Find two consecutive positive integers wjose product is 42. (First integer= x, second integer=x+1

Which equation represents a line that passes through (2,-1/2) and has a slope of 3 ?

Anna11 [10]

Answer:

C. $y + \frac{1}{2} = 3(x - 2)$

Step-by-step explanation:

Given

$Point: (2,\frac{-1}{2})$

$Slope: 3$

Required

Equation of line

Let m represents the slope of the line;

m is calculated as thus

$m = \frac{y - y_1}{x - x_1}$

$where (x_1,y_1) = (2,\frac{-1}{2})$

$So; x_1 = 2; y_1 = \frac{-1}{2}$

$m = 3$

By substituting the right values in the formula above;

$m = \frac{y - y_1}{x - x_1}$ becomes

$3 = \frac{y - \frac{-1}{2}}{x - 2}$

Multiply both sides by $(x - 2)$

$3 *(x - 2) = \frac{y - \frac{-1}{2}}{x - 2} *(x - 2)$

$3 *(x - 2) = (y - \frac{-1}{2})$

$3 *(x - 2) = (y + \frac{1}{2})$

$3(x - 2) = (y + \frac{1}{2})$

$3(x - 2) = y + \frac{1}{2}$

Reorder

$y + \frac{1}{2} = 3(x - 2)$

Hence, the equation that represents the line is $y + \frac{1}{2} = 3(x - 2)$

4 0

3 years ago

If 3 times a square of an integer is added to 1 times the integer, the result is 2

jarptica [38.1K]

Let unknown integer be n.

So then your sentence would translate to 3n² + n = 2.

If you need to solve for n then we can move 2 to left side by subtract both sides by 2:

3n² + n - 2 = 0

Now you can factor:

3n² + 3n -2n - 2 = 0

3n( n + 1 ) - 2( n + 1 ) = 0

( 3n - 2 )( n + 1 ) = 0

3n - 2 = 0 OR n + 1 = 0

3n = 2 OR n = -1

n = 2/3 OR n = -1

Final answer: n = 2/3 OR n = -1

6 0

3 years ago

Select all of the choices that are equal to (-5) – (-12).

krek1111 [17]

The answer is 7 i’m pretty sure

4 0

2 years ago

Read 2 more answers

A certain type of bamboo plant grow 1.2 feet in one day.At that rate how many feeet could the plant grow in 0.5 day

rosijanka [135]

It will grow 0.6 feet in one half day

6 0

3 years ago

Read 2 more answers

The number of electoral votes each state is assigned is determined by the size of its population every ten years. The chart show

sattari [20]

Answer:

D. $Q_3=47$

Step-by-step explanation:

We have been given a table that represents the the number of electoral votes California was assigned each decade of the past century. We are asked to find the 3rd quartile of our given data.

The number of votes are: 9, 13, 13, 22, 25, 32, 40, 45, 47, 54, 55.

We will use upper quartile formula to solve our given problem.

$Q_3=\frac{3}{4}*(n+1)^{\text{th term}}$ , where, n represents the number of elements in the data set.

We can see that our data set has 11 data points, so upon substituting n=11 in above formula we will get,

$Q_3=\frac{3}{4}*(11+1)^{\text{th term}}$

$Q_3=\frac{3}{4}*(12)^{\text{th term}}$

$Q_3=3*3^{\text{th term}}$

$Q_3=9^{\text{th term}}$

Now let us count 9th term of our data set. Upon counting our data set from left to right we can see that 9th term of our data set is 47, therefore, 3rd quartile of our given data is 47 and option D is the correct choice.

3 0

3 years ago

Read 2 more answers

Find two consecutive positive integers wjose product is 42. (First integer= x, second integer=x+1​

Find two consecutive positive integers wjose product is 42. (First integer= x, second integer=x+1