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3 years ago

A handbag originally cost $85.00. now it is priced at $68.00. what is the percent of decrease?

Mathematics

2 answers:

notka56 [123]3 years ago

8 0

first you will need to divide 85 by 100

85÷100=0.85

Then divide 68 by 0.85

68÷0.85=80

80 is what percentage $68 is of $85

So what you left with is a 20% discount

Anastasy [175]3 years ago

6 0

[(68-85) divided by 85] x 100%
= -20%
=decreased 20%

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A sheet of paper 90 cm-by-66 cm is made into an open box (i.e. there's no top), by cutting x-cm squares out of each corner and f

NNADVOKAT [17]

Answer:

$26 - \sqrt{181}$ cm

Step-by-step explanation:

The volume of the box is:

V = height * length * width

V = x*(66 - 2*x)*(90 - 2*x)

V = (66*x - 2*x^2)*(90 - 2*x)

V = 5940*x - 132*x^2 - 180*x^2 + 4*x^3

V = 4*x^3 - 312*x^2 + 5940*x

where x is the length of the sides of the squares, in cm.

The mathematical problem is :

Maximize: V = 4*x^3 - 312*x^2 + 5940*x

subject to:

x > 0

2*x < 66 <=> x < 33

In the maximum, the first derivative of V, dV/dx, is equal to zero

dV/dx = 12*x^2 - 624*x + 5940

From quadratic formula

$x = \frac{-b \pm \sqrt{b^2 - 4(a)(c)}}{2(a)}$

$x = \frac{624 \pm \sqrt{(-624)^2 - 4(12)(5940)}}{2(12)}$

$x = \frac{624 \pm \sqrt{104256}}{24}$

$x = \frac{624 \pm \sqrt{2^6*3^2*181}}{24}$

$x = \frac{624 \pm 8*3*\sqrt{181}}{24}$

$x_1 = \frac{624 + 24*\sqrt{181}}{24}$

$x_1 = 26 + \sqrt{181}$

$x_2 = \frac{624 - 24*\sqrt{181}}{24}$

$x_2 = 26 - \sqrt{181}$

But $x_1 > 33$ , then is not the correct answer.

5 0

3 years ago

zoe paid $18.60 in sales tax and tips for her dinner. The sales tax rate is 11%, and she tipped 20%. (the sales tax does not app

arsen [322]

Answer:

$13.97 was the price of the dinner b4 tax and tip

Step-by-step explanation:

18.60 - 11% (1.84) = 16.76

16.76 - 20%(2.79) = 13.97

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3 years ago

Find the length of the third side. If necessary, round to the nearest tenth

Lilit [14]

$\huge\bold{Given:}$

Length of the base = 8

Length of the hypotenuse = 17

$\huge\bold{To\:find:}$

The length of the third side '' $x$ ".

$\large\mathfrak{{\pmb{\underline{\orange{Solution}}{\orange{:}}}}}$

$\longrightarrow{\purple{x\:=\: 15}}$

$\large\mathfrak{{\pmb{\underline{\red{Step-by-step\:explanation}}{\red{:}}}}}$

Using Pythagoras theorem, we have

(Perpendicular)² + (Base)² = (Hypotenuse)²

$\longrightarrow{\blue{}}$ ${x}^{2}$ + (8)² = (17)²

$\longrightarrow{\blue{}}$ ${x}^{2}$ + 64 = 289

$\longrightarrow{\blue{}}$ ${x}^{2}$ = 289 - 64

$\longrightarrow{\blue{}}$ ${x}^{2}$ = 225

$\longrightarrow{\blue{}}$ $x$ = $\sqrt{225}$

$\longrightarrow{\blue{}}$ $x$ = $15$

Therefore, the length of the missing side $x$ is $15$ .

$\huge\bold{To\:verify :}$

$\longrightarrow{\green{}}$ (15)² + (8)² = (17)²

$\longrightarrow{\green{}}$ 225 + 64 = 289

$\longrightarrow{\green{}}$ 289 = 289

$\longrightarrow{\green{}}$ L.H.S. = R. H. S.

Hence verified.

$\huge{\textbf{\textsf{{\orange{My}}{\blue{st}}{\pink{iq}}{\purple{ue}}{\red{35}}{\green{♨}}}}}$

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Lina20 [59]

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4 years ago

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Step-by-step explanation:

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