Imagine two lines intersect. How can the properties of linear pairs and vertical angles help to determine the angle measures cre

Answer:

I believe it's 2.

Step-by-step explanation:

10, and -10

The diagonal measures 20.68 ft; the shorter base is 17.21 ft. To understand this, we recognize that with base angles summing to 140°, each angle is 70°, given the isosceles trapezoid's properties. We can apply the Law of Cosines to find the diagonal's length, denoted as d. The length of the diagonal determines to be d = 20.68 ft. Determining the shorter base is somewhat more complex. By drawing an altitude from the upper vertices to the base, which measures 22 ft, we create two similar smaller right triangles requiring us to find the height and base measures related to each of the 70-degree angles and the hypotenuse of 7. By working through the calculations for height and base from one triangle, we subsequently find that 22 minus twice the base measure gets us to the shorter base's measure, arriving at x = 17.21 ft.

Answer:

12 pencils per package.

Step-by-step explanation:

Details provided:

Ethan purchased 4 packages of pencils.

Number of Packages = 4

Number of pencils shared with friend = 8 pencils

Pencils remaining = 40 pencils

∴Total Number of Pencils = Pencils given to friend + Pencils remaining =

Total Pencils in each package =

Answer:

Explanation step-by-step:

Let

x represent Hermione's salary prior to the raise

Given:

Therefore, the equation that expresses this relationship is

To find x, divide both sides by 1.05:

The salt enters at a rate of (5 g/L)*(3 L/min) = 15 g/min.

The salt exits at a rate of (x/10 g/L)*(3 L/min) = 3x/10 g/min.

Thus, the total rate of salt flow, represented by in grams, is defined by the differential equation,

which is linear. Shift the term to the right side, then multiply both sides by :

Next, integrate both sides and solve for :

Initially, the tank contains 5 g of salt at time , so we have

The duration required for the tank to contain 20 g of salt is , such that