Answer:
Step-by-step explanation:
First we need to find their rate of speed.
r = d / t
For ant,
Convert millimeters to inches.
1 inch = 25.4 mm
18 mm = 0.7 inch
r = 0.7 / 5
r = 0.14 inches per second
For beetle,
r = 8 / 3
r = 2.7 inches per second
From the rates, you can tell that the beetle crosses the Garden first.
To know how long it takes for the ant to cross is by dividing the length by the rate.
1 yard = 36 inches
13 yards = 468 inches
468 ÷ 0.14 = 668.5 ≈ 669 seconds
In terms of minutes:
11 minutes and 15 seconds
The ant would cross the garden in 11 minutes and 15 seconds (or 669 seconds <em>up to you</em>).
Answer:
2:10:12
Step-by-step explanation:
I multiplied all of the numbers by 2
It doesn't matter what number you multiply the numbers by, as long as you multiply all 3 of them.
Answer:
D. ![y\geq 3x - 2\\x + 2y\leq 4](https://tex.z-dn.net/?f=y%5Cgeq%203x%20-%202%5C%5Cx%20%2B%202y%5Cleq%204)
Step-by-step explanation:
From the graph, we can conclude that,
1. The two lines are continuous lines and not broken lines. So, the inequality sign should be either
.
2. The points on the lines of the shaded region are also included in the solution.
The only option that matches with the above conditions is option D. So, option D is the correct answer.
Let us verify it.
Now, let us consider a point that is inside the shaded region and also on any one line. Let us take
.
Plug in 0 for x and 2 for y in each of the options and check which inequality holds true.
Option A:
![y < 3x-2\\ 2 < 3(0)-2\\2](https://tex.z-dn.net/?f=y%20%3C%203x-2%5C%5C%202%20%3C%203%280%29-2%5C%5C2%3C-2%5C%5C%5C%5Cx%20%2B%202y%20%5Cgeq%20%204%5C%5C0%2B2%282%29%5Cgeq%204%5C%5C4%5Cgeq%204)
So, inequality 1 is wrong as -2 is less than 2.
Option B:
![y < 3x - 2\\ 24\\4>4](https://tex.z-dn.net/?f=y%20%3C%203x%20-%202%5C%5C%202%3C3%280%29-2%5C%5C2%3C-2%5C%5C%5C%5Cx%20%2B%202y%20%3E%204%5C%5C0%2B2%282%29%3E4%5C%5C4%3E4)
Both the inequalities are wrong.
Option C:
![y > 3x - 2\\2>3(0)-2\\2>-2\\\\x + 2y < 4\\0+2(2)](https://tex.z-dn.net/?f=y%20%3E%203x%20-%202%5C%5C2%3E3%280%29-2%5C%5C2%3E-2%5C%5C%5C%5Cx%20%2B%202y%20%3C%204%5C%5C0%2B2%282%29%3C4%5C%5C4%3C4)
Inequality 2 is wrong.
Option D:
![y\geq 3x - 2\\2\geq 3(0)-2\\2\geq -2\\\\x + 2y\leq 4\\0+2(2)\leq 4\\4\leq 4](https://tex.z-dn.net/?f=y%5Cgeq%203x%20-%202%5C%5C2%5Cgeq%203%280%29-2%5C%5C2%5Cgeq%20-2%5C%5C%5C%5Cx%20%2B%202y%5Cleq%204%5C%5C0%2B2%282%29%5Cleq%204%5C%5C4%5Cleq%204)
Here, both inequalities are correct.
So, option D is the correct answer.
Answer:
C 90
Step-by-step explanation: