Let's use J for James's age and A for Austin's age. The equations are:
J = A - 4
3J + A² = 28
Just plug (A - 4) in the place of J in the second equation. This gives you:
3(A - 4) + A² = 28
-->
A² + 3A - 12 = 28
-->
A² + 3A - 40 = 0
-->
(A - 5)(A + 8) = 0
-->
A = 5 or -8
-8 is nonsense, so Austin is 5 years old. Therefore, James is 1 year old.
The translation is (x-4, y+15)
This means you would subtract 4 from the X coordinate and add 15 to the y coordinate.
The original coordinates is (9,-8)
The first number is X and the 2nd number is Y.
9-4 = 5
-8+15 = 7
The new location would be (5,7)
The answer is B.
We will use substitution to solve this system of linear equations, as the first equation has x and y with no coefficients, which makes it easier to find one in terms of the other. We can then substitute that value in the other equation and find the values of x and y.
x = y + 5 ---> equation 1
3x + 2y = 5 ---> equation 2
From equation 1, we get the value of x as y + 5. Using the substitution method, we can find the value of y by substituting (y+5) for x in the 2nd equation.
3(y+5) + 2y = 5
3y + 15 + 2y = 5
5y = 5 - 15
5y = -10
y = -2
Subsituting this value of y in (y+5), we can find x.
x = y + 5
x = -2 + 5
x = 3
Therefore, x = 3 and y = -2.
I will also solve this using elimination method.
Let us multiply equation 1 by 2, so that we get 2y in both equations.
2x = 2y + 10
3x + 2y = 5
Let us add both the equations.
2x + 3x + 2y = 5 + 2y + 10
5x = 15 + 2y - 2y
5x = 15
x = 3
Substituting this value of x in equation 1, we get
x = y + 5
3 = y + 5
y = 3 - 5
y = -2
Therefore, x = 3 and y = -2.
Because you went from 41.5 to 47.6 when the granite was placed in the graduated cylinder, using displacement:
47.6 - 41.5 = 6.1
I don't know about the cubic centimeters part, I don't know for sure if mL and cubic cm are the same, sorry. :(
Write an equation to find the number of each type of ticket they should sell.Let "x" be # of adult tickets; Let "y" be # of student tickets: Value Equation: 5x+3y=450-------------------------- b. Graph your equation.y = (-5/3)x+150
c. Use your graph to find two different combinations of tickets sold.I'll leave that to you.
