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bixtya [17]
2 years ago
11

Two pentagons are similar. the area of one of the Pentagon is 9 times that the other. determine the ratio of the length of the c

orresponding sides and the perimeter of the Pentagon
​
Mathematics
1 answer:
kolbaska11 [484]2 years ago
7 0
<h2><u><em>Answer:</em></u></h2><h2><u><em></em></u></h2><h2><u><em>The ratios of the lengths of the corresponding  sides of the two pentagons is 3:1</em></u></h2><h2><u><em></em></u></h2><h2><u><em>The ratios of the perimeters of the two pentagons is 3:1</em></u></h2><h2><u><em></em></u></h2><h2><u><em>Step-by-step explanation:</em></u></h2><h2><u><em></em></u></h2><h2><u><em>Let the first pentagon be X and the second pentagon be Y.</em></u></h2><h2><u><em></em></u></h2><h2><u><em>Ratio of area of the two pentagons is </em></u></h2><h2><u><em>9</em></u></h2><h2><u><em>Ratio of sides of the pentagon is equal to</em></u></h2><h2><u><em></em></u></h2><h2><u><em>3</em></u></h2><h2><u><em></em></u></h2><h2><u><em>Ratio of perimeters is equal to ration of sides</em></u></h2><h2><u><em></em></u></h2><h2><u><em>Hence,</em></u></h2><h2><u><em>The ratio of the perimeter is 3 as well</em></u></h2>

<u><em></em></u>

<em></em>

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Some body can help me with a geometric mean maze
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Answer:

See explanation

Step-by-step explanation:

Theorem 1: The length of the altitude to the hypotenuse of a right triangle is the geometric mean of the lengths of the segments of the hypotenuse.

Theorem 2: The length of each leg of a right triangle is the geometric mean of the length of the hypotenuse and the length of the segment of the hypotenuse adjacent to that leg.

1. Start point: By the 1st theorem,

x^2=25\cdot (49-25)=25\cdot 24=5^2\cdot 2^2\cdot 6\Rightarrow x=5\cdot 2\cdot \sqrt{6}=10\sqrt{6}.

2. South-East point from the Start: By the 2nd theorem,

x^2=40\cdot (40+5)=4\cdot 5\cdot 2\cdot 9\cdot 5\Rightarrow x=2\cdot 5\cdot 3\cdot \sqrt{2}=30\sqrt{2}.

3. West point from the previous: By the 2nd theorem,

x^2=(32-20)\cdot 32=4\cdot 3\cdot 16\cdot 2\Rightarrow x=2\cdot 4\cdot \sqrt{6}=8\sqrt{6}.

4. West point from the previous: By the 1st theorem,

9^2=x\cdot 15\Rightarrow x=\dfrac{81}{15}=\dfrac{27}{5}=5.4.

5. West point from the previous: By the 2nd theorem,

10^2=8\cdot (8+x)\Rightarrow 8+x=12.5,\ x=4.5.

6. North point from the previous: By the 1st theorem,

x^2=48\cdot 6=6\cdot 4\cdot 2\cdot 6\Rightarrow x=6\cdot 2\cdot \sqrt{2}=12\sqrt{2}.

7. East point from the previous: By the 2nd theorem,

x^2=22.5\cdot 30=225\cdot 3\Rightarrow x=15\sqrt{3}.

8. North point from the previous: By the 1st theorem,

x^2=7.5\cdot 36=270\Rightarrow x=3\sqrt{30}.

8. West point from the previous: By the 2nd theorem,

x^2=12.5\cdot (12.5+13.5)=12.5\cdot 26=25\cdot 13\Rightarrow x=5\sqrt{13}.

9. North point from the previous: By the 1st theorem,

12^2=x\cdot 30\Rightarrow x=\dfrac{144}{30}=4.8.

101. East point from the previous: By the 1st theorem,

6^2=1.6\cdot (x-1.6)\Rightarrow x-1.6=22.5,\ x=24.1.

11. East point from the previous: By the 2nd theorem,

20^2=32\cdot (32-x)\Rightarrow 32-x=12.5,\ x=19.5.

12. South-east point from the previous: By the 2nd theorem,

18^2=x\cdot 21.6\Rightarrow x=15.

13. North point=The end.

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3 years ago
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How do you solve for x in this quadratic equation?: 5x^2 – 34x + 24 = 0
wlad13 [49]
Quadratic formula
factoring
graphing 
completing the square
factoring by grouping
Rational Roots Theorem
synthetic division

Take a look at <span>5x^2 – 34x + 24 = 0.  The last term could have been the result of these different possible muliplications:  1*24, 2*12, 3*8, 4*6.  The leading term is 5, whose factors are 5 and 1.  Thus, possible rational roots would be
4/5 (the 4 is a factor of 24 and the 5 is a factor of 5) and 6/1 (the 6 is a factor of 24 and the 1 is a factor of 5).  

Using synth. div. to check whether 6 is actually a root:
     ___________________
6  /    5      -34          24
                  30         -24
    ------ --------------------------
         5       -4             0

since the remainder is 0, we can safely call 6 a "root."  
Note the remaining coefficients, 5 and -4:  

They correspond to the factor 5x - 4.  If we set this difference = to 0, and solve for x, we get  x = 4/5 (which is correct).

The roots of </span><span>5x^2 – 34x + 24 = 0  are  x = 4/5 and x= 6/1.</span>
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3 years ago
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