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Natasha_Volkova [10]
2 years ago
11

Which is greater: 25% of 15 or 15% of 25? Explain your reasoning using mathematical evidence or visual models.

Mathematics
2 answers:
d1i1m1o1n [39]2 years ago
8 0

15% of 25 is the greatest of the two.

Answer:

25% of 15 is 3.75

15% of 25 is also 3.75

15 - 3.75 = 11.25

25 - 3.75 =21.25

Compare and then determine.

11.25 < 21.25

Ymorist [56]2 years ago
8 0

Answer: 25% x 15=25/100 x 15=.25 x 15=3.75

15% x 25=15/100 x 25=.15 x 25=3.75

Now you can clearly see that they are the same.

Step-by-step explanation:

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In a right triangle, one of the legs is 5 cm smaller than the hypotenuse, and the other leg is 10 cm smaller than the hypotenuse
nata0808 [166]

Answer:

25 cm.

Step-by-step explanation:

If the hypotenuse is  x cm long the 2 legs are  x-5 and x-10 cm long.

So by the Pythagoras theorem:

x^2 = (x - 5)^2 + (x - 10)^2

x^2 = x^2 - 10x + 25 + x^2 - 20x + 100

x^2 - 30x + 125 = 0

(x - 5)(x - 25) = 0

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We can discard x = 5 because that would make the lengths of the legs negative so the hypotenuse = 25 cm long.

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3 years ago
A parallelogram with four right angles? Which one is it??
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Cynthia Besch wants to buy a rug for a room that is 24 ft wide and 33 ft long. She
qaws [65]
<h3>Answer:   16 ft by 25 ft</h3>

=========================================================

Explanation:

Refer to the diagram below.

The outer dimensions 24 ft and 33 ft shrink down to 24-2x ft and 33-2x ft respectively. This subtraction of 2x is due to subtracting two copies of x per side.

The carpet has area of (24-2x)(33-2x)

Cynthia can afford to buy 400 sq ft of carpet

So we set 400 equal to that previous expression and solve for x

(24-2x)(33-2x) = 400

24(33-2x) - 2x(33-2x) = 400

792-48x - 66x + 4x^2 = 400

4x^2 - 114x + 792 = 400

4x^2 - 114x + 792-400 = 0

4x^2 - 114x + 392 = 0

From here, use the quadratic formula to isolate x.

Plug in a = 4, b = -114, c = 392

x = \frac{-b\pm\sqrt{b^2-4ac}}{2a}\\\\x = \frac{-(-114)\pm\sqrt{(-114)^2-4(4)(392)}}{2(4)}\\\\x = \frac{114\pm\sqrt{6724}}{8}\\\\x = \frac{114\pm82}{8}\\\\x = \frac{114+82}{8} \ \text{ or } \ x = \frac{114-82}{8}\\\\x = \frac{196}{8} \ \text{ or } \ x = \frac{32}{8}\\\\x = 24.5 \ \text{ or } \ x = 4\\\\

The two possible solutions are x = 24.5 and x = 4

But if x = 24.5, then 24 - 2x = 24 - 2*24.5 = -25 which isn't possible. We cannot have a negative width or negative length for the carpet.

Luckily x = 4 does work since

24 - 2x = 24 - 2*4 = 16

33 - 2x = 33 - 2*4 = 25

Both results are positive.

Therefore, the carpet has dimensions of <u>16 ft by 25 ft</u>

Check: 16*25 = 400, so the answer is confirmed

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Answer:

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