On Wednesdays at Tara's Taquería four tacos are the same price as three
1 answer:
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Answer:
(2,6)
Step-by-step explanation:
<u><em>The options of the questions are</em></u>
(0,1) (1,3) (2,6) (3,27)
and the given function is
we know that
If a ordered pair lie on the graph of the given equation, then the ordered pair must satisfy the given equation
<u><em>Verify each ordered pair</em></u>
case 1) (0,1)
substitute the value of x and the value of y in the linear equation and then compare the results
----> is true
so
The ordered pair lie on the graph of the given equation
case 2) (1,3)
substitute the value of x and the value of y in the linear equation and then compare the results
----> is true
so
The ordered pair lie on the graph of the given equation
case 3) (2,6)
substitute the value of x and the value of y in the linear equation and then compare the results
----> is not true
so
The ordered pair not lie on the graph of the given equation
case 4) (3,27)
substitute the value of x and the value of y in the linear equation and then compare the results
----> is true
so
The ordered pair lie on the graph of the given equation
We have a rectangle with a diagonal included. That means we have to use Pythagorean's Theorem to find the missing dimensions. We start with the width as w. The length is 31 more than twice the width, so the length is 2w+31. The hypotenuse (diagonal) is 2 more than the length, so the diagonal measures 2w+33. In a right triangle, the hypotenuse is always the longest side, so we set up Pythagorean's Theorem using the bolded values as such: . Distributing by multiplying we simplify to
. We need to solve for w. Once we do that we can use that value to find the length. What's nice is that the 4w^2 terms cancel each other out. So when we combine like terms and get them all on one side of the equals sign to factor we have
. The 2 numbers that add up to -8 and multiply to -128 are 16 and -8. So the width is either 16 inches or the width is -8 inches. The 2 things in math that will never EVER be negative are time and distance/length. So -8 is out. The width is 16 inches. That means that the length is 2(16)+31, which is 63 inches. There you go!