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3 years ago

If x varies directly with y and x=3.5 when y=14 find x when y=18

1 answer:

4 0

$\bf \qquad \qquad \textit{direct proportional variation}
\\\\
\textit{\underline{x} varies directly with \underline{y}}\qquad \qquad x=ky\impliedby 
\begin{array}{llll}
k=constant\ of\\
\qquad variation
\end{array}\\\\
-------------------------------\\\\
\textit{we also know that }
\begin{cases}
x=3.5\\
y=14
\end{cases}\implies 3.5=k14\implies \cfrac{3.5}{14}=k
\\\\\\
\cfrac{1}{4}=k\qquad therefore\qquad \boxed{x=\cfrac{1}{4}y}
\\\\\\
\textit{when y = 18, what is \underline{x}?}\qquad x=\cfrac{1}{4}(18)$

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The measure of one angle of an octagon is twice the measure of one of the other seven congruent angles. What is the measure of e

kondaur [170]

Each one of the smaller angles x = 120 degrees and the larger angle = 2x = 2 × 120 = 240 degrees

<h3>How to find the angle of octagon?</h3>

The angle of an octagon can be found as follows;

An octagon is a polygon that has 8 sides.

The sum of angles in an octagon is 1080 degrees.

Therefore,

x + x + x + x + x + x + x + 2x = 1080

Hence,

9x = 1080

divide both sides by 9

x = 1080 / 9

x = 120

Therefore, each one of the smaller angles x = 120 degrees and the larger angle = 2x = 2 × 120 = 240 degrees

learn more on octagon here:brainly.com/question/8517157

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2 years ago

How can you rewrite 3(2-b) using the distributive property?

77julia77 [94]

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3 years ago

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I have no clue how to do this please help

mel-nik [20]

Answer:

Max = (6,0); min = (-2, 4)

Step-by-step explanation:

1. Summarize the constraints

$\text{Constraints} = \begin{cases}(a)\qquad 2x - y & \leq 12\\(b)\qquad 4x+ 2y & \geq 0\\(c) \qquad x + 2y & \leq 6\\ \end{cases}$

2. Optimization equation

z = 5x + 2y

3. Graph the constraints to identify the feasible region

See the figure below.

The "TRUE" regions for each graph are the shaded areas to the side of the line indicated by the arrows.

The "feasibility region" is the dark green area where all three areas overlap and all three conditions are satisfied.

5. Determine the points of intersection among the constraints

(i) Constraints (a) and (b)

$\begin{array}{rcr}2x - y & = & 12\\4x + 2y & = & 0\\4x - 2y & = & 24\\8x&=&24\\x & = & \mathbf{3}\\6 - y & = & 12\\-y & = &6\\y & = & \mathbf{-6}\\\end{array}\\$

The lines intersect at (3,-6).

(ii) Constraints (a) and (c)

$\begin{array}{rcr}2x - y & = & 12\\x + 2y & = & 6\\4x - 2y & = &24\\5x & = & 30\\x & = & \mathbf{6}\\6 + 2y & = & 6\\2y & = &0\\y & = & \mathbf{0}\\\end{array}$

The lines intersect at (6,0).

(iii) Constraints (b) and (c)

$\begin{array}{rcr}4x+ 2y &= & 0\\x + 2y &=& 6\\3x & = & -6\\x & = & \mathbf{-2}\\-2 +2y & = & 6\\2y & = &8\\y & = & \mathbf{4}\\\end{array}$

The lines intersect at (-2,4).

6. Determine the x- and y-intercepts of the feasible region

The five black dots at (3,-6), (6,0), and (-2,4) are the vertices of the polygon that represents the feasible region.

Each vertex is a possible maximum or minimum of z.

7. Calculate the maxima and minima

Calculate z at each of the vertices.

(i) At (-2,4)

z = 5x + 2y = 5(-2) + 2(4) = -10 + 8 = 2

(ii) At (3,-6)

z = 5(3) + 2(-6) = 15 - 12 = 3

(iii) At (6,0)

z = 5(6)+ 2(0) = 30 + 0 = 30

The maximum of z occurs at (6,0).

The minimum of z occurs at (-2, 4).

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3 years ago

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Firdavs [7]

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3 years ago

What percent of 160 is 56?

kakasveta [241]

160 = 100%
56 = x%

then you would cross multiply

160x = 56(100)

160x = 5600

x = $\frac{5600}{160}$

x = 35

so

35% of 160 is 56.

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3 years ago

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