The original area is \(l \times w\)
The new area is: \(1.2l \times 1.15w = 1.38lw\)
So, the area increased by \(\color{brown}\boxed {38\text%}\)
\((3x+2)(3x+2) = 9x^2 + 12x+4\)
So, \(\color{brown}\boxed{c=4}\)
The sum is \(a\over{1-r}\)
\(a\) = first term
\(r\) = common ratio
So the sum is... \(2\over{1-{1\over16}}\) = \(\color{brown}\boxed{2 {2\over15}}\)
\(n\leq 1000\)
You have...
\(7 \pmod{9}\)
\(5 \pmod {10}\)
\(9 \pmod {11}\)
Plug into a calculator, and you find that there were \(\color{brown}\boxed{295}\)
There are 248 soldiers.
The 3 smallest intercepts are 3*pi/28, pi/4, and 9*pi/28.
Area of triangle ACE = 200.
The possible values of c are 12 and 25.
3x^2 + 20x + 12 = (x + 6)(3x + 2)
3x^2 + 20x + 25 = (x + 5)(3x + 5)
median * height = area
median = 60 / 8
The numbers are x-2 x and x+ 2
x-2 + x = 3 (x+2) - 6
2x-2 = 3x
x = -2 then the numbers are -4 -2 0
sum = -6
100 = -6t^2 + 51t
-6t^2 + 51 t - 100 = 0 use Quadratic Fromula to find the values of 't' where the height = 100
the smaller 't' will be the first time the object hits 100 ft
a = -6 b = 51 c = -100
\(t = {-b \pm \sqrt{b^2-4ac} \over 2a}\)
When you get your final answer...hit the ' = ' sign again
Find the value of B - A.
Hello Guest!
\(x + 3y = -5\\ y=-\frac{x}{3}-\frac{5}{3}\\ m=-\frac{1}{3}\\ P(-7,2)\)
\(y=-\frac{1}{3}(x+7)+2\ (point-direction\ equation )\\ y=-\frac{1}{3}x-\frac{7}{3}+2\\ y=-\frac{1}{3}x-\frac{1}{3}\\ \frac{1}{3}x+y=-\frac{1}{3}\ |\ \times -9\\ \color{blue}-3x-9y=3 \)
\(Ax+By=3\\ \color{blue}B-A=-9-(-3)=-6\)
!
a / s = 3/5 or a = 3/5 s
3/5 s + 1/2 s = 176
s = 160 a =96
Ratio == 5 : 1
5 + 1==6 sum of the rarios
522 / 6 ==87 - constant ratio
87 x 5 ==435 bubble gums sold
87 x 1 ==87 non-bubble gums sold.
123^1234 mod 10^10 ==6,870,286,809 - these are the last 10 digits.
listfor(n, 0,100, (2^n)/3^(n+1))==(1 / 3, 2 / 9, 4 / 27, 8 / 81, 16 / 243, 32 / 729, 64 / 2187, 128 / 6561, 256 / 19683, 512 / 59049, 1024 / 177147......etc.)==converges to 1
Area of trapezoid = (b1 + b2)/2 * h
60 = (b1 + b1+9)/2 * 8
b1 = 3 units then b2 = 12 units and the median = (3+12)/2 = 7.5 units
= 1.
That's not a question.
The remaining coordinate of the rectangle is\((5,-2)\).
The rectangle is \(13\) tall and \(11\) across. Because the line has a slope of \(2\), the line will be in the shape for \(6.5\) units.
We want these \(6.5\) units to be centered across the \(11\) units of the rectangle. This means that there must be \(2.25\) units on each side.
This gives us an equation that crosses the points \((13.75,11)\) and \((7.25,-2)\).
This means that the equation is y=2x-16.5, so \(\color{brown}\boxed{b=-16.5}\)
Here is the image:
Of the \(10\) numbers, \(2\) are less than \(300\). This means that \(20 \text%\) or \(\color{brown}\boxed{1,000}\) would be defective.
I think...
The y-coordinate must be \(12\), because that is the only way to be \(12\) units from the x-axis.
I think of distance as a right triangle, with the distance between the \(2\) points being the hypotenuse.
We know that the height of the triangle is \(6\), and because the hypotenuse(distance) is \(10\), its x-axis is 8 units away from \(8\).
This means that the coordinates are \((9,12)\). It can't be \((-7,12)\), because \(x\) is not greater than \(1\)
This means that \(\color{brown}\boxed{n=15}\)
2 , 4 , 8 , 10 , 14 , 16 , 20 , 22 , 26 , 28 , 32 , 34 , 38 , 40 , 44 , 46 , 50 , 52 , 56 , 58 , 62 , 64 , 68 , 70 , 74 , 76 , 80 , 82 , 86 , 88 , 92 , 94 , 98 , 100>>Total==34 such integers.
The probability is: 34 / 100==17 / 50
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