Answer:
Let's define the variables:
M = mother's age
D = daughter's age.
"a mother is twice as old as her daughter"
This can be written as:
M = 2*D
"5 years from now she will be thrice as old as her daughter"
(M + 5) = 3*D
We want to know how old is the mother five years from now.
First, our equations are:
M = 2*D
(M + 5) = 3*D
First, we need to isolate one of the variables in one of the equations, because for the solution we want the mother's age, we should isolate the daughter's age.
Let's isolate D in the first equation:
M/2 = D
Now we can replace this in the other equation:
Now we can replace this on the other equation:
(M + 5) = 3*(M/2)
M + 5 - (3/2)*M = 0
-(1/2)*M + 5 = 0
5 = (1/2)*M
2*5 = M = 10
So the mother is 10 years old (this hasn't a lot of sense, maybe there is a wrong number on the question)
and 5 years from now, the mother will be:
10 + 5 = 15 years old.
The standard form equation of the line connecting the two points is 
Linear equation in a standard form is given as 
where,
A, B, and C are constants or numbers
x and y are the variables.
To solve this problem, the following steps would be taken:
Step 1: Find the slope of the line connecting points (-3,4) and (2,-6)

where,

Substitute

Step 2: Find the y-intercept (b) of the line by substituting
and
into
(slope-intercept form)

Step 3: Write the equation of the line in slope-intercept form by substituting
and
into 

Step 4: Rewrite the equation in standard form 

Add
to both sides

The standard form equation of the points (-3,4) and (2,-6) is 
Learn more about standard form of two points of a linear equation here:
brainly.com/question/18446164
Answer: the total length of the string is 9 meters.
Step-by-step explanation:
The total number of strings that Emily measured is 3.
The length of the first piece of string measures 642 cm.
The length of the second piece of string measures 124 cm.
The length of the third piece of string measures 134 cm.
Therefore, the total length of the 3 pieces of string would be
642 + 124 + 134 = 900 cm.
100 cm = 1 m,
Converting 900 centimeters to meters, it becomes
900/1100 = 9 meters
Answer: The first blank space is 45 and the one at the bottom is 10