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3 years ago

14

Bracelets use 1/4 yard of string and 10 charms. You have 9/10 yards string and 72 charms. If you use all the string what fractio

n of the 72 charms did you use?

1 answer:

soldier1979 [14.2K]3 years ago

4 0

Answer:

1/2 of the charms used

Step-by-step explanation:

<u>Ratio of string and charms:</u>

1/4 yard of string ⇒ 10 charms
9/10 yard of string ⇒ x

<u>Solve by cross-multiplication</u>

x = 10*9/10 ÷ 1/4
x = 36 charms

<u>The fraction of all charms to number of used:</u>

72/36 = 1/2

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Please include work!

geniusboy [140]

Answer:

x = ± 4

y = - 2

Step-by-step explanation:

y = 0.5x² - 10 ------------------------(I)

y = -x² + 14 ------------------------(II)

Substitute the y value in equation (II)

0.5x² - 10 = -x² + 14 {Add x² to both sides}

0.5x² + x² -10 = 14 {combine like terms}

1.5x² - 10 = 14 {Add 10 to both sides}

1.5x² = 14 + 10

1.5x² = 24 {Divide both sides by 1.5}

1.5x²/1.5 = 24/1.5

x² = 16

x = ±4

Substitute x = 4 in (I)

y = 0.5 * 4² - 10

= 0.5*16 - 10

= 8- 10

y = -2

Substitute x = -4 in (I)

y = 0.5 * (-4)² - 10

= 0.5*16 - 10

= 8- 10

y = -2

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3 years ago

Ivahew [28]

ANSWER

$x=\frac{2-\sqrt{10}} {3}$

or

$x=\frac{\sqrt{10}+2} {3}$

We have

$3x^2-4x-2=0$

Since we cannot factor easily, we complete the square.

Adding 2 to both sides give,

$3x^2-4x=2$

Dividing through by 3 gives

$x^2-\frac{4}{3}x= \frac{2}{3}$

Adding $(-\frac{2}{3})^2$ to both sides gives

$x^2-\frac{4}{3}x+(-\frac{2}{3})^2= \frac{2}{3}+(-\frac{2}{3})^2$

The expression on the Left Hand side is a perfect square.

$(x-\frac{2}{3})^2= \frac{2}{3}+\frac{4}{9}$

$\Rightarrow (x-\frac{2}{3})^2= \frac{10}{9}$

$\Rightarrow (x-\frac{2}{3})=\pm \sqrt{\frac{10}{9}}$

$\Rightarrow (x)=\frac{2}{3} \pm {\frac{\sqrt{10}}{3}$

Splitting the plus or minus sign gives

$x=\frac{2- \sqrt{10}} {3}$

or

$x=\frac{\sqrt{10}+2} {3}$

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