1) All angles of a rectangle are right angles, so the measure of angle CBA is 90 degrees.
2) Since all angles of a rectangle are right angles, angle BAD measures 90 degrees. Subtracting the 25 degrees of angle BAW from this, we get that angle CAD has a measure of 65 degrees.
3) Opposite sides of a rectangle are parallel, so by the alternate interior angles theorem, the measure of angle ACD is 25 degrees.
4) Because diagonals of a rectangle are congruent and bisect each other, this means BW=WA. So, since angles opposite equal sides in a triangle (in this case triangle ABW) are equal, the measure of angle ABW is 25 degrees. This means that the measure of angle CBD is 90-25=65 degrees.
5) In triangle AWB, since angles in a triangle add to 180 degrees, angle BWA measures 130 degrees.
6) Once again, since diagonals of a rectangle are congruent and bisect each other, AW=WD. So, the measures of angles WAD and ADW are each 65 degrees. Thus, because angles in a triangle (in this case triangle AWD) add to 180 degrees, the measure of angle AWD is 50 degrees.
Answer:
domain: (-∞ , ∞)
range: (-∞, 2]
Step-by-step explanation:
the domain is the set of values of what the x value can be. This function is parabolic and upside down, it can have a range of x values from - infinity to positive infinity. The function is most likely y=-x^2 +2
range is the output (y values) the function can possibly have. the max is 2 and includes 2 so we use bracket for that. The smallest y value can reach towards negative infinity.
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To determine the cost of each item, we need to set up equations. From the problem statement, we have three unknowns so we need three equations. We set up equations as follows:
let x cost of small pizzas
y cost of soda
z cost of salad
two small pizzas, a liter of soda, and a salad cost $14
2x + y + z = 14
one small pizza, a liter of soda, and three salads cost $15
x + y + 3z = 15
three small pizzas, a liter of soda, and two salads cost $22
3x + y + 2z = 22
Solving for x, y and z, we will have:
x = $ 5
y = $ 1
z = $ 3
Answer:
Step-by-step explanation:
<u>Given points:</u>
- A(-1, -9) and M(0.5, -2.5)
Let the coordinates of B are (x, y)
<u>Use midpoint formula to determine the point B:</u>
- 0.5 = (- 1 + x)/2 ⇒ 1 = -1 + x ⇒ x = 1 + 1 = 2
- -2.5 = (-9 + y)/2 ⇒ -5 = -9 + y ⇒ y = -5 + 9 = 4
