Step-by-step explanation:
Write the prime factorization of each term:
9r⁵s = 3² × r⁵ × s
6r⁴s² = 2 × 3 × r⁴ × s²
12r²s = 2² × 3 × r² × s
The greatest common factor will have all the common factors raised to their lowest exponent.
So all three terms have 3, r, and s as factors. The lowest exponent of 3 is 1. The lowest exponent of r is 2. The lowest exponent of s is 1.
GCF = 3 × r² × s
GCF = 3r²s
Factor out the GCF:
9r⁵s + 6r⁴s² − 12r²s
3r²s (3r³ + 2r²s − 4)
A = (-7,-6)
B = (8,-9)
Find the slope of line AB
m = (y2-y1)/(x2-x1)
m = (-9-(-6))/(8-(-7))
m = (-9+6)/(8+7)
m = -3/15
m = -1/5
The slope of line AB is -1/5.
Flip the fraction and the sign to go from -1/5 to +5/1 = 5. The perpendicular slope is 5.
Let m = 5.
Use the coordinates of point C (2,12) along with the perpendicular slope to get
y - y1 = m(x - x1)
y - 12 = 5(x - 2)
y - 12 = 5x - 10
y = 5x - 10+12
y = 5x + 2
Lastly, convert this to standard form
y = 5x + 2
5x+2 = y
5x+2-y = 0
5x-y = -2
Choice A is the closest match, but the -56 should be -2 instead. It seems like your teacher made a typo somewhere.
Based on the property of the consecutive angles of a parallelogram, the value of x is calculated as: E. 37.
<h3>What are the Properties of the Angles of a Parallelogram?</h3>
In a parallelogram, the angles that are opposite to each other are congruent while consecutive angles are supplementary.
Angles F and G are consecutive angles and are therefore supplementary (have a sum of 180 degrees.)
Angle F + angle G = 180
4x - 2 + 34 = 180
4x + 32 = 180
4x = 180 - 32
4x = 148
x = 148/4
x = 37
Value of x is: E. 37.
Learn more about parallelogram on:
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Answer:
12
Step-by-step explanation:
The length of the hypotenuse, PQ, can be found from the Pythagorean theorem:
PQ² = QR² +PR²
PQ² = 3² + 4² = 25
PQ = √25 = 5
The perimeter is the sum of side lengths:
P = 3 + 4 + 5 = 12
The perimeter of this triangle is 12 units.
Answer:
AC line = DB line
Step-by-step explanation:
ac line is always larger that db line
