Answer:
Given: It is given that and .
To Prove: ABCD is a parallelogram.
Statements
1. and
Reason: Given
2. are alternate interior angles
Reason: Def of alternate interior angles
3.
Reason: Alternate interior angles are congruent
4.
Reason: Reflexive property
5.
Reason: SAS congruency theorem
6.
Reason: Corresponding Parts of Congruent triangles are Congruent (CPCTC)
7. ABCD is a parallelogram
Reason: Parallelogram Side Theorem
Step-by-step explanation:
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Answer:
x = 8, and y = 12
Step-by-step explanation:
There are 2 variables, so you need 2 equations to form a system of equations in two variables.
The upper left triangle has all angle measures given: 100, 2x + y, 5x + y. We know that the sum of the measures of the angles of a triangle is 180.
First equation:
100 + 2x + y + 5x + y = 180
Simplify:
7x + 2y = 80 (First equation)
Now we see that the upper and lower sides are parallel, so alternate interior angles are congruent. The angles measuring 2x + y and 5x - y are alternate interior angles and are congruent.
Second equation:
2x + y = 5x - y
Simplify:
3x - 2y = 0 (Second equation)
Now we use the first equation and the second equation as a system of simultaneous equations to solve for x and y.
7x + 2y = 80
3x - 2y = 0
Solve the second equation for 2x.
3x = 2y
Now replace 2y in the first equation with 3x.
7x + 3x = 80
10x = 80
x = 8
Replace x with 8 in the second equation.
3(8) - 2x = 0
24 = 2x
x = 12
Answer: x = 8, and y = 12
Answer:
Therefore the general solution is

Step-by-step explanation:
Integration Rule:
Given differential equation is

[ multiplying dx both sides]
[ dividing
both sides]
Integrating both sides



[ c is arbitrary constant]

Therefore the general solution is

Ángulo exterior, la medida de un ángulo exterior de un triángulo es igual a la suma de las medidas de los dos ángulos interiores no adyacentes.
espero que haya ayudado, por favor, marcame el cerebro.
Q: If the 3 inner angles of a triangle are congruent, what is the measure of each one?
A: Exterior Angle The measure of an exterior angle of a triangle is equal to the sum of the mesures of the two non-adjacent interior angles. Hope it helped please mark me brainliest/
Answer:
300 cars must be made to minimize the unit cost
Step-by-step explanation:
Vertex of a quadratic function:
Suppose we have a quadratic function in the following format:

It's vertex is the point 
In which


Where

If a>0, the vertex is a minimum point, that is, the minimum value happens at
, and it's value is
.
The cost of producing x cars is given by:

So a quadratic equation with 
How many cars must be made to minimize the unit cost?
This is the xvalue of the vertex. So

300 cars must be made to minimize the unit cost