diagonals are perpendicular.
i.e. the product of the two slopes equals to -1.
Slope AC x slope BD = 3/2 x -2/3 = -1.
Therefore, the parallelogram is a rhombus.
There are no algebraic methods for finding solutions to a general mix of exponential and polynomial terms. A graphing calculator can be helpful.
This equation has 3 real solutions, approximately ...
x ∈ {-0.802246431546, 1.51677641228, 7.17475582739}
_____
In the folder "iteration for solutions" is an equation for Newton's method iteration, essentially, ...
g(x) = x -f(x)/f'(x)
where f(x) is defined as shown in the picture.
Many graphing calculators can compute a numerical derivative, so you can essentially write the formula in this form without having to do the derivative-taking yourself. This calculator is nicely interactive, so the iteration result is produced at the same time the argument for g(x) is entered. Essentially, you write the answer by copying the answer using the 4-digit zero-crossing values shown on the graph as the iteration starting point.