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2 years ago

Section 2 Topic 3 Homework

Mathematics

1 answer:

VMariaS [17]2 years ago

4 0

Answer:

65$

Step-by-step explanation:

Section 2 Topic 3 Homework

Question 2 of 4

Miguel spends $100 on books, five of which are hardcover and the remaining four are paperback. The prices at the bookstore are based

on whether the book is hardcover or paperback. It charges $2 less for paperback books than for hardcover books. What is the price for

hardcover books?

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The value of

marusya05 [52]

$\large\underline{\sf{Solution-}}$

We have to find out the value of the fraction.

Let us assume that:

$\sf \longmapsto x =2 + \dfrac{1}{2 + \dfrac{1}{2 + \dfrac{1}{2 + ... \infty} } }$

We can also write it as:

$\sf \longmapsto x =2 + \dfrac{1}{x}$

$\sf \longmapsto x =\dfrac{2x + 1}{x}$

$\sf \longmapsto {x}^{2} =2x + 1$

$\sf \longmapsto {x}^{2} - 2x - 1 = 0$

Comparing the given equation with ax² + bx + c = 0, we get:

$\sf \longmapsto\begin{cases} \sf a =1 \\ \sf b = - 2 \\ \sf c = - 1 \end{cases}$

By quadratic formula:

$\sf \longmapsto x = \dfrac{ - b \pm \sqrt{ {b}^{2} - 4ac } }{2a}$

$\sf \longmapsto x = \dfrac{2 \pm \sqrt{ {( - 2)}^{2} - 4(1)( - 1)} }{2 \times 1}$

$\sf \longmapsto x = \dfrac{2 \pm \sqrt{4 + 4} }{2 \times 1}$

$\sf \longmapsto x = \dfrac{2 \pm \sqrt{8} }{2}$

$\sf \longmapsto x = \dfrac{2 \pm2 \sqrt{2} }{2}$

$\sf \longmapsto x = 1 \pm\sqrt{2}$

$\sf \longmapsto x = \begin{cases} \sf 1 + \sqrt{2} \\ \sf 1 - \sqrt{2} \end{cases}$

But "x" cannot be negative. Therefore:

$\sf :\implies x = 1 + \sqrt{2}$

So, the value of the fraction is 1 + √2.

4 0

2 years ago

Given that 3x-y : x+2y = 2 : 5, Determine the ratio x:y

N76 [4]

Answer:

x : y = 9 : 13

Step-by-step explanation:

Given that

3x - y : x + 2y = 2 : 5

Express the ratio in fractional form, that is

$\frac{3x-y}{x+2y}$ = $\frac{2}{5}$ ( cross- multiply )

5(3x - y) = 2(x + 2y) ← distribute parenthesis on both sides )

15x - 5y = 2x + 4y ( subtract 2x from both sides )

13x - 5y = 4y ( add 5y to both sides )

13x = 9y ( divide both sides by 13 )

x = $\frac{9}{13}$ y ( divide both sides by y )

$\frac{x}{y}$ = $\frac{9}{13}$ , that is

x : y = 9 : 13

7 0

3 years ago

A system of linear equations is given by the tables.

almond37 [142]

Answer:

-1

x=4,y=11 (same in both equations)

5 0

2 years ago

You work 40 hours/week for 50 weeks and are given the option to be paid hourly or to go on salary. In which situation will you e

sasho [114]

The answer is:

$30,000/year with a 10% bonus

4 0

2 years ago

What is (2.5 x 10 to the third power) (6 x 10 to the fourth power)

Gelneren [198K]

Answer:

2,500) (60,000

brain pls

Step-by-step explanation:

5 0

2 years ago