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bekas [8.4K]
3 years ago
16

The drama club is selling short-sleeved shirts for $5 each, and long-sleeved shirts for $10 each. They hope to sell all of the s

hirts they ordered, to earn a total of $1,750. After the first week of the fundraiser, they sold  1/3 of the short-sleeved shirts and  1/2of the long-sleeved shirts, for a total of 100 shirts.
This system of equations models the situation.
   5x + 10y = 1,750
1/3x + 1/2y = 100
Let x represent the number of short-sleeved shirts ordered and let y represent the number of long-sleeved shirts ordered.
How many short-sleeved shirts were ordered?

How many long-sleeved shirts were ordered?
Mathematics
2 answers:
Sonbull [250]3 years ago
9 0
150 short-sleeved shirts
100 long-sleeved shirts
barxatty [35]3 years ago
4 0

Answer:

150 short-sleeved shirts and 100 long-sleeved shirts.

Step-by-step explanation:

We will use elimination to solve this system of equations.  We will make the coefficients of x the same in order to eliminate them; to do this, we must multiply the bottom equation by 15 (1/3 of 15 is 5, so 15(1/3) = 5):

\left \{ {{5x+10y=1750} \atop {15(\frac{1}{3}x+\frac{1}{2}y=100)} \right. \\\\\left \{ {{5x+10y=1750} \atop {5x+7.5y=1500}} \right.

Subtract the second equation from the first one:

\left \{ {{5x+10y=1750} \atop {-(5x+7.5y=1500)}} \right. \\\\2.5y=250

Divide both sides by 2.5:

2.5y/2.5 = 250/2.5

y = 100

Substitute 100 in for y in the first equation:

5x+10(100) = 1750

5x+1000 = 1750

Subtract 1000 from both sides:

5x+1000 - 1000 = 1750 - 1000

5x = 750

Divide both sides by 5:

5x/5 = 750/5

x = 150

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MakcuM [25]

Answer:

a) w^{13} x^{5} y^{6}

b) \frac{x}{3y^{6} }

Step-by-step explanation:

a) (w^{2} xy^{3} )^{2}(w^{3}x )^{3}

1. Distribute the second power (2) outside the first pair of parenthesis:

(w^{2(2)} x^{2} y^{3(2)} )

= w^{4} x^{2} y^{6} (w^{3}x )^{3}

2. Distribute the third power (3) outside the second pair of parenthesis:

(w^{3(3)} x^{3} )

= w^{4} x^{2} y^{6} w^{9} x^{3}

3. Combine like terms:

w^{13} x^{5} y^{6}

--------------------------------------------

b) \frac{2x^{2} y^{5} }{6xy^{11} }

1. Factor the number 6 (= 2 · 3):

\frac{2x^{2} y^{5} }{2(3)xy^{11} }

2. Cancel the common factor (2):

\frac{x^{2} y^{5} }{3xy^{11} }

3. Cancel out xy^{5} in the numerator an denominator:

\frac{x}{3y^{6} }

hope this helps!

4 0
2 years ago
Can someone help me plz
wolverine [178]

Answer:

75°

Step-by-step explanation:

Recall: SOH CAH TOA

Reference angle = ? = θ

Side length opposite to reference angle = 27

Hypotenuse length = 28

Apply SOH, which is:

sin(\theta) = \frac{Opposite}{Hypotenuse}

Substitute

sin(\theta) = \frac{27}{28}

\theta = sin^{-1}(\frac{27}{28})

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7 0
3 years ago
Your friend incorrectly factors the expression 15x — 20xy as 5x(3— 4xy
nika2105 [10]

Answer:

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Step-by-step explanation:

15x — 20xy ≠ 5x(3— 4xy)

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when you simplify the bracket, you will have

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3 years ago
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X>-82%.................
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Given two points M & N on the coordinate plane, find the slope of MN , and state the slope of the line perpendicular to MN .
telo118 [61]

Answer:

Problem 1)       m = \dfrac{1}{4}     slope_{perpendicular} = -4

Problem 2)      m = \dfrac{1}{3}     slope_{perpendicular} = -3

Step-by-step explanation:

slope = m = \dfrac{y_2 - y_1}{x_2 - x_1}

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slope = m = \dfrac{6 - 4}{9 - 1} = \dfrac{2}{8} = \dfrac{1}{4}

slope_{perpendicular} = \dfrac{-1}{\frac{1}{4}} = -4

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slope = m = \dfrac{4 - 2}{4 - (-2)} = \dfrac{2}{6} = \dfrac{1}{3}

slope_{perpendicular} = \dfrac{-1}{\frac{1}{3}} = -3

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3 years ago
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