Let the numbers be x and y. They differ by 46. Then x = y + 46.
Their product is P = xy. Since x = y + 46, P = xy = (y + 46)y, or
P = y^2 + 46y. You could graph this and then identify the coordinates of the vertex, which would give you the minimum value of P.
Or you could differentiate P(y) with respect to y, set the result = to 0, and solve for y:
2y + 46 = 0; y = -23. x = y + 46, or +23.
The vertex of the graph of this parabola represents the minimum value of the product P. It is (23, 46), and 46 is the smallest possible product here.
Answer:
Shape 1: 197.04
Shape 2: 125.44
Shape 3: 62.72
Step-by-step explanation:
For shape 1, you first need to find the radius to then find the area of a circle. Which is 394.08. Since this isn't a full circle, you will need to divide it by 2 to get 197.04. For shape 2(Easiest to find) You do 11.2*11.2 to get the answer of 125.44. And lastly for shape 3, you can basically do the same as what you did for shape 2. But since it is a triangle, you divide your answer by 2, to get the answer of 62.72.
Answer:
the first test
Step-by-step explanation: on the second test she got 90% correct on the first test she got 97% correct.
Step-by-step explanation:
1) 
We know that, 
2) 
Again using above property,
3) 
We know that,
So,
4) 
Hence, this is the required solution.
Answer:
Step-by-step explanation:
a. 5 x (c) = -35
Divide each side by 5, which is equal to -6. Remember, two negatives make a positive and one negative and one positive makes a negative.
c. 16/(x) = -4
What times what is equal to a positive 16? To solve, multiply x on both sides of the equation to get 16 = -4x then divide -4 on both sides. You'll get the answer -4. 16/-4 = -4.
e. x/(-3)= -9
Like c, multiply both sides by the denominator, so -3. You'll get x by itself for an equation like x = -9 x -3. Then multiply, remember two negatives equal a positive, so x = 27. 27/-3 = -9.
g. -5000 x y = -10,000
Divide -5000 on both sides to get the equation y = -10,000/-5000. Then solve. y= 2. -5000 x 2 = -10,000.
i. 243/x = -81
Mutiply both sides of the equation by x, so x cancels out. You'll end up getting the equation 243= -81x. Then divide both sides of the equation by -81. Now that we have 1 positive and 1 negative we know our answer has to be negative. The equation should look like 243/-81 = x, which is equal to x=-3. Thus, the answer is 243/(-3)= -81.
k. -92 x y= 184
Divide both sides by -92 to get x by itself. Then you'll get the equation y= 184/-92. y= -2 so, -92 x -2 = 184.
