Answer:
<h2><em>29.4 length and 21.4 width.</em></h2>
Step-by-step explanation:
To fin the dimensions of the pool we need to use the total area of the pool plus the concrete walkway. Lets say that <em>W </em>is the width and <em>L </em>the length. We know that, the walkway has 3 ft wide, this means that the width and length are increased by 6ft (3ft on each side). So, the total area can be expressed like this: 
.
In addition, we know that the total area is 970 and the length is 8 ft longer than the width (
). So:
With this quadratic equation we're gonna have to solution, the most reasonable is part of the answer. So, solving the equation we have as solutions: 
and 
Therefore, the width is 21.4 ft, because the negative number cannot represent distances.
Using the relation between length and width:
<em>Therefore, the dimensions of the pool are 29.4 length and 21.4 width.</em>
Steps:
1. Substitute the y in y=4x + 4 and put
X-6=-4x+4
2. Add 4x to both sides
3. 5x-6=4
4. Add 6 to both sides
5. 5x=10
6. Divide by 5 on both sides
7. X=2
8. Now to find the y, you substitute 2 for x in the problem y=x-6
9. Y=2-6
10. Y=-4
11. Your answer is
(2, -4)
Answer:
Step-by-step explanation:
It is convenient to memorize the trig functions of the "special angles" of 30°, 45°, 60°, as well as the way the signs of trig functions change in the different quadrants. Realizing that the (x, y) coordinates on the unit circle correspond to (cos(θ), sin(θ)) can make it somewhat easier.
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<h3>20.</h3>
You have memorized that cos(x) = (√3)/2 is true for x = 30°. That is the reference angle for the 2nd-quadrant angle 180° -30° = 150°, and for the 3rd-quadrant angle 180° +30° = 210°.
Cos(x) is negative in the 2nd and 3rd quadrants, so the angles you're looking for are
150° and 210°
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<h3>Bonus</h3>
You have memorized that sin(π/4) = √2/2, and that cos(3π/4) = -√2/2. The sum of these values is ...
√2/2 + (-√2/2) = 0
_____
<em>Additional comments</em>
Your calculator can help you with both of these problems.
The coordinates given on the attached unit circle chart are (cos(θ), sin(θ)).
Answer:
Length = 6
Width = 5.5
Step-by-step explanation:
Let's use the variable x to represent the width:
x = width
The question says that the length of the rectangle is "5 ft less than double the width". This length can be represented like this:
2x - 5 = length
To find the area of a rectangle, you multiply the width and length, so we are going to write an equation where we multiply the width and length and set it equal to 33 ft^2, which is the area:
(x)(2x - 5) = 33
Now use basic algebra to solve for x:
2x^2 - 5x = 33
2x^2 - 5x - 33 = 0
2x^2 + 6x - 11x - 33 = 0
(2x^2 + 6x) + (-11x - 33) = 0
2x(x + 3) - 11(x + 3) = 0
(2x - 11) (x + 3) = 0
x = 11/2, -3
x either equals 11/2 or -3. However, remember that x represents the width, and you can't have a negative number for a width, so x = 11/2 or 5.5.
Now plug in 5.5 to the length expression and simplify:
2(5.5) - 5
11 - 5 = 6
The length is 6 and the width is 5.5.
Hope this helps (●'◡'●)
You need to multiply 8 by 60 and that gets you 80. It would look like this <span>8*60 = 80x</span>
