Answer:
x = 5√2
y = 5√6
z = 5√3
ΔABC ~ ΔBDC ~ ΔADB
Step-by-step explanation:
ΔABC, ΔBDC, and ΔADB are all similar triangles to each other.
By definition of similar triangles, the corresponding sides have the same ratios.
CD from ΔBDC corresponds to BD from ΔADB, and BD from ΔBDC corresponds to AD from ΔADB. So:
CD / BD = BD / AD
10 / x = x / 5
x² = 50
x = 5√2
Since ΔBDC is right, we can use the Pythagorean Theorem to solve for y:
CD² + BD² = BC²
10² + (5√2)² = y²
y² = 100 + 50 = 150
y = 5√6
Again, since ΔΔABD is right, we can use the Pythagorean Theorem to solve for z:
AD² + BD² = AB²
5² + (5√2)² = z²
z² = 25 + 50 = 75
z = 5√3
you know 1 gallon is 16 cups.
1/2 a gallon will be 8 cups.
So, its asking how much is 1 1/2 gallon to cups. Add 16+8= 24.
24 is the answer
Area of the entire rectangle 
Solution:
Area of the blue box = length × width
Area of the blue box 
Area of the pink box = length × width
Area of the pink box 
Area of the green box = length × width
Area of the green box 
Area of the orange box = length × width
Area of the orange box = 24
Total area of the rectangle 
Area of the entire rectangle
Answer:
x < -1.5 U x > 9.6
Step-by-step explanation:
12x + 7 < -11
x < -1.5
5x - 8 > 40
5x > 48
x > 9.6
Answer:
The distance A’C’ is 4.47 units
Step-by-step explanation:
Before we go on, we need to get the appropriate transformation
Mathematically, we have a 90 degrees clockwise rotation yielding the following;
(x,y) to (-y,x)
A is (-4,1)
C is (-2,5)
By transforming, we have
A’( -1,-4)
C’ (-5,-2)
To get the magnitude of the line segment, we are going to use the distance formula between points
We have this as;
D = √(x2-x1)^2 + (y2-y1)^2
D = √(-5-(-1))^2 + (-2-(-4))^2
D = √(-4)^2 + (2)^2
D = √(16 + 4)
D = √20
D = 4.47 units
