Please answer the question in the picture

2(3x+1)(x+1)

explanation:

→ 6x²+8x+2

→ 2(3x²+4x+1)

→ 2(3x²+3x+x+1)

→ 2(3x(x+1)+1(x+1))

→ 2(3x+1)(x+1)

2(3x + 1)(x + 1)

Step-by-step explanation:

6x² + 8x + 2

Multiply the coefficient of x² and the constant:  6 x 2 = 12

Find factors of 12 that sum to make the coefficient of x (8):  2 and 6

Therefore,

  6x² + 8x + 2

= 6x² + 6x + 2x + 2

= 6x(x + 1)+2(x + 1)

= (6x + 2)(x + 1)

= 2(3x + 1)(x + 1)

1. The required slope m, for the context is

2. The y-intercept in the context is

3. The graph is on Desmos.

Step-by-step explanation:

Given:

Where,

a is the speed of sound wave.

t is the air temperature.

This is a linear model type equation.

Can be represented in the slope intercept form  which is equal to

Where,

m = Slope of the line.

c = y-intercept.

Now if we compare the given model by slope intercept formula we get

So ,the slope in the context of the problem is .

and the y intercept in the context of the problem

For Sketching the graph we require two point

put t = 0

∴ a = 1052

Let A (1052, 0) be one point.

put a = 0

∴ t = -974.07

Let B (0, -974.07) another point.

So, the x intercept of the linear model is

Here in the graph

X axis represent temperature in degree, Fahrenheit.(t)

Y axis represent Speed of sound wave in feet per second.(a)

Scale on both axes:

1 cm = 100 feet per second on y-axis

1 cm = 100 degree Fahrenheit on x-axis