Answer
54 degrees
Step-by-step explanation:
Using angle sum property(angles in a triangle add up to 180),
y+y+72=180
2y+72=180
2y=180-72
2y=108
y=108/2
y=54 degrees
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Answer:
The correct options are;
D. Triangles ABC and A'B'C' are congruent
E. Angle ABC is congruent to angle A'B'C'
F. Segment BC is congruent to segment B'C'
H. Segment AQ is congruent to segment A'Q'
Step-by-step explanation:
The given information are;
The angle of rotation of triangle ABC = 60°
Therefore, given that a rotation of a geometric figure about a point on the coordinate plane is a form of rigid transformation, we have;
1) The length of the sides of the figure of the preimage and the image are congruent
Therefore;
BC ≅ B'C'
2) The angles formed by the sides of the preimage are congruent to the angles formed by the corresponding sides of the image
Therefore;
∠ABC ≅ ∠A'B'C'
3) The distances of the points on the figure of the preimage from the coordinates of the point of rotation are equal to the distances of the points on the figure of the image from the coordinates of the point of rotation
Therefore;
Segment AQ ≅ A'Q'.
Answer:
The equation in standard form is:
x^2-40x-6000 = 0
Step-by-step explanation:
Let the length of the field be x yards.
Now the width of the field is 40 yards less than the length of the field.
Thus, the width of the field would be (x-40) yards
Now, to calculate the area of the field, we simply multiply the length of the field by the width of the field.
Hence;
Since the shape is rectangular, the area is the product of the length and that of the width
x(x-40) =6,000
x^2 -40x = 6,000
x^2-40x-6000 = 0
Answer:
Correct answer: adult tickets x = 72
Step-by-step explanation:
Given:
x = ? number of the adult tickets
y = ? number of the senior tickets
12$ adult ticket price
8$ senior ticket price
We will solve this problem using a system of two equations with two variables
x + y = 98 we will multiply whole equation with number - 2 and get:
- 2 x - 2 y = - 196
12 x + 8 y = 1072 we will divide the whole equation by the number 4 and get:
3 x + 2 y = 268
- 2 x - 2 y = - 196
we will now add the first equation to the second and get:
3 x - 2 x = 268 - 196
x = 72
x + y = 98 ⇒ 72 + y = 98 ⇒ y = 98 - 72 = 26
y = 26
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