Answer:
Step-by-step explanation:
<u>Completing the square</u>
when 
Given equation:
Subtract 40 from both sides:
Divide both sides by 3:
Add the square of half the coefficient of 
to both sides:
Factor the left side and simplify the right side:
Square root both sides:
Add 4 to both sides and simplify the radical:
84 sq. ft of the wall has to be covered with paint or wallpaper.
Step-by-step explanation:
- Step 1: Find the area of wallpaper to be covered by calculating the area of the wall and subtracting the areas of the window, mirror and fireplace from it. All are rectangular in shape with are given by A = length × width
Area of the wall = 8 × 16 = 128 ft²
Area of the window = 18/12 × 14 = 1.5 × 14 = 21 ft² (since 1 ft = 12 in)
Area of the fireplace = 5 × 3 = 15 ft²
Area of the mirror = 4 × 2 = 8 ft²
- Step 2: Calculate the area to be painted or covered with wallpaper
Area of the wall to be covered with paint or wallpaper = 128 - (21 + 15 + 8)
= 128 - 44
= 84 ft²
Let's look at the second equation and try multiplying it by 4:
4 * (3x + ky) = 4 * 27
Which gives us:
12x + 4ky = 108
This looks almost exactly like the first equation except that instead of -20y, there is 4ky. We could try making them equal to each other and solving for k:
-20y = 4ky
-20 = 4k
k = -5
Then, the answer is k = -5.
I'm gonna use c for circle, t for triangle, and s for square
c+t+s=13
t+s=8
c+8=13
c=5
c+t=7
t=2
s=6
circle is 5, triangle is 2, and square is 6
By the Pythagorean Theorem, the length of x is
a^2 + b^2 = c^2 Pythagorean Theorem
6^2 + b^2 = 10^2 Substitute known variables
6^2 + b^2 - 10^2 = 0 Subtract 10^2 from each side
6^2 - 10^2 = b^2 Subtract b^2 from each side
√6^2-10^2 = √b^2 Take square root of each side
8 = b Simplify
So, the length of x is 8. I hope this helps!
