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Nana76 [90]
3 years ago
13

The Dittany family's vegetable garden is shaped like a scalene triangle. Two of the sides measure 6 feet and 10 feet. Which coul

d be the length of the third side, in feet?
Question 2 options:

18

16

9

6
Mathematics
1 answer:
d1i1m1o1n [39]3 years ago
3 0

Answer:

The length of the third side could be 9 ft

Step-by-step explanation:

we know that

<u>The Triangle Inequality Theorem</u> states that the sum of any 2 sides of a triangle must be greater than the measure of the third side

so

In this problem

Let

c-----> the length of the third side, in feet

Applying the Triangle Inequality Theorem

1) 6+10>c -------> c

2) c+6>10 -----> c>4\ ft

so

The length of the third side must be greater than 4 ft and less than 16 ft

Remember that

The scalene triangle has three different sides

therefore

The length of the third side could be 9 ft

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sp2606 [1]

\displaystyle\\Answer:\ x=\sqrt{2}\ \ \ \ \ x=-\sqrt{2}\ \ \ \ \ x=\frac{ln5}{2}

Step-by-step explanation:

5x^2-x^2e^{2x}+2e^{2x}=10

Let:\ x^2=t  \ \ \ \ \ e^{2x}=v\\Hence,\\5t-tv+2v^2=10\\5t-tv+2v^2-10=10-10\\5t-tv-10+2v^2=0\\t(5-v)-2(5-v)=0\\(5-v)(t-2)=0\\5-v=0\\5-v+v=0+v\\5=v\\5=e^{2x}

<em>Prologarithmize both parts of the equation:</em>

ln5=lne^{2x}\\ln5=2x*lne\\ln5=2x*1\\ln5=2x\\

<u><em> Divide both parts of the equation by 2:</em></u>

\displaystyle\\x=\frac{ln5}{2}

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1 year ago
Grace is planning on purchasing an Akai Professional MPC5000 drum machine for $2195. She's been pre-approved to finance her purc
Genrish500 [490]

1) Her monthly payment is $40.97 if she finance the total amount

2) She will pay $2458.2 for the MPC5000

3)Her monthly payment will be $26.50 if she pay her saved up money upfront

4) She will pay $2365.4 for the MPC5000

5) Yes, I recommend to pay the $775 upfront . If she pay upfront, then the amount she needs to pay for the MPC5000 is less.

Step-by-step explanation:

The cost of the drum machine is $2195

The APR is 12% over 60 months

1) the APR for 60 months is 12%

So, the APR for 1 month is

12/60 = 0.2%

The interest per month = 0.2% of 2195

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2) If she pays $40.97 per month then the total payment (for 60 months) for the drum machine

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The amount to be financed is

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4) If she pay $775 upfront then the remaining $1420 is financed

Her monthly payment is $26.50

Then for 60 months she will pay,

26.50 x 60= $1590.4

The total amount paid for the drum machine is

775+1590.4 =$2365.4

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