Triangle XYZ is isosceles. The measure of the vertex angle, Y, is twice the measure of a base angle. What is true about triangle
XYZ? Select three options.
a. Angle Y is a right angle.
b. The measure of angle Z is 45°.
c. The measure of angle X is 36°.
d. The measure of the vertex angle is 72°.
e. The perpendicular bisector of creates two smaller isosceles triangles.
a. Angle Y is a right angle.
b. The measure of angle Z is 45°.
c. The measure of angle X is 36°.
d. The measure of the vertex angle is 72°.
e. The perpendicular bisector of creates two smaller isosceles triangles.
2 answers:
Answer:
a. Angle Y is a right angle.
b. The measure of angle Z is 45°.
e. The perpendicular bisector of creates two smaller isosceles triangles.
Step-by-step explanation:
Let x represent the measures of base angles X and Z. Then 2x is the measure of vertex angle Y, and the sum of angles is ...
x + x + 2x = 180°
x = 45°
2x = m∠Y = 90°
so the triangle is an isosceles right triangle which has base angles of 45°.
The perpendicular bisector of XZ is the altitude of the triangle XYZ. It creates two smaller right triangles with acute angles of 45°. Hence, those, too, are isosceles right triangles.
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The solution is shown in the graph attached.
Explanation:
I am goind to teach you how to get that solution.
1) Restricctions: both x and y cannot be negative, i.e. x ≥ 0 and y ≥ 0
⇒ the solution is on the first quadrant.
2) Using the prices of the tickets, $ 8 for adults, and $ 6 for children, the linear equation for the costs is: cost = 8x + 6y.
3) Since the radio station is willing to spend a maximum of $ 172 you have the final restriction:
⇒ 8x + 6y ≤ 172.
4) Then the solutions that meet the three restrictions (x ≥0, y ≥ 0, and 8x + 6y ≤ 172) is found graphically by drawing the line 8 x + 6y = 172
5) To draw the line 8x + 6y = 172, use the axis intercepts:
x = 0 ⇒ y = 172/6 = 86/3 ⇒ point (0, 86/3)
y = 0 ⇒ x = 172/8 = 86/4 ⇒ point (86/4, 0)
6) Once you have the line you shade the region that is between the line and the two axis. That region contain of the possible solutions.
Explanation:
I am goind to teach you how to get that solution.
1) Restricctions: both x and y cannot be negative, i.e. x ≥ 0 and y ≥ 0
⇒ the solution is on the first quadrant.
2) Using the prices of the tickets, $ 8 for adults, and $ 6 for children, the linear equation for the costs is: cost = 8x + 6y.
3) Since the radio station is willing to spend a maximum of $ 172 you have the final restriction:
⇒ 8x + 6y ≤ 172.
4) Then the solutions that meet the three restrictions (x ≥0, y ≥ 0, and 8x + 6y ≤ 172) is found graphically by drawing the line 8 x + 6y = 172
5) To draw the line 8x + 6y = 172, use the axis intercepts:
x = 0 ⇒ y = 172/6 = 86/3 ⇒ point (0, 86/3)
y = 0 ⇒ x = 172/8 = 86/4 ⇒ point (86/4, 0)
6) Once you have the line you shade the region that is between the line and the two axis. That region contain of the possible solutions.
Answer:
the answer is k=−23/4
Step-by-step explanation:
hoped I helped:)
