Answer: the system of equations are
x + y = 35
3x + 2y = 100
Step-by-step explanation:
Let x= the number of short answer questions.
Let y= the number of multiple choice questions.
Noah wants 35 questions on the exam. This means that
x + y = 35
He plans to mix short answer questions, worth 3 points, with multiple choice questions worth 2 points. This means that x short answer questions will give 3x points and y multiple choice questions will give 2y points
Since the exam is worth 100 points, then,
3x + 2y = 100 - - - - - - - -1
Substituting x = 35 - y into equation 1, it becomes
3(35 - y) + 2y = 100
105 - 3y + 2y = 100
y = 105 - 100 = 5
x = 35 - y = 35 - 5
x = 30
Answer:
The answer will be D!
Step-by-step explanation:
First, let's find the value of X:
2x + 4x + 3x = 81
9x = 81
x = 9
Then, multiply it by the biggest side which is 4:
9 x 4 = 36
Answer:
And by definition the radius would be lower than the diameter and we have the following relationship:

And then the best answer would be:
B 2r
Step-by-step explanation:
When we have a circle we know that the area is given by:

And we also know that the diameter is the distance between two any points in the circle passing through the center.
And by definition the radius would be lower than the diameter and we have the following relationship:

And then the best answer would be:
B 2r
Answer:
a. 
b. 
Step-by-step explanation:
a. The sides of an Equilateral triangle are all equal.
Then, in this case:

Based on this, you can identify that AD divides the side BC into two equal parts and the triangle into two equal Right triangles. Then:

Knowing the length CD, you can find "x" using the Pythagorean Theorem. This is:

Where "a" is the hypotenuse and "b" and "c" are the legs.
In this case:

Substituting values and solving for "x", you get:

b. By definition, the measure of each interior angle of an Equilateral triangle is 60 degrees. Therefore:
