Answer:
The values of x and y are x = 6 and y = 9
Step-by-step explanation:
MNOP is a parallelogram its diagonal MO and PN intersected at point A
In any parallelogram diagonals:
- Bisect each other
- Meet each other at their mid-point
In parallelogram MNOP
∵ MO and NP are its diagonal
∵ MO intersect NP at point A
- Point A is the mid-point pf them
∴ MO and NP bisect each other
∴ MA = AO
∴ PA = AN
∵ MA = x + 5
∵ AO = y + 2
- Equate them
∴ x + 5 = y + 2 ⇒ (1)
∵ PA = 3x
∵ AN = 2y
- Equate them
∴ 2y = 3x
- Divide both sides by 2
∴ y = 1.5x ⇒ (2)
Now we have a system of equations to solve it
Substitute y in equation (1) by equation (2)
∴ x + 5 = 1.5x + 2
- Subtract 1.5x from both sides
∴ - 0.5x + 5 = 2
- Subtract 5 from both sides
∴ - 0.5x = -3
- Divide both sides by - 0.5
∴ x = 6
- Substitute the value of x in equation (2) to find y
∵ y = 1.5(6)
∴ y = 9
The values of x and y are x = 6 and y = 9
Answer: Total cost is $1.75
Explanation:
Since we have given that
Number of postcards bought by Doug's family= 7
Cost of each postcard including tax = $0.25
Total cost is given by
Now, we want to show this in number line :
On the number line put all the number with a difference of 0.25 and run the number line seven times and we get the answer.
Each step is of length 0.25 and there are 7 jumps to reach required answer.
So, after 7 jumps we reach at 1.75 which is the required answer.
Hence total cost is $1.75
Answer:
The correct answer is 63 cubic inches.
Step-by-step explanation:
Dali rolled up his painting and placed it in a cylinder 2 inches diameter.
Diameter of the painting is 2 inches. This also implies diameter of the cylinder is 2 inches.
Radius of the cylinder is 1 inch.
Length of the cylinder is 20 inches.
Volume of the cylinder is given by π × × h = π × × 20 = 20π = 62.85 cubic inches ≈ 63 cubic inches.
Therefore the volume of the cylinder in which Dali placed his painting is given by 63 cubic inches.
Answer:
21.53 in of fabric on headbands
7.67 in of fabric on wristbands.
Step-by-step explanation:
Step one:
given data
the total amount of person players plus coaches= 27+4= 31
for each person, she uses = 667.43/31= 21.53 in of fabric on headbands
She also uses 237.87inches of fabric on wristbands for just the players
For each player, she will use= 237.87/31= 7.67 in of fabric
Hence for each player, she used
21.53 in of fabric on headbands
7.67 in of fabric on wristbands
Answer:
Step-by-step explanation:
The directrix is a vertical line, so the parabola is horizontal. The focus lies to the left of the directrix, so the parabola opens to the left.
For a left-opening parabola:
x = a(y-k)²+h,
a < 0,
vertex (h,k)
focal length p = 1/|4a|
focus (h-p, k)
directrix: x=h+p
Apply your data
focus (1,-4)
directrix x=2
vertex (1.5,-4).
focal length p = 0.5
a = -1/|4p| = -½
x = -½(y-2)²+ ½