In order for the triangle to be called an isosceles right triangle, it must satisfy both conditions: XZ and XY must be perpendicular to each other, and XZ = XY.
To determine whether two lines are perpendicular, their slopes must be negative reciprocals of each other.
Solving for the slopes of XZ and XY:
slope of XZ = (y₂-y₁) / (x₂-x₁) = (6-3)/(5-1) = 3/4
slope of XY = (y₂-y₁) / (x₂-x₁) = (3--1)/(1-4) = -4/3
-4/3 is the negative reciprocal of 3/4, therefore XZ and XY are perpendicular to each other.
Solving for distance:
XZ = √[(y₂-y₁)²+(x₂-x₁)²] = √[(6-3)²+(5-1)²] = 5
XY = √[(y₂-y₁)²+(x₂-x₁)²] = √[(3--1)²+(1-4)²] = 5
<span>The slope of XZ is 3/4, the slope of XY is -4/3, and XZ = XY = 5. </span>
Answer:
a,c,d,e
dont blame me if i calculated it in a hurry
Answer:
≤ 4.3 gigabytes
Step-by-step explanation:
Flat fee + cost for x gigabytes = her budget
47 + 5 * x ≤ 68.50
5x = 68.50 - 47 ≤ 21.50
x ≤ 21.50/5 = 4.3 gigabytes
Answer: 4 pt= 8c
28 qt= 7 gal
Step-by-step explanation: To convert from pints to cups, multiply by 2. To convert from quarts to gallons, divide by 4.
<u>Given</u>:
The lengths PQ = 4x + 2, QR = 7x – 19, and QU = 34
We need to determine the value of ST.
<u>Value of x:</u>
By two tangent theorem, we have;
PQ = QR
Substituting the values, we get;
Thus, the value of x is 7.
<u>Length of PQ and QR:</u>
Substituting x = 7 in the expressions of PQ and QR, we get the lengths.
Length of PQ = 
Length of QR = 
<u>Radius of the circle:</u>
The radius of the circle PU can be determined using the Pythagorean theorem.
Thus, we have;
Substituting the values, we get;
Thus, the radius of the circle is 16.
<u>Length of ST:</u>
The length of ST is 
Substituting SU = UT = 16 because the radius of the circle is 16.
Thus, we have;
Thus, the length of ST is 32.
