I got the third one: 1395
-MC
1.Use transformations to solve the equations:
5{6+k}=3k
19-3m+ 5+7m <0
2.Find the circumference of a circle with diameter 31 m.
3.What is 186% of 750?
Thanks!!
-MC
-MC
circumference = pi(d)
= 31 pi or appr. 97.39 m
As I said before, I don't know what they mean by "use transformations" to solve
5{6+k} = 3k
I would just ...
30 + 5k = 3k
2k = -30
k = -15
and for
19-3m+ 5+7m <0
4m < -24
m < -6
-MC
Could you have gone wrong somewhere? That's the only one.
-MC
I would just ...
30 + 5k = 3k
2k = -30
k = -15
----------------
This is correct. If the teacher's answer is different there is probably a typo.
5(6) + 5(k) = 3k
30 + 5k = 3k
Next, we want to isolate the variable k on one side of the equation. To do this, we can subtract 3k from both sides:
30 + 5k - 3k = 3k - 3k
30 + 2k = 0
Now, we can isolate k by subtracting 30 from both sides:
30 + 2k - 30 = 0 - 30
2k = -30
Finally, we can solve for k by dividing both sides by 2:
2k/2 = -30/2
k = -15
Therefore, the solution to the equation 5(6+k) = 3k is k = -15.
For the second equation, 19 - 3m + 5 + 7m < 0, we can follow the same process:
Combine like terms on the left side:
(19 + 5) - 3m + 7m < 0
24 + 4m < 0
Subtract 24 from both sides to isolate the variable m:
24 + 4m - 24 < 0 - 24
4m < -24
Divide both sides by 4:
(4m)/4 < (-24)/4
m < -6
Therefore, the solution to the inequality 19 - 3m + 5 + 7m < 0 is m < -6.
2. The circumference of a circle can be found using the formula C = πd, where π is a mathematical constant (approximately 3.14159) and d is the diameter of the circle. Given that the diameter is 31 m, we can substitute this value into the formula:
C = πd
C = π(31)
To find the circumference, multiply 31 by π:
C = 31Ï€
To get a specific numerical value, you can use an approximate value for π, such as 3.14159:
C ≈ 31 × 3.14159
C ≈ 97.40949
Therefore, the circumference of a circle with a diameter of 31 m is approximately 97.40949 m.
3. To find out what 186% of 750 is, multiply 750 by 186% (which is equivalent to 1.86). You can convert a percentage to a decimal by dividing the percentage by 100:
186% = 186/100 = 1.86
Next, multiply 750 by 1.86:
186% of 750 = 750 × 1.86
Calculating this, we get:
186% of 750 = 1395
Therefore, 186% of 750 is equal to 1395.