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3 years ago

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A carpenter has several boards of equal length. He cuts 3/5 of each broads.After cutting the boards the carpenter notices that h

e has enough pieces left over to make up the same length as 4 of the original board. How many boards did the carpenter star with?

1 answer:

Bess [88]3 years ago

4 0

Answer:

10

Step-by-step explanation:

Length of boards are the same :

Let number of boards = x

Fraction cut from each board = 3/5

Total fraction cut = 3/5 * x

Fraction left = 1 - 3/5 = 2/5

Total fraction left = 2/5 * x

Total pieces left = 2/5 * x = 4 times length of original board

Note ; original fraction = 1

Hence,

2/5 * x = 4 * 1

2x / 5 = 4

2x = 4 * 5

2x = 20

x = 20 / 2

x = 10

Number of boards = 10

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Determine whether each expression is equivalent to 49^2t – 0.5.

vampirchik [111]

Answer:

None of the expression are equivalent to $49^{(2t - 0.5)}$

Step-by-step explanation:

Given

$49^{(2t - 0.5)}$

Required

Find its equivalents

We start by expanding the given expression

$49^{(2t - 0.5)}$

Expand 49

$(7^2)^{(2t - 0.5)}$

$7^2^{(2t - 0.5)}$

Using laws of indices: $(a^m)^n = a^{mn}$

$7^{(2*2t - 2*0.5)}$

$7^{(4t - 1)}$

This implies that; each of the following options A,B and C must be equivalent to $49^{(2t - 0.5)}$ or alternatively, $7^{(4t - 1)}$

A. $\frac{7^{2t}}{49^{0.5}}$

Using law of indices which states;

$a^{mn} = (a^m)^n$

Applying this law to the numerator; we have

$\frac{(7^{2})^{t}}{49^{0.5}}$

Expand expression in bracket

$\frac{(7 * 7)^{t}}{49^{0.5}}$

$\frac{49^{t}}{49^{0.5}}$

Also; Using law of indices which states;

$\frac{a^{m}}{a^n} = a^{m-n}$

$\frac{49^{t}}{49^{0.5}}$ becomes

$49^{t-0.5}}$

This is not equivalent to $49^{(2t - 0.5)}$

B. $\frac{49^{2t}}{7^{0.5}}$

Expand numerator

$\frac{(7*7)^{2t}}{7^{0.5}}$

$\frac{(7^2)^{2t}}{7^{0.5}}$

Using law of indices which states;

$(a^m)^n = a^{mn}$

Applying this law to the numerator; we have

$\frac{7^{2*2t}}{7^{0.5}}$

$\frac{7^{4t}}{7^{0.5}}$

Also; Using law of indices which states;

$\frac{a^{m}}{a^n} = a^{m-n}$

$\frac{7^{4t}}{7^{0.5}}$ = $7^{4t - 0.5}$

This is also not equivalent to $49^{(2t - 0.5)}$

C. $7^{2t}\ *\ 49^{0.5}$

$7^{2t}\ *\ (7^2)^{0.5}$

$7^{2t}\ *\ 7^{2*0.5}$

$7^{2t}\ *\ 7^{1}$

Using law of indices which states;

$a^m*a^n = a^{m+n}$

$7^{2t+ 1}$

This is also not equivalent to $49^{(2t - 0.5)}$

6 0

4 years ago

2.8 meters linen divided into 45 cm pieces = # of pieces and waste

pogonyaev

2.8 meter= 2800cms

To solve this, we can create a simple algebraic equation:
45x=2800
Divide both sides by 45.
(45x)/45=(2800)/45
x=62.222

You can make 62 full pieces.

To find the waste, multiply the numbers of pieces by the length of each.
62*45
=2790
2800-<span>2790
=10 centimeters

There would be 10 centimeters of wasted linen.

Hope this helps!
-Benjamin</span>

6 0

3 years ago

Solving Quadratic Equations using the Square Root Property

Afina-wow [57]

Answer:

$x = -2$ or $x = -5$

Step-by-step explanation:

You need to complete the square before you can take the square root of both sides.

$x^2 + 7x + 10 = 0$

Subtract 10 from both sides.

$x^2 + 7x = -10$

To complete the square, you need to add the square of half of the x-term coefficient to both sides.

The x-term coefficient is 7. Half of that is 7/2. Square it to get 49/4. Now we add 49/4 to both sides of the equation.

$x^2 + 7x + \dfrac{49}{4} = -10 + \dfrac{49}{4}$

$(x + \dfrac{7}{2})^2 = -\dfrac{40}{4} + \dfrac{49}{4}$

$(x + \dfrac{7}{2})^2 = \dfrac{9}{4}$

Now we use the square root property, if

$x^2 = k$ , then

$x = \pm \sqrt{k}$

$x + \dfrac{7}{2} = \pm \sqrt{\dfrac{9}{4}}$

$x + \dfrac{7}{2} = \pm \dfrac{3}{2}$

$x + \dfrac{7}{2} = \dfrac{3}{2}$ or $x + \dfrac{7}{2} = -\dfrac{3}{2}$

$x = -\dfrac{4}{2}$ or $x = -\dfrac{10}{2}$

$x = -2$ or $x = -5$

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3 years ago

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s344n2d4d5 [400]

Answer: Length = 15 meters

Width = 2 meters

Step-by-step explanation:

Perimeter of a rectangle = 2l + 2w

Area of a rectangle = l × w

where l = length

w = width

Therefore,

2l + 2w = 34 ...... i

l × w = 30 ........ ii

From equation i

2l + 2w = 34

Divide through by 2.

l + w = 17 ...... iii

Then, l = 17 - w ........ iv

Put equation iv into ii

l × w = 30

(17 - w) × w = 30

17w - w² = 30

w² - 17w + 30 = 0

w² - 15w - 2w + 30 = 0

w(w - 15) - 2(w - 15) = 0

(w - 2) = 0

w = 0 + 2 = 2

w - 15 = 0

w = 0 + 15 = 15

Length = 15 meters

Width = 2 meters

6 0

3 years ago

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iogann1982 [59]

Answer:

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Step-by-step explanation:

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