Answer:
x=6
Step-by-step explanation:
81^x = 27 ^(x+2)
81 = 3^4 and 27 =3^3 so replace 81 and 27 in the equation
3^4^x = 3^3^(x+2)
When we have a power to a power we can multiply the exponents
a ^b^c = a^(b*c)
3^(4x) = 3^(3*(x+2))
Since the bases are the same, the exponents have to be the same
a^b = a^c means b=c
4x = 3(x+2)
Now we can solve for x
Distribute
4x = 3x+6
Subtract 3x from each side
4x-3x = 3x-3x+6
x = 6
Answer:
17
w + 35
Step-by-step explanation:
You get this answer by using PEMDAS.
Answer:
A) 6/71 to attempt to make new friends
Step-by-step explanation:
The probability that she chooses a peanut butter then a chocolate chip cookie is about 6/71 in an attempt to make some new friends!
I hope this helps! Good luck with your assignment/test! <3
- 7v7
All the sides of an equilateral triangle are the same, and all three angles are 60 degrees. If we want the height of the triangle, we can draw a vertical line straight down the center. This will bisect the top angle into two 30 degree angles and form a 90 degree corner at the base. The base will be split into two equal pieces. In this case 14 and 14 (half of 28).
To find the height, we can use a couple methods. First is Pythagorean Theorem which states that a^2 + b^2 = c^2. We know c = 28 and a = 14, so we can solve for the height. b = sqrt(28^2 - 14^2) = sqrt(588).. 588 can be factored into 196 and 3. So we can simplify the radical to 14sqrt(3).
The second way to find the height is to use trigonometry. We can use cos(30) = h/28 and solve for h to get h = 28cos30 or 14sqrt(3).
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The next problem is asking the same thing. The altitude is the height. So use either of the methods above to get 2sqrt(3).
Using the combination formula, it is found that six of these five-ball selections contain exactly five red balls.
The order in which the balls are selected is not important(as balls A, B, C, D and E is the same outcome as balls B, A, C, D and E), hence the <em>combination formula</em> is used to solve this question. If the order was important, then the permutation formula would be used.
<h3>What is the combination formula?</h3>
is the number of different combinations of x objects from a set of n elements, given by:
In this problem, five red balls can be chosen from a set of six, hence the number of selections is the combination of 5 elements from a set of 6, that is calculated from the formula given above:
Hence six of these five-ball selections contain exactly five red balls.
More can be learned about the combination formula at brainly.com/question/25821700
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