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blondinia [14]
3 years ago
10

Please hurry I will mark you brainliest

Mathematics
1 answer:
Minchanka [31]3 years ago
8 0

Answer:

number of pennies = 54

Step-by-step explanation:

(4,60) ; (6, 65)

Find the slope

Slope = \frac{y_{2}-y_{1}}{x_{2}-x_{1}}

          =\frac{65-60}{6-4}\\\\=\frac{5}{2}

m = 5/2 and (4,60)

Equation of the line: y - y1 = m (x -x1)

y - 60 = \frac{5}{2}(x -4)\\\\y - 60 = \frac{5}{2}x-\frac{5}{2}*4\\\\y- 60 = \frac{5}{2}x-10\\\\y =\frac{5}{2}x-10+60\\\\y=\frac{5}{2}x + 50

x-----> determine the number of pennies and y determines the mass of pennies.

Here mass (y -value) is given as 185. We have find the corresponding x-value. So plugin  y  = 185 in the above equation,

185 = \frac{5}{2}x+50\\\\185-50=\frac{5}{2}x\\\\135=\frac{5}{2}x\\\\135*\frac{2}{5}=x\\\\27*2=x

x = 54

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bₙ = 30 - n^2

We want to find a term that belongs to both sequences, (it can be for different integers, we can use n for sequence A and x for sequence B)

Then we want to find:

aₙ = bₓ

where n and x are integer numbers.

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3*n^2 - 1 = 30 - x^2

To find the pair, we could isolate one of the variables, then input different integers in the other variable and see if the outcome is also an integer.

Let's isolate n.

3*n^2 = 30 - x^2 + 1

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n^2 = (31 - x^2)/3

n = √(  (31 - x^2)/3)

Now let's input different values for x, and see if the outcome is also an integer, notice that x is in a negative term inside a square root, then we have only a few values of x such that the equation can be true.

Then let's start with x = 1.

n(1) = √(  (31 - 1^2)/3) = √(30/3) = √10

We know that √10 is not an integer.

now with x = 2,

n(2) = √(  (31 - 2^2)/3)  = √( (31 - 4)/3) = √(27/3) = √9 = 3

then if x = 2, we have n = 3.

Both of them are integers, then we get:

a₂ = 3*(3)^2 - 1 = 27 - 1 = 26

b₃ = 30 - 2^2 = 30 - 4 = 26

The number that belongs to both sequences is 26.

5 0
2 years ago
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