Colton purchased a sofa originally priced at $540 for 30% off. What was the sale price of the sofa?

Mathematics

2 answers:

ss7ja [257]3 years ago

7 0

To find the amount you must multiply percentage by the original number. The correct answer would be $162

horsena [70]3 years ago

4 0

540 * .30 is 162 so it would be $162.

You might be interested in

One of the legs of a right triangle is twice as long as the other, and the perimeter of the triangle is 28. Find the length of t

Nutka1998 [239]

1) If we let the lengths of the legs be x and 2x, then by the Pythagorean theorem,

$x+2x+\sqrt{x^{2}+(2x)^{2}}=28\\3x+x\sqrt{5}=28\\x(3+\sqrt{5})=28\\x=\frac{28}{3+\sqrt{5}} \cdot \frac{3-\sqrt{5}}{3-\sqrt{5}}=21-7\sqrt{5}$

This means that the length of the hypotenuse is:

$\sqrt{5}(21-7\sqrt{5})=\boxed{21\sqrt{5}-35}$

2) (Diagram attached) We know that

$\cos 51^{\circ}=\frac{x}{58}\\x=58 \cos 51^{\circ} \approx \boxed{36.5}$ (in cm)

3) From the Pythagorean identity,

$\sin^{2}\left (\arccos \frac{5}{13} \right)+\cos^{2} \left (\arccos \frac{5}{13} \right)=1\\\left(\frac{5}{13} \right)^{2}+\sin^{2} \left (\arccos \frac{5}{13} \right)=1\\\frac{25}{169}+\sin^{2} \left (\arccos \frac{5}{13} \right)=1\\\sin^{2} \left (\arccos \frac{5}{13} \right)=\frac{144}{169}\\\sin \left (\arccos \frac{5}{13} \right)=\boxed{\frac{12}{13}}$