MATHEMATICS MIDDLE SCHOOL

Y = 4x+1 y=x^2 + 2x - 2 A.6,2 B. 2,6 C. -6,2 D. -6,-2

Answers

Answer 1

Answer:

Answer:

The solution is (3,13) and (-1,-3). So none of the mentioned options is correct.

Step-by-step explanation:

Given that

$y = 4x + 1 (i)$

$y = x^2 + 2x -2 (ii)$

Now, by susbstituting the value of 'y' from equation i to equation ii, we get

$4x+1=x^2 + 2x -2$

$0=x^2 + 2x -2-4x-1$

$0=x^2 + (2x -4x) +(-2-1)$

$0=x^2 + (-2x) +(-3)$

$0=x^2 -2x -3$

$x^2 -2x -3 = 0 (iii)$

Now by factorization, equation iii can be written as

$x^2 -3x +x -3 = 0$

$x(x -3) + 1(x -3) = 0$

$(x -3)(x +1) = 0$

x = 3 and x = -1

By putting the values of x in equation i, we get

y = 4(3) + 1

y = 12 +1

y = 13

and

y = 4(-1) + 1

y = -4 +1

y = -3

Therefore, the solution is (3,13) and (-1,-3). So none of the mentioned options is correct.

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2X^2-5x+2=0
Quadratic formula

Answers

Answer:

The solutions are $x_(1)=2\ and\ x_(2)=0.5$ .

Step-by-step explanation:

Given:

$2x^(2) -5x+2=0$

Now, to solve by using quadratic formula:

$x=\frac{-b\pm \sqrt{b^(2)-4ac}}{2a}$

Here $a=2,b=-5\ and\ c=2$

$x=\frac{-(-5)\pm \sqrt{(-5)^(2)-4* 2* 2}}{2* 2}$

Now, here we will take either $x=(-(-5)+√(25-16))/(4)$ and then $x=(-(-5)-√(25-16))/(4)$ .

$x=(-(-5)+√(25-16))/(4)$ $x=(-(-5)-√(25-16))/(4)$

$x=(5+√(9))/(4)$ $x=(5-√(9))/(4)$

$x=(5+3)/(4)$ $x=(5-3)/(4)$

$x=(8)/(4)$ $x=(2)/(4)$

$x_(1)=2$ $x_(2)=(1)/(2)=0.5$

Therefore, the solutions are $x_(1)=2\ and\ x_(2)=0.5$ .

One cellular phone carrier charges 26.50 a month plus .15cents a minute. Another carrier charges 14.50 a month plus .25 cents a minute. For how many minutes is the cost of the plans the same? Please show work thanks

Answers

i'm going to use m for minutes
Cell carrier 1
0.15 per minute (0.15m)
$26.50 first, and then add on for every minute

cost carrier 1 = 0.15m + 26.50

carrier 2
0.25 per minute (0.25m)
$14.50 first, and then add on for every minute.

cost carrier 2 = 0.25m + 14.50

to find out when they cost the same, make the two costs equal to each other:

0.15m + 26.50 = 0.25m + 14.50

all that's left is to solve for m

0.15m + 26.50 = 0.25m + 14.50
subtract both sides by 0.15 m
26.50 = 0.2m + 14.50
subtract both sides by 14.50
12 = 0.1 m
divide both sides by 0.1
m = 120

the phone carriers will have the same cost at 120 minutes

Define the rates of each carrier:

(1) $26.50 + $0.15m
(2) $14.50 + $0.25m

Set the two equations equal to each other and solve for m minutes . . .

26.50 + 0.15m = 14.50 + 0.25m

26.50 - 14.50 = 0.25m - 0.15m

12.00 = (0.25 - 0.15)m

12 = 0.10m

m = 12/0.10 = 120

m = 120 minutes

by visual inspection, determine the best-fitting regression model for the data plot below. A. No pattern B. Quadratic C.Linear D. Exponential

Answers

Answer:

C) Linear

Step-by-step explanation:

We can see from the plot that the data approach a straight line.

This means we can draw a line of best fit through this data and it should hit several data points; thus the answer is linear.

By visual inspection, the best-fitting regression model for the data plot above is: C. linear.

What is a regression line?

A regression model can be defined as a statistical tool which best describes the behavior of a data set. Thus, a regression line is a type of line that best fits a set of data.

By visual inspection, we can logically deduce that the best-fitting regression model for the data plot shown in the image attached above is linear because there exist a direct relationship between the data set.

Read more on regression here: brainly.com/question/26059078

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The question is in my screenshot I took. :) Need help, please.