Answer:
Use the Pythagorean theorem
Step-by-step explanation:
The pythagorean theorem is 
where a is a height, b is a height, and c is the hypotenuse, which is the longest side of a triangle. For example, if the triangle has two side with lengths of three and four we would put them into the equation to get:
Simplify the equation to get:
Add 16 and 9 to get 25 and take the square root of both sides:
The sqrt of 25 is 5. Therefore, the length of the hypotenuse, or c, is 5.
Answer: $ 18681.45
Step-by-step explanation:
Given: Future value : 
The rate of interest : 
The number of time period : 
The formula to calculate the future value is given by :-
, where P is the initial amount deposited.
Hence, the lump that must be deposit today : $ 18681.45
Answer:
19.8 and 8/(sin(theta))+ 6/(cos(theta))
Step-by-step explanation:
If you make a table you can see that L_1 + L_2 gets larger as you increase theta prom pi/2 and decrease theta from pi/2. This means that pi/2 is the theta that will yield the smallest length for the ladder. Plugging this into L_1 + L_2 you get 19.8 (rounded to the nearest hundred)
C = 8/(sin(theta))+ 6/(cos(theta))
Look at the first line in the first problem.
x y
<span>–6 –6
–4 –3</span>
find the slope:
y2-y1 / x2-x1
-3+6 / -4+6
3 / 2
the slope is 3/2. now plug this into point-slope form, along with one of the ordered pairs. i'll use (-4,-3) because the numbers are smaller.
y-y1=m(x-x1)
y+3=3/2(x+4)
y+3=3/2x+6
y=3/2x+3
now do the same for the other line.
<span>x y
0 3
2 6
actually, this one's convenient, because it tells you the y-intercept is 3 (when an ordered pair has a 0 as its x coordinate, that means its on the y axis). so we just have to find the slope.
y2-y1 / x2-x1
6-3 / 2-0
3/2
the line is y=3/2x+3. it's the same line as before. that means there are infinitely many solutions, because there are an infinite amount of points where the lines "cross" each other (since they lie on top of each other).
follow the same procedure for the next problem. if the equations turn out to be the same, it has infinite solutions. if the two lines have the same slope but different intercepts, that means they're parallel, and have no solution since the lines will never intersect. if the lines have different slopes, they will have one solution. and it makes no sense for lines to intersect at two different points, so you can ignore that option altogether.
hope this helps
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