volume of a pyramid = 1/3 Ab h using eha as base area = Ab = 1/2 5 * 6
using h as EF = 4
1/3 (1/2 5*6) * 4
= 20 units3 Anyone else?
The exception is D sqrt(90)
The largest integer is 6, and the smallest integer is -3, so the answer is 6 - (-3) = 9.
AB = 55.
The sum of all digits: 1 + 2+ 3 +4..........9 + 9 +9 +1 +0 +0+ 0=13,501 - which includes both 1 and 1000.
The area of a rectangle is length x width. We multiply the given length, 3x-5, by the given width, x+1.
(3x-5)(x+1)
= 3x^2+3x-5x-5
=3x^2-2x-5
We complete the square.
\(3x^2+4x+1\\ =3(x^2+\frac{4}{3}x+\frac{1}{3})\\ =3(x+\frac{2}{3})^2-\frac{1}{3}\)
So a=3, h=2/3, and k=-1/3.
3x^2 + 4x + 1 divide by 3
x^2 + 4/3 x + 1/3 complete the square
(x+ 4/6)^2 -16/36 +1/3 =
(x + 4/6)^2 - 1/9 now put the '3' back in
3 (x+4/6)^2 -1/3 now you can see a h and k
The answer is (d) -14.
Let m and n be the two numbers. We already know one of them is 90.
mn=gcd(m, n) * lcm[m, n]
90n=gcd(90, n)* lcm[90, n]
90n=18 * 180
90n = 3240
n = 36
LCM of 180 and 18 = 180 GCD of 180 and 18 = 18 LCM of 90 and 36 = 180 GCD of 90 and 36 = 18 LCM of 36 and 90 = 180 GCD of 36 and 90 = 18 LCM of 18 and 180 = 180 GCD of 18 and 180 = 18
17. Plug in the answer choices. The answer is {(4,0), (0,4)}.
18. At least one of the factors must be 0.
x-3=0
x=3
x+2=0
x=-2
x-2=0
x=2.
So the zeroes are 3, -2, 2.
The integral works out to 0.
Speed= distance/time.
We plug in the given expressions for distance and time.
Speed=
\(\frac{\frac{4}{3x-6}}{\frac{8}{9x-18}}\\ =\frac{4}{3x-6}\cdot\frac{9x-18}{8}\\ =\frac{1\cdot3}{1\cdot2}\\ =\frac{3}{2}\)
This is 3/2 feet per second.
(4/(3x-6)) feet / (8/(9x-18)) seconds = (4* (9x-18) / (8 (3x-6)) = (36x -72)/(24x-48) = (3x-6)/(2x-4) f/s = 3/2 f/s
**edited....misread Q ****
.65 x = 10 for each station
x = 10/.65 = 15.385 for EACH station
15.385 x 15 = ~~ 231 seeds
It's simple...count 7 units right and 6 units up so the point is B.
Well.....from the little dot in the lower left (the 'origin) count across 7 to the right .....then 6 up.....which point is there?
By properties of angle bisectors, angle C = 180 - 109 = 71 degrees.
oh you were so close! you got everything right except that you have to multiply 126 by 120 because there are 5!=120 ways to permute the trucks. so the answer according to the website is 126*120=15120
thanks for the help though! i really appreciate it! :)
Multiply their moduli and add their arguments
8*4 (cos(20+60) isin (20+60) =.........
a .5 = 3-1 + 3-2+3-3+3-4+3-5+3-6 =.111111 (in base 3 )
b 0.111111111 (see a patern here....for the next question)
c my guess is it is .1111111
you will have 3(-5) + 2(1) -4(-5) = ........
Due to the leading negative on the t^2 term, this is a dome shaped parabola
Maximum will occu at t = -b/2a b = 8 a = -1
use this value of 't' in the equation to find the maximum value ....
1/60 +1/30 = 1/x
(1+2)/60 = 1/x
60/3 = x = 20 min
