Kaity W.

Mathematics Teacher/Tutor 4 years

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Pre-Calculus

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Question:

Find the inverse function on $$ y = 4x+5$$

Kaity W.

Answer:

To find the inverse of a function we must switch the x and y variables and solve for y. So the function, $$y=4x+5$$ becomes, $$x=4y+5$$ To solve for y we must subtract 5 from both sides $$x-5=4y$$ And divide by 4. $$\frac{x-5}{4} = y$$ Therefore, the inverse function is $$y=\frac{x-5}{4}$$

Geometry

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Question:

The sun casts a shadow for a tree that is 26 ft tall. From the top of the tree to the top of the shadow is 34 ft. How long is the shadow? Round to the nearest tenth.

Kaity W.

Answer:

If you draw a diagram you'll notice that the tree and the shadow for a 90 degree angle where they meet. Since we can create a right triangle, we will use the Pythagorean Theorem. ($$ a^2 + b^2 = c^2$$) The tree length and the shadow length are the two legs (a and b) of the triangle. While the length from the top of the tree to the top of the shadow is the hypotenuse (c). So we will be solving for the length of a leg of the triangle. $$26^2 +b^2 = 34^2$$ $$ 676 + b^2 = 1,156$$ (Subtract 676 from both sides) $$b^2 = 1,156 - 676$$ $$ b^2 = 480$$ (Take the Square Root of both Sides) $$b = \sqrt{480}$$ $$b = 21.9089...$$ The shadow is 21.9 ft long.

Algebra

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Question:

Jane, Sarah, Daniel, Jake and Ross went out for dinner. Jane, Jake and Ross all ordered drinks which were $2.50 a piece. Everyone ordered off the $8.99 value menu. If Daniel decides to treat everyone, how much will Daniel pay?

Kaity W.

Answer:

There is a total of 5 people. We know that everyone ordered a meal that is $8.99. To find out the cost of the food we multiply the total number of people by how much each meal cost. 5 x 8.99 = cost of food Three people ordered a beverage with their food. Drinks are $2.50 a piece. To find the total cost of the drinks we multiply the total number of people who ordered drinks by the cost of each drink. 3 x 2.50 = cost of drinks To find the total amount Daniel has to pay we will create an equation with the cost of food plus the cost of drinks. Let total amount Daniel will pay = x cost of food + cost of drinks = x (5 x 8.99) + (3 x 2.50) = x 44.95 + 7.50 = x 52.45 = x Daniel will pay $52.45.

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