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wel
2 years ago
13

A poster has an area of 432 square inches. The length x in inches is 6 inches longer than the width of the poster. Which can be

solved to determine the length, in inches, of the poster?
A) x^2 -6 =432
B) x^2 -6x =432
C) x^2 + 6 =432
D) x^2 +6x =432
Mathematics
1 answer:
Naily [24]2 years ago
3 0
The correct answer is D
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A sequence has a common ratio of Three-halves and f(5) = 81. Which explicit formula represents the sequence? f(x) = 24(Three-hal
Ede4ka [16]

Answer:

f(x)=16\, (\frac{3}{2} )^{x-1}

Step-by-step explanation:

Since we are given the common ratio (3/2), all we need to find to define the geometric sequence, is its multiplicative factor (a) that corresponds to the first term of the sequence - remember that all consecutive terms will be generated by multiplying this first value repeatedly by the common ratio (3/2) as shown below:  

f(1)=a\\f(2)=a\,*\,(\frac{3}{2} )\\f(3)=a\,*\,(\frac{3}{2} )^2\\f(4)=a\,*\,(\frac{3}{2} )^3\\f(5)=a\,*\,(\frac{3}{2} )^4

Since we are given the information that f(5)=81 we can use this to find the value of the first term:

f(5)=\,a\,*\,(\frac{3}{2} )^4\\81=\,a\,*(\frac{81}{16} )\\a\,*\,81=\,81\.*\,16\\a\,=\,16

Notice as well that the first term doesn't contain the common ratio, the second term contains the common ration (3/2) to the power one, the third one contains the common ratio to the power two, the fourth one contains it to the power three, and so forth. So the exponent at which the common ratio appears is always one unit less than the order (x) of the term in question. This concept helps us finalize the expression for the sequence's formula:

f(x)=16\,*\,(\frac{3}{2} )^{x-1}

6 0
2 years ago
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Three right triangles surround a shaded triangle; together they form a rectangle measuring 12 units by 14 units. The figure belo
Alchen [17]

Answer:

its not a right angled triangle

Step-by-step explanation:

this is because it doesnt follow the rule of pytagorous theorem

7 0
2 years ago
Elisha is a photographer and charges a set fee to photograph weddings. This is an example of _____ income.
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<span>Elisha is a photographer and charges a set fee to photograph weddings. This is an example of Passive income. Passive income because it is a limited partnership and is not stable income.</span>
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Three containers have capacities if 3,5,and 9. How can you use these containers to measure exactly 9 liters of water
pishuonlain [190]
I'll have to know what the measurements of the containers. If it is in liters, then you would just use the container with the capacity of 9 liters. 

Hope this helped :)
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4 0
2 years ago
an original piece of art work is 3 feet by 2.5 feet. a reprint of the artwork is 6 inches by 5 inches. are the pieces similar? i
RoseWind [281]
For this case we observe that the dimensions of the original piece are:
 3 feet
 2.5 feet
 Let's multiply these dimensions by a scale factor k:
 3 * k
 2.5 * k
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 2.5 * k = 5
 Clearing k we have:
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 Answer:
 
The pieces are similar.
 
The ratio of their corresponding side lengths is: 
 
k = 2
3 0
2 years ago
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