Andre has 45 sheets of paper and needs to buy more. A store has 5 reams of paper, and each ream contains 500 sheets of paper. Th
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For this case we must find the product of the following expression:
So, we have:
By law of signs of multiplication is fulfilled:
ANswer:
Answer:
Step-by-step explanation:
<u>Given equation</u>:
This is an equation for a horizontal hyperbola.
<u>To complete the square for a hyperbola</u>
Arrange the equation so all the terms with variables are on the left side and the constant is on the right side.
Factor out the coefficient of the x² term and the y² term.
Add the square of half the coefficient of x and y inside the parentheses of the left side, and add the distributed values to the right side:
Factor the two perfect trinomials on the left side:
Divide both sides by the number of the right side so the right side equals 1:
Simplify:
Therefore, this is the standard equation for a horizontal hyperbola with:
- center = (1, 2)
- vertices = (-2, 2) and (4, 2)
- co-vertices = (1, 0) and (1, 4)
Answer:
h = 1.4
c = 2.8
Step-by-step explanation:
For each problem, remember the special triangle side ratios then use a proportion. To solve, isolate the variable.
For the triangle with the variable h:
Since two of the angles are 45, this is an isosceles triangle. All isosceles triangles have two equal sides that are not the hypotenuse.
In a right isosceles triangle, the ratio for regular side to hypotenuse is 1 to √2.
h = √2
h ≈ 1.4
For the triangle with the variable c:
The is an equilateral triangle cut in half because the angles are 30 and 60.
The side ratio of altitude to hypotenuse is √3 to 2.
c = 2√2
c ≈ 2.8