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neonofarm [45]
3 years ago
5

The first term of an arithmetic sequence is -3 and the fifteenth term is 53. What is the common difference of the sequence?

Mathematics
1 answer:
Maru [420]3 years ago
4 0

C: 4 is the right answer

Step-by-step explanation:

Given

a1 = -3

a15 = 53

We know that explicit formula for the arithmetic sequence is:

a_n=a_1+(n-1)d

For the 15th, term it will be

a_{15}=-3+(15-1)d\\53=-3+14d

Adding 3 on both sides

53+3 = -3+3 + 14d\\56 = 14d

Dividing both sides by 14

\frac{56}{14}=\frac{14d}{14}\\d=4

Hence,

C: 4 is the right answer

Keywords: Arithmetic sequence, Common Difference

Learn more about arithmetic sequence at:

  • brainly.com/question/12896802
  • brainly.com/question/12973601

#LearnwithBrainly

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The general form of an parabola is 2x2−12x−3y+12=0 .
Murljashka [212]

Answer:

The standard form of the parabola is (x-3)^2=4*\frac{3}{8}(y+2)

Step-by-step explanation:

The standard form of a parabola is

(x-h)^2=4p(y-k).

In order to convert 2x^2-12x-3y+12=0 into the standard form, we first separate the variables:

2x^2-12x+3y+12=0\\\\2x^2-12x+12=3y

we now divided both sides by 2 to remove the coefficient from 2x^2 and get:

x^2-6x+6=\frac{3}{2}y.

We complete the square on the left side by adding 3 to both sides:

x^2-6x+6+3=\frac{3}{2}y+3

x^2-6x+9=\frac{3}{2}y+3

(x-3)^2=\frac{3}{2}y+3

now we bring the right side into the form 4p(y-k) by first multiplying the equation by \frac{2}{3}:

\frac{2}{3} *(x-3)^2=\frac{2}{3} *(\frac{3}{2}y+3)\\\\\frac{2}{3} *(x-3)^2=y+2

and then we multiplying both sides by \frac{3}{2} to get

(x-3)^2=\frac{3}{2} (y+2).

Here we see that

4p=\frac{3}{2}

\therefore p=\frac{3}{8}

Thus, finally we have the equation of the parabola in the standard form:

\boxed{(x-3)^2=4*\frac{3}{8}(y+2)}

5 0
3 years ago
The table represents a linear function.
Scilla [17]

Answer:

the correct answer is: 5

Step-by-step explanation:

i put -5 at first and that was incorrect so then i put 5 and it said that was correct

6 0
3 years ago
Read 2 more answers
A student is assessing the correlation between the number of workers in a factory and the number of units produced daily. The ta
lukranit [14]

The number of units produced increases from 2 to 452 as the number of factory workers increases from 0 to 90, which gives;

Part A:

  • Yes there is a strong positive correlation

Part B:

  • The function is <em>y</em> = 5•x + 2

Part C:

  • The slope indicates the number of units produced by each worker daily

  • The y-intercept indicates that two units can be produced without workers.

<h3>How can the existence of a correlation and the best fit function for the data be found?</h3>

Part A:

The correlation is the relationship between variables based on statistical data.

From the given table, the difference between consecutive terms of the <em>x </em>and y-values are constant, therefore as the x-values increases, the corresponding y-value increases.

Change in x-values, ∆x = 10 - 0 = 20 - 10 = 30 - 20 = 10

Change in y-values, ∆y = 52 - 2 = 102 - 52 = 152 - 102 = 50

Therefore;

  • There is a strong positive correlation between the number of workers, <em>x</em>, and the number of units produced, <em>y</em>.

Part B:

Given that the rate of change of the x-values is constant, and the rate of change of the y-values is a constant, the function relating the <em>x </em>and y-values is a linear function, which can be found as follows;

Slope of the equation, <em>m </em>= ∆y/∆x

Which gives;

m = 50/10 = 5

y - 2 = 5•(x - 0)

The function that best fits the data is therefore;

  • y = 5•x + 2

Part C:

The slope of the function is the coefficient of the variable <em>x </em>in the equation, <em>y </em>= m•x + c

  • The slope of the plot, 5, indicates that each worker produces 5 units daily

The y-intercept of the function is the value of the constant term, c, in the equation, y = m•x + c

  • The y-intercept of the linear equation, y = 5•x + 2, which is 2, indicates that the initial number of units of products at the factory before workers arrive is 2.

Learn more about finding relationship between variables here:

brainly.com/question/4219149

#SPJ1

7 0
1 year ago
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Jet001 [13]
65 would be your answer take all 8 numbers add them up and divide by 8
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3 years ago
What expression represents 6 less than the quotient of a number and 4 is 15
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