Find the inverse of the function f(x)= x^2-5
To find the inverse of a function, first replace the f(x) with a y. y = x^2-5 Then, switch x and y x = y^2-5 Then, solve for y. x = y^2 - 5 Add 5 to both sides x + 5 = y^2 Take the square root of both sides (+ or -) sqrt(x + 5) = y. Since we took the square root of a variable, we also need to include the negative side of the function
The cosA= 12/15. What is the tanB in the triangle ABC?
In a typical right triangle, angle C is the right angle, so we will use that for our question, which means that angle B is the other acute angle in the triangle. To solve this problem, we must first find the other side of the triangle. Since cosine is adjacent/hypotenuse, we are missing the other leg of the triangle. We will use the Pythagorean theorem, a^2 + b^2 = c^2, and solve for b. a= 12 and c = 15 (hypotenuse is always c) Set up the equation as follows: 12^2 + b^2 = 15^2 Simplify 144 + b^2 = 225 Subtract 144 from both sides b^2 = 81 Take the square root of both sides to solve for b b= 9 now, we can find the tanB. Tangent = opposite/adjacent in regards to the sides of the triangle. Opposite angle B is b,which equals 9 and adjacent to angle B is a, which equals 12, so tanB= 9/12.
The amount of commission earned in a day varies directly to the amount of sales made in the day. when John sells $10,000 in merchandise, he receives $2,100 in commission. Find the constant of variation, k, write the direct variation equation and evaluate how much commission John will make if he sells $16,300 in merchandise.
First: find the constant of variation. To do that, use the equation for direct variation, y=kx, where y varies directly as x, and plug in the values for x and y from above. 2100=k(10000). Divide both sides by 10,000 and find k to equal 0.21. Then, use that to write a general direct variation equation that can be used for any values given. y=0.21x would be that equation by substituting 0.21 for k. Next, use the general equation to find the commission for $16,300 in sales by substituting 16300 in for x, y = 0.21(16300) , and multiply to solve for y. By solving this, we see that John will make $3,423 if he sells $16,300 in merchandise.