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Nataly [62]
3 years ago
5

Classify triangle ABC by its sides if side AB = 6x, side AC = 4x + 6 and side BC = 8x + 3. The perimeter of triangle ABC is 63.

Show all your work
Mathematics
2 answers:
Bad White [126]3 years ago
8 0

Answer:

AB = 18

AC = 18

BC = 27

Step-by-step explanation:

Solve for x first:

6x + 4x + 6 + 8x + 3 = 63

6x + 4x + 8x + 6 + 3 = 63

18x + 9 = 63

18x = 63 - 9

18x = 54

x = 54 / 18

x = 3

Now substitute x to all sides.

AB = 6x

6(3) = 18

AC = 4x + 6

4(3) + 6

12 + 6 = 18

BC = 8x + 3

8(3) + 3

24 + 3 = 27

18 + 18 + 27 = 63

63 = 63

sladkih [1.3K]3 years ago
3 0
6x + 4x+6 + 8x+3 = 63
6x+4x+8x = 63 - 3 - 6
18x = 54
x = 54/18
x = 3

Side AB = 6(3) = 18
Side AC = 4(3)+6 = 18
Side BC = 8(3)+3 = 27
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\bf \begin{array}{ccccccccc}
&&x_1&&y_1&&x_2&&y_2\\
%  (a,b)
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%  (c,d)
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\end{array}
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% slope  = m
slope =  m\implies 
\cfrac{\stackrel{rise}{ y_2- y_1}}{\stackrel{run}{ x_2- x_1}}\implies \cfrac{1-(-4)}{5-3}\implies \cfrac{1+4}{5-3}\implies \cfrac{5}{2}
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% point-slope intercept
\stackrel{\textit{point-slope form}}{y- y_1= m(x- x_1)}\implies y-(-4)=\cfrac{5}{2}(x-3)\implies y+4=\cfrac{5}{2}x-\cfrac{15}{2}

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5 0
3 years ago
The height of a tree in feet over x years is modeled by the function f(x). f(x)=301+29e−0.5x which statements are true about the
Karo-lina-s [1.5K]
Given this equation:

f(x)=301+29^{-0.5x}

That represents t<span>he height of a tree in feet over (x) years. Let's analyze each statement according to figure 1 that shows the graph of this equation.
</span>
The tree's maximum height is limited to 30 ft.

As shown in figure below, the tree is not limited, so this statement is false.

<span>The tree is initially 2 ft tall

The tree was planted in x = 0, so evaluating the function for this value, we have:

</span>f(0)=301+29^{-0.5(0)}=301+1=302ft
<span>
<span>So, the tree is initially \boxed{302ft} tall.
</span>
Therefore this statement is false.

</span>Between the 5th and 7th years, the tree grows approximately 7 ft.
<span>
if x = 5 then:

</span>f(5)=301+29^{-0.5(5)}=301ft<span>

</span>if x = 7 then:

f(7)=301+29e^{0.5(7)}=301ft

So, between the 5th and 7th years the height of the tree remains constant
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\Delta=f(7)-f(5)=301-301=0ft

This is also a false statement.

<span>After growing 15 ft, the tree's rate of growth decreases.</span>

It is reasonable to think that the height of this tree finally will be 301ft. Why? well, if x grows without bound, then the term 29^{-\infty} approaches zero.

Therefore this statement is also false.

Conclusion: After being planted this tree won't grow. 


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Answer:

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Step-by-step explanation:

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