These data represent the population of a certain city.
Year Population(in thousands)
1950 18
1960 23
1970 29
1980 32
1990 38
2000 42
Use the line graph to predict the population in the year 2010
I recommend graphing the points, draw a best fit line, then project it to 2010.
I need help with this problem:
5p-2q=1
4p+5q=47
To solve the system of equations 5p - 2q = 1 and 4p + 5q = 47, you can use the method of substitution.
Step 1: Solve one of the equations for one variable in terms of the other variable.
Let's solve the first equation, 5p - 2q = 1, for p:
5p = 2q + 1
p = (2q + 1)/5
Step 2: Substitute the expression for p obtained in Step 1 into the other equation.
Substitute (2q + 1)/5 for p in the second equation, 4p + 5q = 47:
4((2q + 1)/5) + 5q = 47
Step 3: Solve the resulting equation for q.
Multiply both sides of the equation by 5 to eliminate the fraction:
4(2q + 1) + 5q = 47
8q + 4 + 5q = 47
13q + 4 = 47
13q = 43
q = 43/13 = 3.3077 (rounded to four decimal places)
Step 4: Substitute the value of q obtained in Step 3 into the expression for p from Step 1 to find p.
p = (2q + 1)/5
p = (2(3.3077) + 1)/5
p = (6.6154 + 1)/5
p = 7.6154/5
p = 1.5231 (rounded to four decimal places)
Therefore, solving the system of equations 5p - 2q = 1 and 4p + 5q = 47 gives the values p = 1.5231 and q = 3.3077.
To solve the system of equations 5p - 2q = 1 and 4p + 5q = 47, you can use the method of substitution or elimination.
Let's solve it using the method of substitution:
1. Solve one equation for one variable in terms of the other variable. Let's solve the first equation, 5p - 2q = 1, for p:
5p = 2q + 1
Divide both sides by 5:
p = (2q + 1)/5
2. Substitute the expression you found for one variable into the other equation. Substitute p = (2q + 1)/5 into the second equation, 4p + 5q = 47:
4((2q + 1)/5) + 5q = 47
Simplify:
(8q + 4)/5 + 5q = 47
Multiply both sides by 5 to get rid of the denominator:
8q + 4 + 25q = 235
Combine like terms:
33q + 4 = 235
Subtract 4 from both sides:
33q = 231
Divide both sides by 33:
q = 7
3. Substitute the value of q into either of the original equations to solve for p. Let's use the first equation:
5p - 2(7) = 1
5p - 14 = 1
Add 14 to both sides:
5p = 15
Divide both sides by 5:
p = 3
Therefore, the solution to the system of equations 5p - 2q = 1 and 4p + 5q = 47 is p = 3 and q = 7.