Answer:
<em>Thus, the dimensions of the metal plate are 10 dm and 8 dm.</em>
Step-by-step explanation:
For a quadratic equation:
The sum of the roots is -b and the product is c. Note the leading coefficient is 1.
We know the perimeter of the rectangular metal plate is 36 dm and its area is 80 dm^2. Being L and W its dimensions, then:
P=2(L+W)=36
A=L.W=80
Note both formulas are closely related to the roots of the quadratic equation, we only need to adjust the data for the perimeter to be exactly the sum of L+W and not double of it.
Thus we use the semi perimeter instead as P/2=L+W=18
The quadratic equation is, then:
Factoring by finding two numbers that add up to 18 and have a product of 80:
The solutions to the equation are:
x=10, x=8
Thus, the dimensions of the metal plate are 10 dm and 8 dm.
<h3>
Answer: 14 feet</h3>
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Explanation:
Check out the diagrams below.
We'll start with the left diagram (marked "before") which is a right triangle with the horizontal leg of 25 feet and hypotenuse 65 feet.
Use the pythagorean theorem to find the vertical side x.
a^2 + b^2 = c^2
25^2 + x^2 = 65^2
625 + x^2 = 4225
x^2 = 4225 - 625
x^2 = 3600
x = sqrt(3600)
x = 60
The top of the ladder is 60 feet high when placed against the wall in this configuration.
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If the upper end is moved down 8 feet, then x-8 = 60-8 = 52 feet is the new height of the ladder. Refer to the "after" in the diagram below.
Like earlier, we'll use the pythagorean theorem to find the missing side.
a^2 + b^2 = c^2
y^2 + 52^2 = 65^2
y^2 + 2704 = 4225
y^2 = 4225 - 2704
y^2 = 1521
y = sqrt(1521)
y = 39
The horizontal distance from the ladder base to the wall is now 39 feet.
Earlier it was 25 feet, so it has increased by 39-25 = 14 feet.
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Answer:
860 beads
Step-by-step explanation:
60 times 77=4620
40 times 113=4520
4620+4520=9140
10000-9140=860
Answer:
18 cents
Step-by-step explanation:
3.28/18 = .18
