Step-by-step explanation:
A playing card is in the form of a rectangle whose perimeter is equal to 28 cm and area is 45 cm².
If l and b are length and breadth of the rectangle.
Area,
![A=lb](https://tex.z-dn.net/?f=A%3Dlb)
![45=lb\\\\l=\dfrac{45}{b}\ .....(1)](https://tex.z-dn.net/?f=45%3Dlb%5C%5C%5C%5Cl%3D%5Cdfrac%7B45%7D%7Bb%7D%5C%20.....%281%29)
Perimeter,
![P=2(l+b)\\\\28=2(l+b)\\\\14=(l+b)\ ....(2)](https://tex.z-dn.net/?f=P%3D2%28l%2Bb%29%5C%5C%5C%5C28%3D2%28l%2Bb%29%5C%5C%5C%5C14%3D%28l%2Bb%29%5C%20....%282%29)
Put the value of l from equation (1) to equation (2). So,
![14=\dfrac{45}{b}+b\\\\14=\dfrac{45+b^2}{b}\\\\14b=45+b^2\\\\b^2-14b+45=0\\\\b^2-9b-5b+45=0\\\\b(b-9)-5(b-9)=0\\\\b=5\ cm, 9\ cm](https://tex.z-dn.net/?f=14%3D%5Cdfrac%7B45%7D%7Bb%7D%2Bb%5C%5C%5C%5C14%3D%5Cdfrac%7B45%2Bb%5E2%7D%7Bb%7D%5C%5C%5C%5C14b%3D45%2Bb%5E2%5C%5C%5C%5Cb%5E2-14b%2B45%3D0%5C%5C%5C%5Cb%5E2-9b-5b%2B45%3D0%5C%5C%5C%5Cb%28b-9%29-5%28b-9%29%3D0%5C%5C%5C%5Cb%3D5%5C%20cm%2C%209%5C%20cm)
Put the value of b in equation (1),
If b = 5 cm
![l=\dfrac{45}{5}=9\ cm](https://tex.z-dn.net/?f=l%3D%5Cdfrac%7B45%7D%7B5%7D%3D9%5C%20cm)
If b = 9 cm
![l=\dfrac{45}{9}=5\ cm](https://tex.z-dn.net/?f=l%3D%5Cdfrac%7B45%7D%7B9%7D%3D5%5C%20cm)
So, the dimensions of the playing card is 9 cm by 5 cm.
Step-by-step explanation:
the average rate of change is
(f(x2) - f(x1)) / (x2 - x1)
(a)
(f(4) - f(-6)) / (4 - -6) = (3 - 1) / (4 + 6) = 2 / 10 = 1/5
(b)
(f(2) - f(-2)) / (2 - -2) = (-1 - -3) / (2 + 2) = (-1 + 3) / 4 = 2/4 = 1/2
9514 1404 393
Answer:
17n+9 feet
Step-by-step explanation:
The perimeter of a rectangle is twice the sum of length and width.
P = 2(L +W)
P = 2((4.5n +9) +(4n -4.5)) = 2(8.5n +4.5)
P = 17n +9
The perimeter of the rectangle is 17n +9 feet.
Answer:
The correct answer is D) 200
Step by step explanation:
Let x be the number:
Then,
→15/100(x)=30
→3/20(x)=30
→3x/20=30
→3x=20⋅30
→3x=600
→x=600/3=200
Hope it helps!
Answer:
C
Step-by-step explanation:
∠ AFD = ∠ AFB + ∠ BFC + ∠ CFD
The 3 angles form a straight angle and sum to 180°, that is
4x + 5 + 6x + 3 + 5x + 7 = 180, that is
15x + 15 = 180 ( subtract 15 from both sides )
15x = 165 ( divide both sides by 15 )
x = 11
∠ CFD = 5x + 7 = 5(11) + 7 = 55 + 7 = 62°, thus
∠ AFE = ∠ CFD = 62° ( vertical angles are congruent )