Let's solve this problem using substitution. Given that x-y=8, x = 8 + y.
(Then x^2 = 64 + 16y + y^2)
This other equation is (x-2)^2 + (y-1)^2 = 25.
Easier to substitute 8 + y for x in (x-2)^2:
(8 + y - 2)^2 + (y-1)^2 = 25
(6 + y)^2 + (y-1)^2 = 25
36 + 12y + y^2 + y^2 - 2y + 1 = 25
Re-writing this in descending powers of y:
2y^2 + 10y + 36 + 1 = 25
Then 2y^2 + 10y - 12 = 0
Reduce by division by 2: y^2 + 5y - 6 = 0 = (y+3)(y+2) = 0
Then y=-3 and y=-2. From each of these we get x: x = 8 + y
So x = 8 - 3 = 5 and x = 8 - 2 = 6. There are common solutions.
Try (5, -3) and (6, -2). Do these points satisfy both of the given equations? If they do, you've shown that we have common solutions.
Answer:
Step-by-step explanation:
This is good! The length of the metal is 20 inches longer than the width. But we fold up 4-inch flaps on each side, so the height of the box is 4 inches, and the length and width will each decrease by 8 inches (4 inches on each side). Since the length and width decrease by the same amount, the length will still be 20 inches longer than the width. So the equations would be:
l = w + 20
vol = l x w x h = 1716 in3
1716 = (w + 20)(w)(4)
1716 = 4w2 + 80w
4w2 + 80w - 1716 = 0
4(w2 + 20w - 429) = 0
4(w + 33)(w - 13) = 0
w + 33 = 0, so w = -33
w - 13 = 0, so w = 13
Since the width can't be negative, the width of the box is 13 and the length is 33 (13 + 20).
But remember, the length and width of the piece of metal are each 8 inches longer than the box, so it was 41 inches by 21 inches.
Answer:
9/10 pounds
Step-by-step explanation:
3/5 × 1 1/2
= 9/10
Answer:
Triangle Q R P is shown. The length of Q R is 5 and the length of R P is 6. Angle Q R P is 40 degrees.
Step-by-step explanation:
The trigonometric formula refers the two sides length of the triangle and it also consists of included angle to find out the area
A = 
ab sin C
QPR contains two sides and the included angle
XYZ has one side and the two angles
DEF has only three sides
And, the ABC contains two sides but does not have the included angle
Based on the explanation above, the correct option is B
