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Alex787 [66]
3 years ago
12

A 9-kilogram bag of sugar cost $27.54. what is the unit price ?

Mathematics
1 answer:
shusha [124]3 years ago
4 0

Answer:

$3.06

Step-by-step explanation:

1 kg = $27.54

27.54/9 kilogram

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Ivan
X= 100 would be the answer
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Write an equation (a) in slope-intercept form and (b) in standard form for the line passing through (-3,5) and parallel to x + 4
Dmitry [639]

Answer:

  • \boxed{\sf Standard-form :x + 4y -17=0 }\\

  • \boxed{\sf Slope-intercept\ form :y =\dfrac{-1}{4}x +\dfrac{17}{4}}

Step-by-step explanation:

Here a equation of the line is given to us and we need to find out the equation of line which passes through the given point and parallel to the given line , the given equation is ,

\longrightarrow x + 4y = 7\\

Firstly convert it into <em>s</em><em>l</em><em>o</em><em>p</em><em>e</em><em> </em><em>i</em><em>n</em><em>t</em><em>e</em><em>r</em><em>c</em><em>e</em><em>p</em><em>t</em><em> </em><em>f</em><em>o</em><em>r</em><em>m</em><em> </em>of the line which is <u>y</u><u> </u><u>=</u><u> </u><u>m</u><u>x</u><u> </u><u>+</u><u> </u><u>x</u><u> </u>, as ;

\longrightarrow 4y = -x + 7  \\

\longrightarrow y =\dfrac{-x}{4}+\dfrac{7}{4}\\

On comparing it to <em>y</em><em> </em><em>=</em><em> </em><em>m</em><em>x</em><em> </em><em>+</em><em> </em><em>c</em><em> </em>, we have ,

\longrightarrow m =\dfrac{-1}{4}\\

\longrightarrow c =\dfrac{7}{4}\\

Now as we know that the <em>s</em><em>l</em><em>o</em><em>p</em><em>e</em><em> </em><em>o</em><em>f</em><em> </em><em>t</em><em>w</em><em>o</em><em> </em><em>p</em><em>a</em><em>r</em><em>a</em><em>l</em><em>l</em><em>e</em><em>l</em><em> </em><em>l</em><em>i</em><em>n</em><em>e</em><em>s</em><em> </em><em>i</em><em>s</em><em> </em><em>s</em><em>a</em><em>m</em><em>e</em><em> </em>. Therefore the slope of the parallel line will be ,

\longrightarrow m_{||)}=\dfrac{-1}{4}\\

Now we may use <em>p</em><em>o</em><em>i</em><em>n</em><em>t</em><em> </em><em>s</em><em>l</em><em>o</em><em>p</em><em>e</em><em> </em><em>f</em><em>o</em><em>r</em><em>m</em><em> </em>of the line as ,

\longrightarrow y - y_1 = m(x-x_1) \\

On substituting the respective values ,

\longrightarrow y - 5 =\dfrac{-1}{4}\{ x -(-3)\}\\

\longrightarrow y -5=\dfrac{-1}{4}(x+3)\\

\longrightarrow 4(y -5 ) =-1(x +3) \\

\longrightarrow 4y -20 = - x -3 \\

\longrightarrow x + 4y -20+3=0\\

\longrightarrow \underset{Standard \ Form }{\underbrace{\underline{\underline{ x + 4y -17=0}}}} \\

Again the equation can be rewritten as ,

\longrightarrow y - 5 = \dfrac{-1}{4}(x +3) \\

\longrightarrow y = \dfrac{-1}{4}x -\dfrac{3}{4}+5  \\

\longrightarrow y = \dfrac{-1}{4}x -\dfrac{20-3}{4}  \\

\longrightarrow \underset{Slope-Intercept\ form }{\underbrace{\underline{\underline{  y =\dfrac{-1}{4}x +\dfrac{17}{4}}}}}\\

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2 years ago
2x + 4y = 22<br> What is the answer?
Goryan [66]

Answer:

Step-by-step explanation:

y=-\frac{1}{2}x+\frac{11}{2}

5 0
2 years ago
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The sum of 27 and seven times a number is 125. Find the number.
zysi [14]
The number is 14

Here's the solution:

Let the number be x

According to the question,

27+7x=125

//Subtract 27 from both the sides

7x=125-27

7x=98

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x=98/7

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3 years ago
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Vladimir79 [104]

Answer:

<h2>A. 4t² - 32t + 64</h2>

Step-by-step explanation:

Instead of x put (t - 3) in the equation of the function f(x) = 4x² - 8x + 4:

f(t - 3) = 4(t - 3)² - 8(t - 3) + 4

<em>use (a - b)² = a² - 2ab + b² and the distributive property a(b + c) = ab + ac</em>

f(t - 3) = 4(t² - (2)(t)(3) + 3²) + (-8)(t) + (-8)(-3) + 4

f(t - 3) = 4(t² - 6t + 9) - 8t + 24 + 4

f(t - 3) = (4)(t²) + (4)(-6t) + (4)(9) - 8t + 28

f(t - 3) = 4t² - 24t + 36 - 8t + 28

f(t - 3) = 4t² + (-24t - 8t) + (36 + 28)

f(t - 3) = 4t² - 32t + 64

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3 years ago
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