12 x 250 m^2 * 1 ft / .3048 m * 1 ft / .3048 m * 1 gal / 200 ft2 = 161.45 gal = ~~ 162 gallons needed
6 (y^2 - 1/6 y - 15/6)
6 ( y - 1 2/3) (y +1 1/2 ) <========= you can finish
the smallest possible value for k must be ____ degrees.
Hello Julia!
\(cos(k)=-\frac{\sqrt{3}}{2}\\ arccos(-\frac{\sqrt{3}}{2})=k\in\{(150+n\cdot 360)deg,(210+n\cdot 360)deg\}\)
\(\{510deg,570deg\} \) \(\subset \{k\) | 450deg < k < 630deg\(\}\)
The smallest possible value for k must be: k = 510 degrees.
!
(1, 2, 3, 4, 5, 10, 11, 12, 13, 14, 15, 20, 21, 22, 23, 24, 25, 30, 31, 32, 33, 34, 35, 40, 41, 42, 43, 44, 45, 50, 51, 52, 53, 54, 55) ==2,530 in base 6
Five sevenths of what amount is equal to 20?
Hello Guest!
\(\frac{5}{7}\cdot x=20\ |\ \cdot \frac{7}{5}\\ x=20\cdot \frac{7}{5}\\ \color{blue}x=28\)
Five sevenths of 28 amount is equal to 20.
Thank you so much!
Which of the following ordered pairs must be part of the original function f(x) ?
Hello Julia,
the ordered pair a) (-5,0) is part of the original function f(x) = x+5.
PV ==769.59 / [1 + 0.073/4]^(2*4) * [1 + 0.08/4]^(3*4)]
PV ==769.59 / 1.4656741 ==$525.08 - original principal 5 years ago.
By what percent does the length of the arc increase?
Hello proyaop!
If the angle of the arc increases by 20% and the radius of the circle increases by 25%, the arc will increase by 1.20 * 1.25 = 1.50. So the arc will be 50% larger.
nvm Thanks for the reminder melody I am new, also i solved it so yea
Tough question!!!
Hint: RQ = TQ
Hint: AM = BM
\(2x(x + 10) = -50\)
\(2x^2+20x=-50\)
\(2x^2+20x+50=-50+50\)
\(2x^2+20x+50=0\)
\(x_{1,\:2}=\frac{-20\pm \sqrt{20^2-4\cdot \:2\cdot \:50}}{2\cdot \:2}\)
\(x_{1,\:2}=\frac{-20\pm \sqrt{0}}{2\cdot \:2}\)
\(x=\frac{-20}{2\cdot \:2}\)
\(x=-5\)
so the value is -5
so -5!
hope this helps!,
XxmathguyxX
an example.
if x is 2,
\(7x-2=12\) so 13 for the large one
\(3x+5=11\) so 9 for the small one
\(13-9=4\)
\(2a+b=4\)
either a is 2 and b is 0 or a is 1 and b is 2, so i guess 2 or 3!
Hope this helps!
uh..... what is 32.532.5? i am assuming you mean 32.5 and 4.23.....
the answer is 13.06(after rounding)
adding onto geno, i'm going to explain the difference
negative number raised without parenthesis: you will calculate the expression WITHOUT including the negative (for example, if it was -5^4, do 5^4 first before adding the negative) and then add the negative sign to your answer. so, you would do 5*5*5*5*-1 to get -625
negative number raised with parenthesis: you will calculate the expression using -5*-5*-5*-5 to get 625.
apologize that the explanation is kind of messy. feel free to let me know if you have any other questions or concerns :]
5 cos θ = 3
cos θ = 3/5
arccos 3/5 = θ
θ = 53.13 degrees
if the answer should be in radians, you can simply follow my steps but use the radians instead (for calculator use)
Triangle inequalities declares that the sum of two sides of a triangle must be greater than the third side of the triangle.
Then applying the triangle inequality to the problem, to find the third side 'x', we can write:
\(11 + 17 > x\)
Then the largest value of x that is under 28 is 27.
The longest possible integer length for the third side of the triangle is 27 units.
1) Make certain that the coefficient of the x2 term is 1 ( it is )
2) Divide the coefficient of the x-term by 2 ( 3 divided by 2 is 3/2 )
3) Square this answer ( (3/2)2 = 9/4 )
4) Add this answer to both sides.
x2 + 3x + 9/4 = -3 + 9/4
Since x is a 3 digit integer, then the equation is:
\(100x = 11 + 997k\)
The smallest value of k is 11, or else x could not be a 3 digit integer satisfying the restrictions.
100x must end with two 0's, so 997k must end with 89.
Since 7 is the only number that can multiply the last digit of 997 to make the new number end with a 9.
After some testing we get k = 37.
Here is our new equation:
100x = 11 + 997 * 37
100x = 36900
x = 369.
(-5)4 = -5 x -5 x -5 x -5 = 625
-54 = -(54) = -1 x (5 x 5 x 5 x 5) = -625
There are 64 ways for the product of a 4-digit number to equal 24
6 x 4 x 1 x 1 = 12 numbers
6 x 2 x 2 x 1 = 12 numbers
4 x 3 x 2 x 1 = 24 numbers
8 x 3 x 1 x 1 = 12 numbers
3 x 2 x 2 x 2 = 4 numbers
Add all of them up, and you get 64.
12 = \(2 \over 3\)
6 = \(1 \over 3 \)
So, the answer is 6.
!
