Find the surface area of the prism. Can you show the work please?
1 answer:
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Answer:
Total area equation = tex]w(w+6)=91[/tex]
b/2 = 3
Dimensions of the patio: width = 7 feet, length = 13 feet
Step-by-step explanation:
The area of a rectangle is given the formula:
where
is the width
is the length
We know from our problem that the area of the patio is 91 square feet, so . We also know that the length is 6 feet longer then the width, so
.
Replacing values in our area equation
Expanding the left side:
Remember that to complete the square we need to add half the coefficient of the linear term squared. The lineal term is , so its coefficient is 6. Now, half its coefficient or
. Finally,
.
To complete the square we need to add 9 to both sides of the equation:
Notice that the left side is a perfect square trinomial (both and 9 are perfect squares), so we can express it as:
Now that we completed the square, we can solve our equation
- Take square root to both sides
- Subtract 3 from both results
Since length cannot be negative, is the solution of our equation.
We now know that the width of our rectangular patio is 7 feet, so we can find its length:
We can conclude that half the coefficient of the width is , the width of the patio is 7 feet, and its length is 13 feet.
Answer:
0.0083 = 0.83% probability that the boys will stand in alphabetical order from left to right in the picture
Step-by-step explanation:
Probability:
A probability is given by the number of desired outcomes divided by the number of total outcomes.
Arrangments of x elements:
The total number of arrangments of x elements is given by:
Desired outcomes:
Standing in alphabetical order, so only 1 possible outcome, which means that
Total outcomes:
Arrangments of 5 people, so
Probability:
0.0083 = 0.83% probability that the boys will stand in alphabetical order from left to right in the picture