For this you would use Pythagorean theorem (a^2+b^2=c^2) a=15 and c=sqrt 514 plug the numbers in and you’ll be set
Answer:
The longest length which you are given.
Step-by-step explanation:
The hypotenuse is the longest side in a right angled triangle. The largest side in a right angled triangle is known as the hypotenuse.
Answer:
x = -5
Step-by-step explanation:
Since these two triangles are similar, the ratio between the corresponding lengths of each triangle will be the same.
This means the ratio between one side of each triangle (e.g. AD and DC) will be the same as the ratio between a different side of each triangle (e.g. BE and BC).
So, to create an equation for the sides which contain the unknown 'x', we must first find the ratio between the two sides by using a different set of sides.
On the right side we are given 9 for AD, and 18 for DC.
9/18 = 0.5
This means that the extra length of the larger triangle from the smaller one (AD) is half the length of the smaller triangle (DC). We can use this to make an equation for x:
If AD/DC = 0.5, then BE/EC will also = 0.5
BE = x+23
EC = x+41
Therefore:

Now we can solve by multiplying both sides by x+41 to eliminate the fraction:

Now we multiply out the brackets and move the terms to different sides:



And if we substitute the -5 into the equations:
-5+23 = 18
-5 + 41 = 36
We will see that -5 does indeed give us the same ratio between the lengths:
18/36 = 0.5
Hope this helped!
Answer:
y=-2x-3
Step-by-step explanation:
Since our equation is in standard form Ax+By=C we must first manipulate the equation so that we have it in the slope-intercept form such that y=mx+b. Therefore:

Therefore, our slope is 1/2 and our y-intercept is 2. Now in order to determine a perpendicular line to the one stated above we must then get the negative inverse of our slope meaning
(negative reciprocal). Now we must use the point slope formula:

Where m is the slope, x1 is -2 and y1 is 1 (because of the ordered pair given). And so:

Therefore, the line that is perpendicular to -x+2y=4 is y=-2x-3.
Answer:
504
Step-by-step explanation: