Answer:
The number that belongs <em>in</em> the green box is equal to 909.
General Formulas and Concepts:
<u>Algebra I</u>
Equality Properties
- Multiplication Property of Equality
- Division Property of Equality
- Addition Property of Equality
- Subtraction Property of Equality
<u>Trigonometry</u>
[<em>Right Triangles Only</em>] Pythagorean Theorem:
- a is a leg
- b is another leg
- c is the hypotenuse
Step-by-step explanation:
<u>Step 1: Define</u>
<em>Identify given variables</em>.
<em>a</em> = 30
<em>b</em> = 3
<em>c</em> = <em>x</em>
<em />
<u>Step 2: Find </u><u><em>x</em></u>
Let's solve for the <em>general</em> equation that allows us to find the hypotenuse:
- [Pythagorean Theorem] Square root both sides [Equality Property]:
Now that we have the <em>formula</em> to solve for the hypotenuse, let's figure out what <em>x</em> is equal to:
- [Equation] <em>Substitute</em> in variables:
- <em>Evaluate</em>:
∴ the hypotenuse length <em>x</em> is equal to √909 and the number <em>under</em> the square root, our answer, is equal to 909.
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Learn more about Trigonometry: brainly.com/question/27707750
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Topic: Trigonometry
We are asked to determine the correlation factor "r" of the given table. To do that we will first label the column for "Quality" as "x" and the column for "Easiness" as "y". Like this:
Now, we create another column with the product of "x" and "y". Like this:
Now, we will add another column with the squares of the values of "x". Like this:
Now, we add another column with the squares of the values of "y":
Now, we sum the values on each of the columns:
Now, to get the correlation factor we use the following formula:
Where:
Now we substitute the values, we get:
Solving the operations:
Therefore, the correlation factor is 0.858. If the correlation factor approaches the values of +1, this means that there is a strong linear correlation between the variables "x" and "y" and this correlation tends to be with a positive slope.
(B)
Step-by-step explanation:
Rewrite the equations into their standard forms. The first one can be rewritten as
and the 2nd can be rewritten as
Solving this system either by substitution or elimination, we get
If you add x + y, you'll get a negative number.
Step 1: 6x - 2x - 5 = -6 + 21
Step 2: 6x - 2x - 5 = 15
Step 3: 4x - 5 = 15
The next step would be to add 5 to both sides of the equation.
so Step 3: 4x - 5 = 15 .......add 5 to both sides would make
Step 4: 4x = 20
So after the next step you would have 4x = 20
Hope this helps! :)
Answer:
x = 0 and x = 1
Step-by-step explanation:
From the table of values
f(x) = g(x) = 1 when x = 0 , and
f(x) = g(x) = 0.25 when x = 1
The solution to f(x) = g(x) are x = 0 and x = 1
