\(x^2+y^2+2xy=30+2xy\\ (x+y)^2=30+2xy\\ \)
You can finish it.
Hint: The sum of any two sides of a triangle MUST be longer than the 3rd side.
The exterior angles of a k-sided polygon form an arithmetic sequence. The smallest and largest interior angles of the polygon are 136 and 176. What is k?
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I've tried hard but couldn't solve it, so I had to use the calculator.
k = 15
There are 288 possible arrangements.
The answer is 52.
The weights 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 20, 30, 40, 50, 60, 70, 80, 90 can be used. This gives an answer of 18 (weights).
It literally says "(Give your answer in the form ax+by+c >0 or ax+by+c>=0 where a, b and c are integers with no common factor other than 1.)"
y = .2(7) + 2.42 - .2x
y = 3.82 - .2x
First find equation of the line ....the shaded area INCLUDES the line (because it isn't dashed
everything less than or equal to this line is what ya need
Line equation is y = 2x-4
soooo y <= 2x-4
3y = 2x-12
y = 2/3 x - 4 slope = 2/3 perpindicular = -1 / 2/3 = 3/2
Point slope form of your new line y-5 = 3/2 ( x+3)
The probability is 3/56.
Franklin can reach any point inside the square with vertices (10,10), (10,-10), (-10,-10), and (-10,10), so the answer is 21^2 = 441.
b + 1/2 b + .8(b + 1/2b) = 81
b = 30
THANKSSSS THANKSSSS
THANKS SOOOOOO MUCHHHH
\(\displaystyle \sqrt{\frac{16}{25}+\frac{9}{4}}\ =\ \sqrt{\frac{16\cdot4}{25\cdot4}+\frac{9\cdot25}{4\cdot25}}\ =\ \sqrt{\frac{64}{100}+\frac{225}{100}}\ =\ \sqrt{\frac{289}{100}}\ =\ \frac{\sqrt{289}}{\sqrt{100}}\ =\ \frac{17}{10}\)
= sqrt ( 64/100 + 225/100) = sqrt ( 289/100) = 17/10
5.29 x 103 * 6.8 x 10-7
= 5290 * . 00000068 or 5.29 * 6.8 x 103-7 = 35.972 x 10-4 = .0035972
Average = total distance/total hours
total distance = .3 + .3 + .5 + .24 = 1.34 miles
total hours .3m / 7.5 m/hr + .3 / 7.5 + .5/10 + .24/12 =.......... hrs
1.34 miles/ total hours = .......... m/hr average
Thanks a lot! This really clarified things for me!
x^2 + 12x + 9
Take 1/2 of 12 = 6
Square this = 36
Add and subtract this
x^2 + 12x + 36 + 9 - 36 factor the first three terms, simplifythe rest
1(x + 6)^2 - 27
"a" is an understood 1
u = 6
v = -27
Since [CDP ] = 4
Then the area is (1/2) CD height = (1/2)(2) height = (1/2) (2) (4) = 4
So the height is 4
And triangles CDP and ABP are similar
So the bases are 5/2 = scale factor
So height of ABP = ( 5/2) height of CDP = (5/2) (4) = 10
So....the whole height of ABCD = 10 + 4 = 14
And ABCD is a trapezoid....so its area =
(1/2) (height) ( sum of bases AB + CD) =
(1/2) ( 14) ( 5 + 2) =
7 * 7 =
49 = [ ABCD ]
The problem here is that A, B could take on infinite values
For example A =180 B = 45
Tan A = 0 Tan B = 1
So ( 1 + Tan A) (1 + Tan B) = ( 1 + 0) (1 + 1) = 2
However
A = 270 B = - 45
Tan A = undefined....so (1 + Tan A) (1 + Tan B) is also undefined
I'm assuming that the first situation might be what is intended
f(x) = 4x - 7
g(x) = x^2 + 2x + 1
f(x) + g(x) = x^2 + 6x - 6
So s(3) = (3)^2 + 6(3) - 6 = 21
Second one ....add like you normally would after aligning the terms
2x ^2 + 3x - 9
+ 5x +11
-3x^2 + 1
_______________
-x^2 + 8x + 3
Max height occurs at t = -b/2a = -8.5/(2 * -4.9) = .8673 seconds
Height will be -4.9(.86732) + 8.5(.8673) + 15 = ........... meters above the water
