The area of the of a rectangle is 336 square inches. If the perimeter is 76. What is the shorter sides length?
Answers
Answer:
hello :
the perimeter is : p = 2 ( w + l )
The area is : A= w ×l w : width l : length w ?
2 ( w + l ) = 76
w ×l = 336
you have the system :
w + l = 38 ...(1)
w ×l = 336...(2)
by (1) : l = 38 - w
subst in (2) : w ( 38 - w ) =336
38w - w²= 336
w² - 38w +336 = 0
delta = b² -4ac when : a = 1 and b= -38 c = 336
delta = (-38)² -4(1)(336) = 1444 - 1344 = 100 = 10²
w1 = (38-10)/2 = 14( the shorter sides length)
w2 = (38+10)/2 = 24( refused )
The shorter side's length of the rectangle is 24 inches. This is determined by solving the system of equations derived from the area (336 square inches) and perimeter (76 inches) constraints, resulting in a quadratic equation with two possible solutions, and the shorter side being 24 inches.
- To find the shorter side's length of a rectangle with an area of 336 square inches and a perimeter of 76 inches, we'll use a system of equations.
- Let's denote:
- Length of the rectangle as L (in inches).
- Width of the rectangle as W (in inches).
- We have two pieces of information:
- The area of the rectangle is 336 square inches:
- L * W = 336
- The perimeter of the rectangle is 76 inches:
- 2L + 2W = 76
- Now, we can solve this system of equations for L and W.
- First, isolate L in the perimeter equation:
- 2L + 2W = 76
- 2L = 76 - 2W
- L = (76 - 2W) / 2
- L = 38 - W
- Now, substitute this expression for L into the area equation:
- (38 - W) * W = 336
- Expand and rearrange the equation:
- 38W - W^2 = 336
- Move all terms to one side to create a quadratic equation:
- W^2 -
- Now, we can solve this quadratic equation for W. We can either factor it or use the quadratic formula. In this case, let's use the quadratic formula:
- W = (-b ± √(b² - 4ac)) / (2a)
- Where:
- a = 1 (coefficient of W^2)
- b = -38 (coefficient of W)
- c = 336
- W = (-(-38) ± √((-38)² - 4 * 1 * 336)) / (2 * 1)
- W = (38 ± √(1444 - 1344)) / 2
- W = (38 ± √100) / 2
- W = (38 ± 10) / 2
- Now, we have two possible values for W:
- W = (38 + 10) / 2 = 48 / 2 = 24 inches (shorter side)
- W = (38 - 10) / 2 = 28 / 2 = 14 inches (longer side)
- So, the shorter side's length is 24 inches.
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Answers
Answer:
8 units apart
Step-by-step explanation:
if you look at the grid and mark the numbers 3 and also -5 they are 8 units apart from each other
Answer:
8 units
Step-by-step explanation:
if you look at a grid and mark the numbers, 3 and -5 are 8 units apart.
Answers
Answers
First, take away '3x' from both sides.
Second, subtract '8x - 3x' to get '5x'.
Third, take away '15' from both sides.
Fourth, add '-20 - 15' to get '-35'.
Fifth, divide both sides by '5'.
Sixth, how many times does 5 go into 35? 35 ÷ 5 = 7.
Answer: x = -7
You said 8x + 15 = 3x - 20
Subtract 3x from each side: 5x + 15 = - 20
Subtract 15 from each side: 5x = - 35
Divide each side by 5 : x = - 7
Answers
Exact Form:
917
Decimal Form:0.52941176…
3.Frank bought a Game Square for $43.20 during Game World's Semi-Annual Gaming Blowout. If the original price of the Game Square is $180.00, which percent of discount below is closest to the percent of discount that Frank received?
4.Mrs. Davidson rode 300 miles on a passenger train. It took her 5 hours to reach her destination. What was the average speed of her train?
Answers
You then add these together, and this gives you $15.70
2. For this, you've got to add the percentage decrease (10/.01) to 1, and then multiply $45.26, and this gives you $49.786 (essentially $50 rounded)
3. You've got to divide the smaller number (43.20) by the larger number (180), and this gives you 0.24, and you've then got to multiply this by 100, giving you 24%. Therefore, he received a 76% discount.
4. The best thing to do here is to divide the larger number (300) by the smaller number (5), and this gives you 60, therefore, the average speed of the train is 60 miles per hour.
Hope this helps :)
Answers
Answer:
height = 12.7 feet
Step-by-step explanation:
To find the height of the giraffe, we just need to use the tangent relation of the angle of elevation.
The opposite side to the angle is the height of the giraffe, and the adjacent side of the angle is the distance between the giraffe and the narutalist.
So, we have that:
tangent(30) = height / distance
0.5774 = height / 22
height = 22 * 0.5774 = 12.7 feet
Answer:
12.7
Step-by-step explanation: