The temperature of a chemical solution is originally 21^\circ\text{c}21 ∘ c. a chemist heats the solution at a constant rate, and the temperature of the solution is 75^\circ\text{c}75 ∘ c after 1212 minutes of heating. the temperature, tt, of the solution in ^\circ\text{c} ∘ c is a function of xx, the heating time in minutes. write the function's formula.

The required function is,

T(x) = 21 + 4.5 x

Step-by-step explanation:

The original temperature of the solution = 21° C

Let the temperature is increasing with a constant rate of y degree per minutes,

Thus, the temperature of the solution after 12 minutes = 21 + 12 y

According to the question,

21° + 12 y = 75°

⇒ 12 y = 54°

⇒ y = 4.5°

Hence, the constant rate of increasing the temperature = 4.5° per minutes,

Thus, the temperature of the solution after x minutes,

T(x) = 21 + 4.5 x

Which is the required function.

T = 21 + 4.5x

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5x + 3y = - 4

step-by-step explanation:

the equation of a line in standard form is

ax + by = c ( a is a positive integer and b, c are integers )

express the line first of all in slope- intercept form

y = mx + c ( m is the slope and c the y-intercept )

to calculate m use the gradient formula

m = ( y₂ - y₁ ) / ( x₂ - x₁ )

with (x₁, y₁ ) = (7, - 3) and (x₂, y₂ ) = (4, - 8)

m = = -

y = - x + c ← is the partial equation

to find c substitute either of the 2 points into the partial equation

using (4, - 8 ), then

- 8 = - + c ⇒ c = -

y = - x - ← in slope-intercept form

multiply all terms by 3 to eliminate the fractions

3y = - 5x - 4 ( add 5x to both sides )

5x + 3y = - 4 ← in standard form