Answer:
5 miles
Step-by-step explanation:
distance = speed · time
Tom's distance = (50 mi/h)·(2.5 h) = 125 mi
Albert's distance = (65 mi/h)·(2 h) = 130 mi
Albert drove 130 -125 = 5 miles farther than Tom.
1. Understand what multi-variable equations are.
Two or more linear equations that are grouped together are called a system. That means that a system of linear equations is when two or more linear equations are being solved at the same time.
[1] For example:
• 8x - 3y = -3
• 5x - 2y = -1
These are two linear equations that you must solve at the same time, meaning you must use both equations to solve both equations.
2. Know that you are trying to figure out the values of the variables, or unknowns.
The answer to the linear equations problem is an ordered pair of numbers that make both of the equations true.
In the case of our example, you are trying to find out what numbers ‘x’ and ‘y’ represent that will make both of the equations true.
• In the case of this example, x = -3 and y = -7. Plug them in. 8(-3) - 3(-7) = -3. This is TRUE. 5(-3) -2(-7) = -1. This is also TRUE.
3. Know what a numerical coefficient is.
The numerical coefficient is simply the number that comes before a variable.[2] You will use these numerical coefficients when using the elimination method. In our example equations, the numerical coefficients are:
• 8 and 3 for the first equation; 5 and 2 for the second equation.
4. Understand the difference between solving with elimination and solving with substitution.
When you use elimination to solve a multivariable linear equation, you get rid of one of the variables you are working with (such as ‘x’) so that you can solve the other variable (‘y’). Once you find ‘y’, you can plug it into the equation and solve for ‘x’ (don’t worry, this will be covered in detail in Method 2).
• Substitution, on the other hand, is where you begin working with only one equation so that you can again solve for one variable. Once you solve one equation, you can plug in your findings to the other equation, effectively making one large equation out of your two smaller ones. Again, don’t worry—this will be covered in detail in Method 3.
5. Understand that there can be linear equations that have three or more variables.
Solving for three variables can actually be done in the same way that equations with two variables are solved. You can use elimination and substitution, they will just take a little longer than solving for two, but are the same process.
Answer:
-3x^2 - 5y^2 = 36
Step-by-step explanation:
x^2+y^2=r^2
Answer:
R1 - given
R2 - subtraction property of equality
R3 - distribution
S4 - 9x = 61
R5 - division prop. of equality
Step-by-step explanation:
hope this helps :)
The surface area of the figure is 96 + 64π ⇒ 1st answer
Step-by-step explanation:
* Lats revise how to find the surface area of the cylinder
- The surface area = lateral area + 2 × area of one base
- The lateral area = perimeter of the base × its height
* Lets solve the problem
- The figure is have cylinder
- Its diameter = 8 cm
∴ Its radius = 8 ÷ 2 = 4 cm
- Its height = 12 cm
∵ The perimeter of the semi-circle = πr
∴ The perimeter of the base = 4π cm
∵ The area of semi-circle = 1/2 πr²
∴ The area of the base = 1/2 × π × 4² = 8π cm²
* Now lets find the surface area of the half-cylinder
- SA = lateral area + 2 × area of one base + the rectangular face
∵ LA = perimeter of base × its height
∴ LA = 4π × 12 = 48π cm²
∵ The dimensions of the rectangular face are the diameter and the
height of the cylinder
∴ The area of the rectangular face = 8 × 12 = 96 cm²
∵ The area of the two bases = 2 × 8π = 16π cm²
∴ SA = 48π + 16π + 96 = 64π + 96 cm²
* The surface area of the figure is 96 + 64π
