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Alex_Xolod [135]
4 years ago
10

Simplify the following expression. 20 points !!!!

Mathematics
1 answer:
Marrrta [24]4 years ago
6 0

Answer:

a^(2)/e^(7)b^(2)c

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The areas of two similar triangles are 72dm2 and 50dm2. The sum of their perimeters is 226dm. What is the perimeter of each of t
zloy xaker [14]

Answer:

103=  p small

plarge = 123

Step-by-step explanation:

We know that the the ratio of the areas is the scale factor squared/

Larger triangle over smaller triangle

72

----- = scale factor ^2

50

simplify by dividing by 2 on top and bottom

36

----- = scale factor ^2

25

Take the square root of each side

sqrt(36)

-------------- = sqrt(scale factor ^2)

sqrt(25)

6

-------------- = scale factor

5

The ratio of the perimeters is the scale factor

p large             6

-------------- = ----------------

 p small                5

Using cross products

6 p large = 5 p small

We know the sum is 226

p large + p small = 226

p large = 226 - p small

We have 2 equation and 2 unknowns

6 p large = 5 p small

Substitute for p large

6 (226 - p small) = 5 p small

1356 - 6 p small = 5 p small

Add 6 p small to each side

1356 = 11 p small

divide by 11

1356/11 =  p small

P large = 226-1356/11

p large = 2486/11-1356/11

plarge = 1130/11

The solution requires whole number answers so

1356/11 =  p small

123.27 which rounds to 123

plarge = 1130/11

plarge = 102.7272 = 103

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Step-by-step explanation:

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2 years ago
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CD has the endpoints C(3, 2) and D(–5, –2). Charlie wants to place the point E at the point that partitions this line segment in
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So ... notice the picture below... the ratio is 3:1 from C to D, meaning the segment CE takes 3 units, whilst the ED segment takes 1

anyhow

\bf \textit{internal division of a line segment}&#10;\\ \quad \\\\&#10;C(3,2)\qquad D(-5,-2)\qquad&#10;ratio1=3\qquad ratio2=1\qquad 3:1&#10;\\\\\\&#10;\cfrac{C\underline{ E }}{\underline{ E }D}=\cfrac{ratio1}{ratio2}\implies &#10;ratio2\cdot C=ratio1\cdot D&#10;\\\\\\&#10;1(3,2)=3(-5,-2)&#10;\\ \quad \\\\&#10;{{ E=\left(\cfrac{\textit{sum of "x" values}}{ratio1+ratio2}\quad ,\quad \cfrac{\textit{sum of "y" values}}{ratio1+ratio2}\right)}}

\bf \qquad thus&#10;\\\\\\&#10;E=\left(\cfrac{(1\cdot 3)+(3\cdot -5)}{3+1}\quad ,\quad \cfrac{(1\cdot 2)+(3\cdot -2)}{3+1}\right)

6 0
3 years ago
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