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2 years ago

At a fabric store, fabrics are sold by the yard. A dressmaker spent $36.35 on 4.25 yards of

Mathematics

1 answer:

ArbitrLikvidat [17]2 years ago

8 0

Answer:

Silk = x = 1.5 yards

Cotton = y = 2.75 yards

Step-by-step explanation:

x + y = 4.25

16.90x + 4y = 36.35

1. The solution to the equation represent number of yards of silk and number of yards of cotton bought.

x + y = 4.25 (1)

16.90x + 4y = 36.35 (2)

Multiply (1) by 4

4x + 4y = 17 (3)

16.90x + 4y = 36.35 (2)

Subtract (3) from (2)

16.90x - 4x = 36.35 - 17

12.90x = 19.35

Divide both sides by 12.90

x = 19.35 / 12.90

= 1.5

x = 1.5 yards

Substitute x = 1.5 yards into (1)

x + y = 4.25

1.5 + y = 4.25

y = 4.25 - 1.5

= 2.75

y = 2.75 yards

Silk = x = 1.5 yards

Cotton = y = 2.75 yards

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Answer:

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Step-by-step explanation:

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2 years ago

Find the equation of the line that passes through (1, -1) and is parallel to

daser333 [38]

keeping in mind that parallel lines have exactly the same slope, let's check for the slope of the equation above

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so we're really looking for the equation of a line with a slope of -2 and that passes through (1 , -1)

$(\stackrel{x_1}{1}~,~\stackrel{y_1}{-1})\qquad \qquad \stackrel{slope}{m}\implies -2 \\\\\\ \begin{array}{|c|ll} \cline{1-1} \textit{point-slope form}\\ \cline{1-1} \\ y-y_1=m(x-x_1) \\\\ \cline{1-1} \end{array}\implies y-\stackrel{y_1}{(-1)}=\stackrel{m}{-2}(x-\stackrel{x_1}{1}) \\\\\\ y+1=-2x+2\implies y=-2x+1$

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2 years ago

Find parametric equations for the path of a particle that moves along the circle x2 + (y − 1)2 = 16 in the manner described. (En

ArbitrLikvidat [17]

Answer:

a) $x = 4\cdot \cos t$ , $y = 1 + 4\cdot \sin t$ , b) $x = 4\cdot \cos t$ , $y = 1 + 4\cdot \sin t$ , c) $x = 4\cdot \cos \left(t+\frac{\pi}{2} \right)$ , $y = 1 + 4\cdot \sin \left(t + \frac{\pi}{2} \right)$ .

Step-by-step explanation:

The equation of the circle is:

$x^{2} + (y-1)^{2} = 16$

After some algebraic and trigonometric handling:

$\frac{x^{2}}{16} + \frac{(y-1)^{2}}{16} = 1$

$\frac{x^{2}}{16} + \frac{(y-1)^{2}}{16} = \cos^{2} t + \sin^{2} t$

Where:

$\frac{x}{4} = \cos t$

$\frac{y-1}{4} = \sin t$

Finally,

$x = 4\cdot \cos t$

$y = 1 + 4\cdot \sin t$

a) $x = 4\cdot \cos t$ , $y = 1 + 4\cdot \sin t$ .

b) $x = 4\cdot \cos t$ , $y = 1 + 4\cdot \sin t$ .

c) $x = 4\cdot \cos t''$ , $y = 1 + 4\cdot \sin t''$

Where:

$4\cdot \cos t' = 0$

$1 + 4\cdot \sin t' = 5$

The solution is $t' = \frac{\pi}{2}$

The parametric equations are:

$x = 4\cdot \cos \left(t+\frac{\pi}{2} \right)$

$y = 1 + 4\cdot \sin \left(t + \frac{\pi}{2} \right)$

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2 years ago

I need help with this one <img src="https://tex.z-dn.net/?f=%20%5Cfrac%7B1%7D%7B3%7D%20" id="TexFormula1" title=" \frac{1}{3} "

Vanyuwa [196]

To solve this questions, we can turn 2 into a fractions.

2 as a fraction is 2/1 (because 2 divide by 1 is still 2)
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1/3 ÷ 2/1
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= 1/6 (1 x 1 / 3 x 6)

Or 0.16666.. as a decimal

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2 years ago

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Aneli [31]

Answer:

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Step-by-step explanation:

You have to put square root of 36 in one box and square root of 5 in the other box.

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2 years ago

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