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Svetlanka [38]
3 years ago
12

There are 45 new houses being built in a neighborhood. Last month, 1/3 of them were sold. This month, 1/5 of the remaining house

s were sold. How many houses are left be sold?
Mathematics
2 answers:
Nastasia [14]3 years ago
6 0
45 new houses...
1/3 were sold......1/3(45) = 45/3 = 15 houses sold.....leaving 45 - 15 = 30 houses left. 1/5 of remaining houses sold....1/5(30) = 30/5 = 6...so 6 more houses were sold.....leaving 30 - 6 = 24 houses

24 houses are left <==
sertanlavr [38]3 years ago
3 0
45(1-1/3)(1-1/5)

45(2/3)(4/5)

(45*2*4)/(3*5)

360/15

24
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Mumz [18]

Answer:

\textsf{12.} \quad y = 6x - 5

\textsf{17.} \quad y=-\dfrac{1}{4}x-2

Step-by-step explanation:

<h3><u>Question 12</u></h3>

Find the slope of the line by substituting two points from the given table into the slope formula.

<u>Define the points</u>:

  • Let (x₁, y₁) = (2, 7)
  • Let (x₂, y₂) = (3, 13)

\implies \textsf{slope}\:(m)=\dfrac{y_2-y_1}{x_2-x_1}=\dfrac{13-7}{3-2}=\dfrac{6}{1}=6

Substitute the found slope and point (2, 7) into the point-slope formula to create an equation of the line:

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

\implies y-7=6(x-2)

\implies y-7=6x-12

\implies y=6x-5

<h3><u>Question 17</u></h3>

Given:

  • f(4) = 3
  • f(0) = -2

Therefore, two points on the line are:

  • (4, -3)
  • (0, -2)

The y-intercept is the y-value when x = 0.

Therefore, the y-intercept of the line is -2.

\boxed{\begin{minipage}{6.3 cm}\underline{Slope-intercept form of a linear equation}\\\\$y=mx+b$\\\\where:\\ \phantom{ww}$\bullet$ $m$ is the slope. \\ \phantom{ww}$\bullet$ $b$ is the $y$-intercept.\\\end{minipage}}

Substitute the y-intercept and the point (4, 3) into the slope-intercept formula and solve for <em>m</em> to find the slope:

\implies y=mx+b

\implies -3=m(4)-2

\implies -1=4m

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

Therefore, the equation of the line is:

y=-\dfrac{1}{4}x-2

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