Answer:
MN = 68
Step-by-step explanation:
LN = 91
LM = 23
Points L, M, and N are collinear, therefore, according to the segment addition postulate, the following can be deduced:
LM + MN = LN
23 + MN = 91 (Substitution)
Subtract 23 from both sides
23 + MN - 23 = 91 - 23
MN = 68
Answers:
1) 
2) 
Step-by-step explanation:
In mathematics there are rules related to complex numbers, specifically in the case of addition and multiplication:
<u>Addition:
</u>
If we have two complex numbers written in their binomial form, the sum of both will be a complex number whose real part is the sum of the real parts and whose imaginary part is the sum of the imaginary parts (similarly as the sum of two binomials).
For example, the addition of these two binomials is:
Similarly, the addition of two complex numbers is:
Here the complex part is the number with the 
<u>Multiplication:
</u>
If we have two complex numbers written in their binomial form, the multiplication of both will be the same as the multiplication (product) of two binomials, taking into account that 
.
For example, the multiplication of these two binomials is:
Similarly, the multiplication of two complex numbers is:
Answer:
X=34°
Y= 56°
Angle HIF are 90° when we bisectors YI 90-34
Therfore y = 56°
FGI are a triangle sum of it is 180 = 90+56
146 - 180
X= 34
Answer:
16 cm²
Step-by-step explanation:
The figure is a trapezoid with two parallel sides.
The formula for the area is
A = ½(a + b)h
Data:
a = 5 cm
b = 3 cm
h = 4 cm
Calculation:
A = ½(5 + 3) × 4 = ½ × 8 × 4 = 16 cm²
The area of the trapezoid is 16 cm².
Answer:
a) There is no solution to the equation.
b) Solution: x = 16
Step-by-step explanation:
Hi there!
a) Let´s write the equation:
√(x + 5) - 9 = -12
add 9 to both sides of the equation
√(x + 5) = -12 + 9
√(x + 5) = -3
Square both sides of the equation
x + 5 = 9
Subtract 5 to both sides
x = 9 - 5
x = 4
Let´s check the solution:
√(x + 5) - 9 = -12
√(4 + 5) - 9 = -12
√9 - 9 = -12
3 - 9 = -12
-6 ≠ -12
Then x = 4 is not a solution to the equation.
b) Let´s write the equation:
√(4x - 7) = √(3x + 9)
square both sides of the equation
4x - 7 = 3x + 9
subtract 3x and add 7 to both sides of the equation
4x - 3x = 9 + 7
x = 16
Let´s check the solution:
√(4x - 7) = √(3x + 9)
x = 16
√(4(16) - 7) = √(3(16) + 9)
√57 = √57
Then x = 16 is the solution to the equation
