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PolarNik [594]
1 year ago
5

Draw an area model to represent 4x^2+12x+9 = (2x+3)^2. Label the length and width of the whole square and label each individual

small square and rectangle.
Mathematics
1 answer:
My name is Ann [436]1 year ago
7 0

See attachment for the area model of the equation 4x^2+12x+9 = (2x+3)^2

<h3>What are area models?</h3>

Area models are shapes used to model or illustrate products, multiplications, divisions and quotients

<h3>How to draw the area model?</h3>

The equation is given as:

4x^2+12x+9 = (2x+3)^2

Express (2x+3)^2 as the product of (2x+3) and (2x+3)

4x^2+12x+9 = (2x+3) * (2x+3)

The above means that the area model is a square.

So, the side lengths of the model must be equal, where the side lengths are 2x + 3 and the area of the square is 4x^2+12x+9

See attachment for the area model of the equation 4x^2+12x+9 = (2x+3)^2

Read more about area models at:

brainly.com/question/12245811

#SPJ1

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10 points
Sergeu [11.5K]

Step-by-step explanation:

The mode is 7 because it is 5 times

8 0
3 years ago
Which pair of words describes this system of equations 3y=9x-6 2y+6x=4
pishuonlain [190]

Answer:

Consistent and dependent

Step-by-step explanation:

Given

3y = 9x - 6

2y + 6x = 4

Required

The words that describe the equations

Make y the subject in (2)

2y + 6x = 4

Collect like terms

2y = 4 - 6x

Divide through by 2

y = 2 - 3x

Substitute: y = 2 - 3x in (1)

3y = 9x - 6

3(2 - 3x) = 9x - 6

6 - 9x = 9x - 6

Collect like terms

9x+9x = 6+6

18x = 12

Solve for x

x = \frac{12}{18}

Simplify

x = \frac{2}{3}

Substitute x = \frac{2}{3} in y = 2 - 3x

y = 2 - 3*\frac{2}{3}

y = 2 - 2

y =0

So, we have:

x = \frac{2}{3} and y =0

<em>The system is consistent because it has at least 1 solution</em>

<em>The system is dependent because it has more than 1 solution</em>

6 0
3 years ago
Simplest form for 16/56
VARVARA [1.3K]
The answer is 2/7 because you're finding the greatest common factor of both numbers. The gcf is 8, so divide both by 8 and you'll get 2/7
4 0
3 years ago
The table below models the cost, y, of using a high-efficiency washing machine and a standard washing machine over x number of y
SSSSS [86.1K]

ANSWER:

i) y = 25x + 500

ii) y = 30x + 400

iii) The washing machines would cost the same amount after 20 years of use

iv) Standard machine

Step-by-step explanation:

i)

We are to determine a straight line equation that models the cost of High-Efficiency washing machine over the years;

The first step step is to determine the slope of the line,

( change in y) / ( change in x ) = (550 - 525) / ( 2 - 1) = 25

The equation is slope-intercept form will be;

y = 25x + c

Where y is the cost of the High-Efficiency washing machine and x the number of years. To determine the y-intercept, c, we use any pair of points given in the data table;

when x = 1, y = 525

525 = 25(1) + c

c = 500

Therefore;

y = 25x + 500

ii)

The straight line equation that models the cost of Standard washing machine over the years;

Slope = (460 - 430) / (2 - 1) = 30

The equation is slope-intercept form will be;

y = 30x + c

when x = 1, y = 430

430 = 30(1) + c

c = 400

Therefore;

y = 30x + 400

Where y is the cost of the standard washing machine and x the number of years.

iii)

Given the cost functions for both machines over the number of years, we simply equate the two equations and determine the value of x when both machines would cost the same amount;

We have the cost functions;

y = 25x + 500

y = 30x + 400

Equating the two and solving for x;

25x + 500 = 30x + 400

500 - 400 = 30x - 25x

100 = 5x

x = 20

Therefore, the washing machines would cost the same amount after 20 years of use.

iv)

In order to determine which machine would be the more practical purchase if kept for 9 years we use the cost functions obtained in i) and ii)

The cost function of the High-Efficiency washing machine is;

y = 25x + 500

To determine the cost, we solve for y given x = 9

y = 25(9) + 500

y = 725

The cost function of the Standard washing machine is;

y = 30x + 400

We solve for y given x = 9

y = 30(9) + 400

y = 670

Comparing the two values obtained, the cost for the Standard washing machine is more practical.

3 0
3 years ago
Read 2 more answers
You have fit a regression model with two regressors to a data set that has 20 observations. The total sum of squares is 1000 and
Llana [10]

Answer:

Hence the adjusted R-squared value for this model is 0.7205.

Step-by-step explanation:

Given n= sample size=20  

Total Sum of square (SST) =1000  

Model sum of square(SSR) =750  

Residual Sum of Square (SSE)=250  

The value of R ^2 for this model is,  

R^2 = \frac{SSR}{SST}  

R^2 = 750/1000 =0.75  

Adjusted R^2 :

Adjusted R^2 =1- \frac{(1-R^2)\times(n-1)}{(n-k-1)}

Where k= number of regressors in the model.

Adjusted R^2 =1-(19\times 0.25/((20-2-1)) = 0.7205

3 0
3 years ago
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