Algebra Answers

f(t)= 1+0.12t, compute f(t) if t=2.

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1. Find the domain of the function 𝑓(𝑥)=ln(−2𝑥2−𝑥−6)+√𝑥2−1.

2. Find the inverse function of the function 𝑓(𝑥)=𝑥2−4𝑥+5,𝑥∈〈3,4⟩. Find the domain and the range of the inverse function.

3. Construct the tangent line to the graph of the function 𝑓(𝑥)=4𝑥⋅√𝑥−2⋅√𝑥 which is parallel to the line 𝑦=𝑥.

4. Find the maximal intervals of monotonicity of the function 𝑓(𝑥)=𝑒𝑥+3𝑥2+2𝑥+6.

5. Find the integral ∫6⋅𝑥3⋅𝑒𝑥2+2𝑑𝑥.

6. Find the general solution of the differential equation 𝑥2+1+𝑦′⋅cos(𝑦)=0. 

An element with mass 140 grams decays by 21.6% per minute. How much of the element is remaining after 20 minutes, to the nearest 10th of a gram?

Solve this system of equations and provide a graphical representation of the solution. (12)

x² + y² = 5

x + y = 1

Solve this system of equations.

(x + 1)² + (y + 1)² = 25,x + y = 5

1. Teaching long division of 357÷19 for instrumental understanding

2. Teaching long division of 357÷19 for relational understanding

How would you use a teacher-centred media resource to explain the meaning of (7×8) to grade 5 learner? Use two different illustrations to show your understanding

Bryan’s father is now twice as old as Bryan is.  His father was four times as old as him 16 years ago.  How old is his father now?

In the following problems, perform the operations and simplify as much as possible.

a. (x2 + 2x)/(3x2 – 18x + 24) ÷ (x2 – x – 6)/(x

2 – 4x + 4)

b. (x2 + 6x + 9)/x/(x + 3)

c. 1/(3x – 1) + x/(x2 – 9)