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3 years ago

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The owner of a lemonade stand that costs 2 dollars per gallon with juice that costs 7 dollars per gallon. He gets 20 gallons of

punch that costs 4 dollars per gallon. How much of each juice does he use?

1 answer:

Karo-lina-s [1.5K]3 years ago

7 0

Answer:

Step-by-step explanation:

Your answer

62.222 gallons

Mark it as Brainlist answer. Follow me.

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What fraction is equivalent to 30/360?

Firdavs [7]

Answer:

1/12

Step-by-step explanation:

Given that

30/360 to lowest fraction equivalent

Now, we can write 30 as 3×10

Also, we can write 360 as 36×10

Then, we have

(3×10)/(36×10)

Then, 10 cancel 10, we are left with

3/36

Also we can write 36 as 12×3

Then, we have

3/(12×3)

Also, 3 cancel 3, we are left with

1/12

Then the lowest fraction is 1 / 12

1/12

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2 years ago

Read 2 more answers

What is the answer to try and find the Surface area of a triangular prism for this question

Drupady [299]

Answer: The answer is 288.99

Step-by-step explanation:

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2 years ago

Use Cramer Rule to solve the following system: 8x−5y=70 and 9x+7y=3

nlexa [21]

Answer:

$(x,y) = (5,-6)$

Step-by-step explanation:

$\underline{\textbf{Determinant of a matrix.}}\\\\\text{For a}~ 2 \times 2 ~ \text{matrix,}\\\\\begin{vmatrix} a_1&a_2\\b_1&b_2 \end{vmatrix} = a_1b_2 - a_2b_1\\\\\\\text{For a}~ 3 \times 3 ~ \text{matrix,}\\\\\begin{vmatrix} a_1&a_2&a_3\\ b_1&b_2&b_3\\ c_1&c_2&c_3 \end{vmatrix} = a_1\begin{vmatrix} b_2&b_3\\c_2&c_3 \end{vmatrix} - a_2 \begin{vmatrix} b_1&b_3\\c_1&c_3 \end{vmatrix}+ a_3 \begin{vmatrix} b_1&b_2\\c_1&c_2 \end{vmatrix}\\\\\\$

$~~~~~~~~~~~~~~~~~~=a_1(b_2c_3-b_3c_2) -a_2(b_1c_3-b_3c_1) +a_3(b_1c_2-b_2c_1)$

$\underline{\textbf{Cramer's Rule to solve a system of two equations.}}\\\\\text{Consider the system of two equations:}\\\\~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~a_1x + b_1 y= c_1\\\\~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~a_2x +b_2 y = c_2\\\\\text{Here,}\\\\x = \dfrac{D_x}{D}= \dfrac{\begin{vmatrix} c_1&b_1\\c_2&b_2 \end{vmatrix}}{\begin{vmatrix} a_1&b_1\\a_2&b_2 \end{vmatrix}}\\\\\\ y= \dfrac{D_y}{D}= \dfrac{\begin{vmatrix} a_1&c_1\\a_2&c_2 \end{vmatrix}}{\begin{vmatrix} a_1&b_1\\a_2&b_2 \end{vmatrix}}\\\\$

$\underline{\textbf{Solution:}}\\\\~~~~~~~~~~~~~~~~~~~~~~~8x-5y = 70~~~~~~...(i)\\\\~~~~~~~~~~~~~~~~~~~~~~~9x +7y = 3~~~~~~~...(ii)\\\\\text{Applying Cramer's rule:}\\\\x = \dfrac{D_x}{D}\\\\\\~~=\dfrac{\begin{vmatrix} 70& -5 \\3&7 \end{vmatrix}}{\begin{vmatrix} 8& -5\\ 9& 7\end{vmatrix}}\\\\\\~~=\dfrac{70(7) -(-5)(3)}{(8)(7)-(-5)(9)}\\\\\\~~=\dfrac{490+15}{56+45}\\\\\\~~=\dfrac{505}{101}\\\\\\~~=5$

$y = \dfrac{D_y}{D}\\\\\\~~=\dfrac{\begin{vmatrix} 8& 70 \\9&3 \end{vmatrix}}{\begin{vmatrix} 8& -5\\ 9& 7\end{vmatrix}}\\\\\\~~=\dfrac{(8)(3) -(70)(9)}{(8)(7)-(-5)(9)}\\\\\\~~=\dfrac{24-630}{56+45}\\\\\\~~=-\dfrac{606}{101}\\\\\\~~=-6$

$\textbf{Hence, the solution to the system of equation is}~ (x,y) = (5,-6)$

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1 year ago

Which points are solutions to the system of inequalities? Select ALL that apply.

ZanzabumX [31]

Answer:

0,0

2,-1

-2,4

Step-by-step explanation:

3 0

3 years ago

Solve by substitution 3x+y=3 and 7x+2y=1

balu736 [363]

3x + y = 3

7x + 2y = 1

First isolate one of the variables (x or y) in one of the equations.

Isolate "y" in the first equation(because it is the easiest to isolate) and substitute it into the second equation.

3x + y = 3 Subtract 3x on both sides

3x - 3x + y = 3 - 3x

y = 3 - 3x

7x + 2y = 1

7x + 2(3 - 3x) = 1 [since y = 3 - 3x, you can substitute (3-3x) for "y"]

Multiply/distribute 2 into (3 - 3x)

7x + (3(2) - 3x(2)) = 1

7x + 6 - 6x = 1

x + 6 = 1 Subtract 6 on both sides

x = -5

Now that you know "x", substitute it into one of the equations (I will do both)

3x + y = 3

3(-5) + y = 3 [since x = -5, you can plug in -5 for "x"]

-15 + y = 3 Add 15 on both sides

y = 18

7x + 2y = 1

7(-5) + 2y = 1

-35 + 2y = 1 Add 35 on both sides

2y = 36 Divide 2 on both sides

y = 18

x = -5, y = 18 or (-5, 18)

5 0

2 years ago