Answer:
· Use properties of equality together to isolate variables and solve algebraic equations.
· Use the properties of equality and the distributive property to solve equations containing parentheses, fractions, and/or decimals.
Introduction
There are some equations that you can solve in your head quickly. For example – what is the value of y in the equation 2y = 6? Chances are you didn’t need to get out a pencil and paper to calculate that y = 3. You only needed to do one thing to get the answer, divide 6 by 2.
Other equations are more complicated. Solving without writing anything down is difficult! That’s because this equation contains not just a variable but also fractions and terms inside parentheses. This is a multi-step equation, one that takes several steps to solve. Although multi-step equations take more time and more operations, they can still be simplified and solved by applying basic algebraic rules.
Using Properties of Equalities
Remember that you can think of an equation as a balance scale, with the goal being to rewrite the equation so that it is easier to solve but still balanced. The addition property of equality and the multiplication property of equality explain how you can keep the scale, or the equation, balanced. Whenever you perform an operation to one side of the equation, if you perform the same exact operation to the other side, you’ll keep both sides of the equation equal.
If the equation is in the form, ax + b = c, where x is the variable, you can solve the equation as before. First “undo” the addition and subtraction, and then “undo” the multiplication and division.
Step-by-step explanation:
Answer:
The top left graph is the correct one.
Step-by-step explanation:
The graph of y = 1/2x - 4 will rise to the right , have a slope of 1/2 and pass through the point (0, -4) on the y-axis.
Since the inequality sign is 'less than or equal to' the line will be continuous and the shading will be below this line.
Answer:
At 1.5 seconds and 2.5 seconds
Step-by-step explanation:
Because this is parabolic motion, the object will reach the height of 68 feet when it's going up AND when it's coming down. In order to find out those times, you set the h on the left side of the equation equal to 68, because h stands for height.
Set that equal to 0 and factor to solve for t:
Using the quadratic formula, we get t = 1.5 and t = 2.5
You would need 27 more dollars because f(x)=7x+2 plug in the 5 in x’s spot and you get 37 and so subtract it from 10 to get 27
