Answer:
b = 3 and a = -1
Step-by-step explanation:
You have your given equation:
2a - 3b = -11
a + 3b = 8
You need to find what a and b is.
To find b:
2a - 3b = -11
-2a - 6b = -16
I multiplied a + 3b = 8 by -2. When you multiply a number you have to multiply all of them. You have to choose a number that would cancel out all of a.
So now your equation would look like this when you solve for b:
2a - 3b = -11
-2a - 6b = -16
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a - 9 = -27 then you divide -9 to -27 which is 3 so b = 3.
To find a:
2a - 3b = -11
a + 3b = 8
I multiplied a + 3b = 8 by -1 and 2a - 3b = -11 by -1 as well.
Your equation will look like this when you solve for a:
-2a + 3b = 11
-1a - 3b = -8
------------------
-3a = 3 then divide -3 to 3 which is -1 so a = -1.
Check to see if you have the correct answer by plugging in the number you got for a and b into the equation and solve.
1. 2(-1) -3(3) = -11
-2 - 9 = -11
2. -1 + 3(3) = 8
-1 + 9 = 8
Answer:
y = 5
z = 55
Step-by-step explanation:
90 - 35 = 55
z = 55
7y = 35

y= 5
The answer is 19.4
Most of the time when you try to find a missing length of a right triangle you use Pythagorean theorem. Pythagorean theorem is A squared plus B squared equals C squared. C squared is always going to be the longest length/diagonal line otherwise known as your hypotenuse. In this case the ladder is the hypotenuse. So instead of adding five squared +20 squared you’re going to square 20 and then subtract five squared to get the missing length which would be B squared and then you have to find the square root of B squared. So 20 squared is 4000. 5squared is 25 400-25 = 375 square root of 375 is about 19.4.
Answer:
The option is C i.e 115°, 65°. proof is given below.
Step-by-step explanation:
Given:
ABCD is a quadrilateral.
m∠ A = 100 + 5x
m∠ B = 77 - 4y
m∠ C = 106 + 3x
m∠ D = 47 + 6y
To Prove:
ABCD is a parallelogram if opposing angles are congruent by finding the measures of angles.
m∠ A = m∠ C and
m∠ B = m∠ D
Proof:
ABCD is a quadrilateral and is a parallelogram if opposing angles are congruent.
∴ m∠ A = m∠ C
On substituting the given values we get
∴ 100 + 5x = 106 +3x
∴ 
m∠ A = 100 + 5x = 100 + 5 × 3 =100 + 15 = 115°
m∠ C = 106 + 3x = 106 + 3 ×3 =106 + 9 = 115°
∴ m∠ A = m∠ C = 115°
Similarly,
∴ m∠ B = m∠ D
77 - 4y = 47 + 6y
10y = 77 - 47
10y =30
∴
m∠ B = 77 - 4y =77 - 4 × 3 = 77 - 12 = 65°
m∠ D = 47 + 6y = 47 + 6 × 3 = 47 + 18 = 65°
∴ m∠ B = m∠ D = 65°
Therefore the option is C i.e 115°, 65°