The complete question in the attached figure
we know that
m∡4=65°
m∡4=m∡2---------> by internal alternate angles
m∡5=m∡3---------> by internal alternate angles
m∡1=180°-m∡2---------> 180°-65°--------> m∡1=115°
the answer is
m∡1=115°
Answer:
Karen has to at least spend 11 minutes.
Step-by-step explanation:
This is because 57 - 13 = 44. 44 divided by 4 = 11. This means that in 11 minutes Karen will have a 57 liter tank. But she could keep going, but the least number of minutes would be 11 minutes, to get to 57 liters.
I hope this helps! Please mark me Brainliest if it did! Thank you and have a nice day!
Hello!
Simplifying
5x2 + -7x + -3 = 8
Reorder the terms:
-3 + -7x + 5x2 = 8
Solving
-3 + -7x + 5x2 = 8
Solving for variable 'x'.
Reorder the terms:
-3 + -8 + -7x + 5x2 = 8 + -8
Combine like terms: -3 + -8 = -11
-11 + -7x + 5x2 = 8 + -8
Combine like terms: 8 + -8 = 0
-11 + -7x + 5x2 = 0
Begin completing the square. Divide all terms by
5 the coefficient of the squared term:
Divide each side by '5'.
-2.2 + -1.4x + x2 = 0
Move the constant term to the right:
Add '2.2' to each side of the equation.
-2.2 + -1.4x + 2.2 + x2 = 0 + 2.2
Reorder the terms:
-2.2 + 2.2 + -1.4x + x2 = 0 + 2.2
Combine like terms: -2.2 + 2.2 = 0.0
0.0 + -1.4x + x2 = 0 + 2.2
-1.4x + x2 = 0 + 2.2
Combine like terms: 0 + 2.2 = 2.2
-1.4x + x2 = 2.2
The x term is -1.4x. Take half its coefficient (-0.7).
Square it (0.49) and add it to both sides.
Add '0.49' to each side of the equation.
-1.4x + 0.49 + x2 = 2.2 + 0.49
Reorder the terms:
0.49 + -1.4x + x2 = 2.2 + 0.49
Combine like terms: 2.2 + 0.49 = 2.69
0.49 + -1.4x + x2 = 2.69
Factor a perfect square on the left side:
(x + -0.7)(x + -0.7) = 2.69
Calculate the square root of the right side: 1.640121947
Break this problem into two subproblems by setting
(x + -0.7) equal to 1.640121947 and -1.640121947.
Subproblem 1
x + -0.7 = 1.640121947
Simplifying
x + -0.7 = 1.640121947
Reorder the terms:
-0.7 + x = 1.640121947
Solving
-0.7 + x = 1.640121947
Solving for variable 'x'.
Move all terms containing x to the left, all other terms to the right.
Add '0.7' to each side of the equation.
-0.7 + 0.7 + x = 1.640121947 + 0.7
Combine like terms: -0.7 + 0.7 = 0.0
0.0 + x = 1.640121947 + 0.7
x = 1.640121947 + 0.7
Combine like terms: 1.640121947 + 0.7 = 2.340121947
x = 2.340121947
Simplifying
x = 2.340121947
Subproblem 2
x + -0.7 = -1.640121947
Simplifying
x + -0.7 = -1.640121947
Reorder the terms:
-0.7 + x = -1.640121947
Solving
-0.7 + x = -1.640121947
Solving for variable 'x'.
Move all terms containing x to the left, all other terms to the right.
Add '0.7' to each side of the equation.
-0.7 + 0.7 + x = -1.640121947 + 0.7
Combine like terms: -0.7 + 0.7 = 0.0
0.0 + x = -1.640121947 + 0.7
x = -1.640121947 + 0.7
Combine like terms: -1.640121947 + 0.7 = -0.940121947
x = -0.940121947
Simplifying
x = -0.940121947
Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {2.340121947, -0.940121947}
Because the triangles are similar the ratio of all the sides would be the same. So you need to find the ratio of the common sides and then use that ratio to find the unkown side.
In this picture sides FG = 52, FV would be the same side and is 24.
Dividing 24/52 = 0.461, so the unkown side WV would be 0.444 of it's common side HG.
HG = 39
39 * 0.461= 18.
The answer is C. 18
Answer:
780
Step-by-step explanation:
round up to the nearest ten
