Ok here are a few more
1. collect like terms
12r+6s-3r-9s
A:9r-3s
2. translate to an algebraic expression
The product of 46% and some number
A: y=0.46x
3. In 1993, the life expectancy of males in a certain country was 61.3 yrs. In 1999, it was 64.7yrs. Let E represent the life expectancy in year t and let t represent the number of years since 1993.
The linear function E(t) that fits the data is
A: E(t)=-0.03t+61.3
Use the function to predict the life expectancy of males in 2003.
A: E(10)=61.6
4. solve by substitution
3x+2y=12
x=52-6y
A: (-2,9)
5. solve by elimination
2r-7s=-31
7r+2s=24
A:(2,5)
They are all correct except #3
For #4 and #5 it is very simple to try your answer in both equations.
Why did you not do that?
for #3, you should define t as the number of years since 1993
I got a "slope" of (64.7-61.3)/6 = .566667
so E(t) = .566667t + 61.3
check for the second point
LS = 64.7
RS = .566667(6) + 61.3 = 64.7
then E(10) = .566667(10) + 61.3 = 66.966
or 67.0
You should have realized that your answer of 61.6 for 2003 could not be right, since it was less than the 1999 figure.
Thank you very much.
1. To collect like terms, combine the terms with the same variable. In the given expression 12r + 6s - 3r - 9s, you can add the coefficients of r and s separately.
Combine the terms with r: 12r - 3r = 9r.
Combine the terms with s: 6s - 9s = -3s.
Therefore, the simplified expression is 9r - 3s.
2. To translate a phrase into an algebraic expression, you need to identify the unknown quantity (represented as a variable) and the operation involved. In this case, the unknown quantity is "some number" and the operation is "the product of."
The phrase "The product of 46% and some number" can be translated into the algebraic expression y = 0.46x, where y represents the product and x represents the unknown number.
3. To find the linear function E(t) that fits the given data, you need to determine the equation of a line using two points. The two points are (0, 61.3) and (6, 64.7) corresponding to (year t, life expectancy E).
Using the formula for the equation of a line, y = mx + b, where m is the slope and b is the y-intercept, you can calculate the equation.
First, find the slope:
m = (64.7 - 61.3) / (6 - 0) = 0.6 / 6 = 0.1.
Next, substitute one of the points into the equation and solve for the y-intercept (b):
61.3 = 0.1(0) + b
61.3 = b
Therefore, the linear function E(t) that fits the data is E(t) = 0.1t + 61.3.
To predict the life expectancy in 2003:
Substitute t = 10 into the equation: E(10) = 0.1(10) + 61.3 = 61.3 + 1 = 62.3.
Thus, the predicted life expectancy of males in 2003 is E(10) = 62.3.
4. To solve a system of equations by substitution, you substitute one equation into the other equation to eliminate one variable.
In this case, we'll substitute x = 52 - 6y into the equation 3x + 2y = 12.
Substitute x in terms of y:
3(52 - 6y) + 2y = 12
156 - 18y + 2y = 12
-16y = -144
y = 9
Now substitute the value of y back into x = 52 - 6y:
x = 52 - 6(9)
x = 52 - 54
x = -2
Thus, the solution to the system of equations is x = -2 and y = 9, represented as (-2, 9).
5. To solve a system of equations by elimination, you need to eliminate one variable by manipulating the equations.
In the given system:
2r - 7s = -31
7r + 2s = 24
Multiply the first equation by 7 and the second equation by 2 to make the coefficients of s cancel each other out when added.
14r - 49s = -217
14r + 4s = 48
Now, subtract the second equation from the first equation:
(14r - 49s) - (14r + 4s) = (-217) - 48
14r - 49s - 14r - 4s = -217 - 48
-53s = -265
s = (-265) / (-53) = 5
Substitute the value of s back into one of the original equations, such as 2r - 7s = -31:
2r - 7(5) = -31
2r - 35 = -31
2r = 4
r = 4 / 2 = 2
Therefore, the solution to the system of equations is r = 2 and s = 5, represented as (2, 5).