Answer:
Original number is 86
Step-by-step explanation:
Original: 10x + y
Double reversed: 2(10y + x)
Constraints:
x + y = 14 ===> x = 14 - y
2(10y + x) + 10x + y = 222 ===> 21y + 12x = 222
Substitution to find y:
21y + 12x = 222
21y + 12(14 - y) = 222
21y + 168 - 12y = 222
9y + 168 = 222
9y = 54
y = 6
Substitution to find x:
x = 14 - y
x = 14 - 6
x = 8
Original: 10x + y
10(8) + (6)
80 + 6
86
Answer:
7 square units
Step-by-step explanation:
Two of the points are on the horizontal line y = -3, so it is convenient to call that the "base" of the triangle. The length of the base is the difference in the x-coordinates of its end points:
b = 3 -(-4) = 7
The height is measured perpendicular to the base, so is the vertical distance from the line y=-3 to the third point. That distance is the difference between -3 and the y-coordinate of point A:
-3 -(-5) = 2
The triangle has a base of length 7 and a height of 2. Its area is ...
A = 1/2bh
A = 1/2(7)(2) = 7 . . . . square units
Answer:
4 horses and 8 ducks.
Step-by-step explanation:
Let the number of ducks be d and the number of horses be h.
d + h = 12
Now ducks have 2 feet and horses have 4 so:
2d + 4h = 32
Multiply the first equation by 2
2d + 2h = 24
Subtract this equation from the second equation:
4h - 2h = 32 - 24
2h = 8
h = 4.
So there were 4 horses and 12 - 4 = 8 ducks.
As you can probably tell, this is a 30, 60, 90 triangle. That means the degree measures are 30, 60, and 90. These are special triangles. For every 30, 60, 90 triangle in the world, the shorter leg (in your case, x) is ALWAYS two times shorter than the hypotenuse (6). 6/2=3, so x=3. Also, the longer leg for a 30, 60, 90 triangle is always equal to the shorter leg times the square root of 3. So, 3 times the square root of 3 is about 5.2. So, y=5.2. Hope it helps!
Answer:
84 cm^2
Step-by-step explanation:
Area of triangle + area of rectangle
Area of triangle = 1/2*l*b
= 1/2*8*3= 12 cm^2
Area of rectangle = l*b
= 12*6 = 72 cm^2
Total area= 72+12
= 84 cm^2
