Perimeter of ∆ABC = 25
Difference between the two sides is 4
Find: AB, BC, AC
List the sides of ΔRST in in ascending order (shortest to longest) if:
m∠R = 3x+42°, m∠S = 4x−11°, and m∠T = x+13°
List the sides of ΔRST in in ascending order (shortest to longest) if:
m∠R = 2x+11°, m∠S = 3x+23°, and m∠T = x+42°
Answer with Step-by-step explanation:
1.In triangle ABC
AB=BC
Let AB=BC=x and AC=y
Perimeter of triangle ABC=25
...(1)
...(2)
Adding equation (1) and (2)
Substitute x=9.67 in equation (2)
2.
By using triangle angle sum property
Substitute the values then we get
Substitute the value
(Side ST is opposite to angle R, Side RT is opposite to angle S
(side RS is opposite to angle T)
When a>b
Then , opposite side of a> opposite side of b
RS<RT<ST
3.
By using triangle angle sum property
Substitute the values then we get
Substitute the value
RT>RS
RS>ST
ST<RS<RT
Answer:
x = 10/9
Step-by-step explanation:
Solve for x:
(4 x)/5 + 4/3 = 2 x
Put each term in (4 x)/5 + 4/3 over the common denominator 15: (4 x)/5 + 4/3 = (12 x)/15 + 20/15:
(12 x)/15 + 20/15 = 2 x
(12 x)/15 + 20/15 = (12 x + 20)/15:
(12 x + 20)/15 = 2 x
Multiply both sides by 15:
(15 (12 x + 20))/15 = 15×2 x
(15 (12 x + 20))/15 = 15/15×(12 x + 20) = 12 x + 20:
12 x + 20 = 15×2 x
15×2 = 30:
12 x + 20 = 30 x
Subtract 30 x from both sides:
(12 x - 30 x) + 20 = 30 x - 30 x
12 x - 30 x = -18 x:
-18 x + 20 = 30 x - 30 x
30 x - 30 x = 0:
20 - 18 x = 0
Subtract 20 from both sides:
(20 - 20) - 18 x = -20
20 - 20 = 0:
-18 x = -20
Divide both sides of -18 x = -20 by -18:
(-18 x)/(-18) = (-20)/(-18)
(-18)/(-18) = 1:
x = (-20)/(-18)
The gcd of 20 and -18 is 2, so (-20)/(-18) = (-(2×10))/(2 (-9)) = 2/2×(-10)/(-9) = (-10)/(-9):
x = (-10)/(-9)
Multiply numerator and denominator of (-10)/(-9) by -1:
Answer: x = 10/9
Which statement is true about the solution to the set of equations? (5 points)
There are infinitely many solutions.
There are two solutions.
There is one solution.
There is no solution.