Answer:
x ≈ 53°
General Formulas and Concepts:
<u>Pre-Algebra</u>
Order of Operations: BPEMDAS
- Brackets
- Parenthesis
- Exponents
- Multiplication
- Division
- Addition
- Subtraction
Equality Properties
<u>Trigonometry</u>
- [Right Triangles Only] SOHCAHTOA
- [Right Triangles Only] tan∅ = opposite over adjacent
Step-by-step explanation:
<u>Step 1: Identify</u>
Opposite Leg of <em>x</em> = 12
Adjacent Leg of <em>x</em> = 15
<u>Step 2: Solve for </u><em><u>x</u></em>
- Substitute [tangent]: sinx° = 12/15
- Trig inverse: x° = sin⁻¹(12/15)
- Evaluate: x = 53.1301°
- Round: x ≈ 53°
We can start this problem by finding out what the lowest consecutive number's value is (x). Since consecutive numbers are numbers that are 1 apart from each other, the sum of 9 consecutive numbers would look like
x + (x+1) + (x+2) + (x+3) + (x+4) + (x+5) + (x+6) + (x+7) + (x+8)
Since we know that they equal 153,
x + (x+1) + (x+2) + (x+3) + (x+4) + (x+5) + (x+6) + (x+7) + (x+8) = 153
Now we combine like terms
9x + 36 = 153
Simplify
9x = 117
x = 13
Now, we need to find what the 5th consecutive number is equal to. The fifth consecutive number is (x+4), so 13 + 4 is 17, meaning that the 5th of 9 consecutive numbers that add up to 153 is 17.
Answer:
or 6
gallons of gas.
Step-by-step explanation:
First, you have to convert both of your mixed numbers into a improper fractions.
2
= 9/4
4
= 26/6
Second, find the greatest common multiple of the denominators of both. In this case, it would be 12.
Then find the number that the first improper fraction's denominator would be multiplied by to get the GCM. Multiply both the nominator and the denominator by that number.
<em>4 would need to be multiplied by 3 to get 12. So we multiply 9/4 by 3/3. We would get 27/12.</em>
<em />
Repeat that for the second fraction's denominator.
<em>6 would need to be multiplied by 2 to get 12. So we multiply 26/6 by 2/2. We would get 52/12. </em>
<em />
Then add both fractions together.
![=\frac{79}{12}](https://tex.z-dn.net/?f=%3D%5Cfrac%7B79%7D%7B12%7D)
If you need to, simplify.
![\frac{79}{12} = 6\frac{7}{12}](https://tex.z-dn.net/?f=%5Cfrac%7B79%7D%7B12%7D%20%3D%206%5Cfrac%7B7%7D%7B12%7D)
Hope that helped!
Answer:
62.8318530718 inches^3
Step-by-step explanation:
The volume of a cylinder can be found using:
V=πr^2h
Substitute 2 in for r (radius), and 5 in for h (height)
V=π2^2*5
V=π4*5
V=π20
V=62.8318530718
62.8318530718 inches^3
Hope this helps! :)
3 x 2 + 2x -5 = x or 1x. or 3x 2 + 2x - 5 = 5x + 3.
-4 + 7x 2 = -2 + 7x