I really dont get why there are two NQ and 2 CA. can someone explain
1) Find the value of the variable and MN if N is between M and Q. Round to the nearest hundredth if necessary.
MQ = 5m + 1, NQ = 4m, NQ = 12
Select one:
a. m = 4, MN = 5
b. m = 3, MN = 4
c. m = 2, MN = 9
d. m = 3, MN = 16
2) Find the value of the variable and CD if A is between C and D.
CA = 8b, AD = 7b, CA = 56
Select one:
a. b = 3.73, CD = 29.87
b. b = 7, CD = 105
c. b = 8, CD = 120
d. b = 7, CD = 49
NQ = 4 m = 13
so
m = 3
MQ = 5 m + 1 = 15 + 1 = 16
8 b = 56
so b = 7
CD = 8 b + 7 b = 56 + 49 = 105
To solve these problems, we need to use the information given in the question and apply basic algebraic reasoning. Let's break it down step by step:
1) In the first question, we are given the following information:
- MQ = 5m + 1 (equation 1)
- NQ = 4m (equation 2)
- NQ = 12 (equation 3)
We are asked to find the value of the variable "m" and the length of MN.
To find the value of "m," we can equate equations 2 and 3:
4m = 12
Dividing both sides by 4, we get:
m = 3
Now, to find the length of MN, substitute the value of "m" into equation 1:
MQ = 5(3) + 1
MQ = 15 + 1
MQ = 16
Since N is between M and Q, the length of MN is the difference between MQ and NQ:
MN = MQ - NQ
MN = 16 - 12
MN = 4
Therefore, the correct answer is "d. m = 3, MN = 4."
2) In the second question, we are given the following information:
- CA = 8b (equation 1)
- AD = 7b (equation 2)
- CA = 56 (equation 3)
We are asked to find the value of the variable "b" and the length of CD.
To find the value of "b," we can equate equations 1 and 3:
8b = 56
Dividing both sides by 8, we get:
b = 7
Now, to find the length of CD, substitute the value of "b" into equation 2:
AD = 7(7)
AD = 49
Since A is between C and D, the length of CD is the difference between CA and AD:
CD = CA - AD
CD = 56 - 49
CD = 7
Therefore, the correct answer is "d. b = 7, CD = 7."