9514 1404 393
Answer:
a) w(4w-15)
b) w²
c) w(4w -15) = w²
d) w = 5
e) 5 by 5
Step-by-step explanation:
a) If w is the width, and the length is 15 less than 4 times the width, then the length is 4w-15. The area is the product of length and width.
A = w(4w -15)
__
b) If w is the side length, the area of the square is (also) the product of length and width:
A = w²
__
c) Equating the expressions for area, we have ...
w(4w -15) = w²
__
d) we can subtract the right side to get ...
4w² -15w -w² = 0
3w(w -5) = 0
This has solutions w=0 and w=5. Only the positive solution is sensible in this problem.
The side length of the square is 5 units.
__
e) The rectangle is 5 units wide, and 4(5)-15 = 5 units long.
The rectangle and square have the same width and the same area, so the rectangle must be a square.
Answer:
csc π.
Step-by-step explanation:
csc π because csc = hypotenuse / opposite side and the opposite side = 0. Anything divided by zero is undefined.
Another way to the same conclusion is: we know that sin π = 0 and csc π = 1 / sin π = 1 / 0 which is indeterminate.
76.002 i think honestly don’t know but have it a try
2 numbers can be represented by the variables x and y.
Set up a system of equations:
The two numbers added together will result in a sum of 33. However, one number subtracted from another will result in a difference of 1.
In both systems of equations, there are inverses of variable y. Therefore, we can combine the systems of equations by adding them together:
Divide both sides by 2 to get x by itself:
One of the numbers will be 17.
Plug the value into one of the equations:
Add y to both sides:
Subtract both sides by 1 to get y by itself:
The two numbers that sum up to 33, with a difference of 1 between them, will be 16 and 17.
<h3>
Answer: x = 40</h3>
===================================================
Work Shown:
A+B+C = 180 ..... three angles of any triangle add to 180
(2x+10)+(x)+(2x-30) = 180
5x-20 = 180
5x = 180+20 .... adding 20 to both sides
5x = 200
x = 200/5 ... dividing both sides by 5
x = 40
This is the measure of angle B
We can stop here.
If you need to know the values of the other angles, then,
- angle A = 2x+10 = 2*40+10 = 90
- angle C = 2x-30 = 2*40-30 = 50
Then note how A+B+C = 90+40+50 = 90+90 = 180 which helps confirm our answer.
