Adding the parts in the ratio gives 18 so there are two triangles possible with perimeters less than 54cm where the side lengths are all integers: a 5, 6, 7 triangle or a 10, 12, 14 triangle.
Therefore the length of the longest side must be either 7cm or 14cm (unless you want to include non-integer side lengths, then it could also be 3.5cm, 1.75cm etc)
Answer: 5 and 14.
Step-by-step explanation:
We know that the Raiders and Wildcats both scored the same number of points in the first quarter so let a,a+d,a+2d,a+3d be the quarterly scores for the Wildcats. The sum of the Raiders scores is a(1+r+r^{2}+r^{3}) and the sum of the Wildcats scores is 4a+6d. Now we can narrow our search for the values of a,d, and r. Because points are always measured in positive integers, we can conclude that a and d are positive integers. We can also conclude that $r$ is a positive integer by writing down the equation:
a(1+r+r^{2}+r^{3})=4a+6d+1
Now we can start trying out some values of r. We try r=2, which gives
15a=4a+6d+1
11a=6d+1
We need the smallest multiple of 11 (to satisfy the <100 condition) that is 1 (mod 6). We see that this is 55, and therefore a=5 and d=9.
So the Raiders' first two scores were 5 and 10 and the Wildcats' first two scores were 5 and 14.
Answer:x=22 degrees
Step-by-step explanation:
We are given a circle C.
Centre is at C
A line passes through the centre makes angle x and 68 on either side
A triangle is formed with angles x, 68 and another angle at the circumference.
Since the line passing through the centre is diameter of the circle, we have
the third angle of the triangle = 90 degrees ( BY semi circle angle theorem)
In the triangle sum of three angles
=90+x+68 =180
x =22 degrees
The a and b determine how big or small the shape of the conic section is.
<span>For the different conic sections given through the equations </span>
<span>Circle: x^2/a^2 + y^2/a^2=1 </span>
<span>Ellipse: x^2/b^2+y^2/a^2 = 1 </span>
<span>Hyperbola: x^2/a^2 - y^2/b^2 = 1 </span>
<span>When trying to isolate cos and sin from those equations to get cos^2t + sin^2 t = 1 you can determine the conic section when substituting cos t = x/a and sint = y/b into cos^2t+sin^2t square it and then refer to the conic section equations to determine the conic section. x defines the major axis and y is the minor axis. a and b provide the coordinate pairs</span>
Answer:
x = -8
x = 8
Step-by-step explanation:
x(18 – x) = 2(9x – 32)
distribute
18x - x² = 18x - 64
Subtract 18x from both sides
-x² = -64
multiply both sides by -1
x² = 64
Take the square root of both sides
x = ± 8
x = -8
x = 8
