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2 years ago

Please help asap no one has been able to solve it :( I need help

Mathematics

1 answer:

Katyanochek1 [597]2 years ago

7 0

Answer:

given
Multiplication property of equality
Multiplicative inverse property
Multiplicative identity property
Addition property of equality
Additive inverse property
Additive identity property

Step-by-step explanation:

You are given the solution to a 2-step linear equation and asked to identify the properties of equality and operations that support the steps of the solution.

<h3>Steps</h3>

5(x -3) = 20 . . . . This is the Given equation we're solving.

(1/5)(5(x -3)) = (1/5)(20) . . . . Both sides are multiplied by 1/5. The Multiplication property of equality says you can do this without changing the value of the variable.

1(x -3) = 4 . . . . (1/5)(5) is replaced by 1. The Multiplicative inverse property tells you the product of a number and its multiplicative inverse is 1.

x -3 = 4 . . . . 1(x -3) is replaced by (x -3). The Multiplicative identity property tells you multiplication by 1 changes nothing. These properties of multiplication are what allow you to remove the factor of 5 from the equation.

Now, we're about to do the same thing with addition: use its properties to remove the unwanted -3.

x -3 +3 = 4 +3 . . . . 3 is added to both sides. The Addition property of equality says you can do this without changing the value of the variable.

x +0 = 7 . . . . -3+3 is replaced by 0. The Additive inverse property tells you the sum of a number and its additive inverse is zero.

x = 7 . . . . x+0 is replaced by x. The Additive identity property tells you addition of 0 changes nothing. These properties of addition are what allow you to remove the added -3 from the equation.

Additional comment

Clearly, for exercises like this, it is essential to know the names of these properties and what they mean. Once you understand cancelling multiplication using multiplicative inverses, and cancelling addition using additive inverses, you are on your way to solving most algebra problems.

You must always keep in mind the properties of equality that tell you the same operation must be performed on both sides of the equal sign.

Understanding these properties can also help you understand the relation between multiplication and division, addition and subtraction. Division is multiplication by the multiplicative inverse; subtraction is addition of the additive inverse.

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4 years ago

Determine whether each table below models a linear, quadratic or exponential function.

Virty [35]

The correct answers are:

The first table is linear.
The second table is exponential.

Explanation:

To see if a set of data is linear, we find the slope. Slope is given by the formula

$m=\frac{y_2-y_1}{x_2-x_1}$ .

We check each pair of points in the first table. The slope between the first two points is:
$m=\frac{1-4}{6-5}=\frac{-3}{1}=-3.$

The slope between the second two points is:
$m=\frac{-2-1}{7-6}=\frac{-3}{1}=-3$

The slope between the third two points is:
$m=\frac{-5--2}{8-7}=\frac{-5+2}{8-7}=\frac{-3}{1}=-3$

Since the slope is the same between any two pairs of points, this is a linear set of data.

Checking each pair of points in the second table, we have:
$m=\frac{1-0}{6-5}=\frac{1}{1}=1$ for the first two points.

For the second pair of points, we have:
$m=\frac{4-1}{7-6}=\frac{3}{1}=3$

Since the slope is not the same between each pair of points, we know the data is not linear.

Next we will check the second table to see if it is quadratic. Since the x-coordinates go up the same number each time, we can check the y-coordinates, specifically looking at the second differences.

For the second differences, we first find the difference between each y-value:
1-0=1
4-1=3
8-4=4

Now we find the difference between each first difference:
3-1=2
4-3=1

Since these second differences are not the same, the data is not quadratic.

From graphing the data in the table, we can see that the data in the second table is exponential.