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Ber [7]
3 years ago
6

Find four numbers that form a geometric progression such that the third term is greater than the first by 12 and the fourth is g

reater than the second by 36. Answer:
Mathematics
1 answer:
olchik [2.2K]3 years ago
4 0

If x is the first number in the progression, and r is the common ratio between consecutive terms, then the first four terms in the progression are

\{x,xr,xr^2,xr^3\}

We want to have

\begin{cases}xr^2-x=12\\xr^3-xr=36\end{cases}

In the second equation, we have

xr^3-xr=xr(r^2-1)=36

and in the first, we have

xr^2-x=x(r^2-1)=12

Substituting this into the second equation, we find

xr(r^2-1)=12r=36\implies r=3

So now we have

\begin{cases}9x-x=12\\27x-3x=36\end{cases}\implies x=\dfrac32

Then the four numbers are

\left\{\dfrac32,\dfrac92,\dfrac{27}2,\dfrac{81}2\right\}

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2 years ago
Jenna wants to build 8 birdhouses. She needs 2 3/5 square feet of plywood for each birdhouse. If the plywood costs $0.56 per squ
goldenfox [79]

Answer:

$11.76

Step-by-step explanation:

We first need to find the amount of plywood for all birdhouses.

2 3/5 * 8 = 104/5 or 20.8 or 20 4/5

Now we can solve the cost for all the birdhouses by multiplying the total amount of plywood needed by the price per square foot.

20.8 * 0.56 = $11.648 or estimated $11.65

Remember, the question might be different, so don't submit anything yet. If the people who sell the plywood only sell in integer numbers (meaning you can't buy 4/5 of a square foot of wood but can only by amounts with no fractions), then Jenna must buy 21 square feet of plywood and will have a little bit of wood left over. Now solve just like before.

21 * 0.56 = $11.76

Therefore the answer is $11.76 if she can only buy an integer amount of plywood or estimated $11.65. I think the best answer is 11.76.

3 0
3 years ago
Aaron is growing two plants. At the last measurement,the first plant was 6.53 inches tall and the second was 2.7 inches tall.
AlekseyPX
Just subtract the two numbers and the answer is 3.83 inches
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Anna71 [15]
4/5-3/7. First they need the same denominater: 4/5(7)=28/35, 3/7(5)=15/35. 28/35-15/35. Now subtract numerators: 28-15=13. So your answer H. 13/35 :)
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Problem: – 12 = - Зу
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Answer:

4y or 4 (divide)

Step-by-step explanation:

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