En matemáticas, un conjunto contable es un conjunto con la misma cardinalidad (número de elementos) que un subconjunto del conjunto de números naturales. Un conjunto contable es un conjunto finito o un conjunto contable infinito.
The equation of the line that passes through the point (-6,-3) and has a slope of 0 is y = -3
The line is passing through the point = (-6,-3)
The slope of the line = 0
The point slope form is

Substitute the values in the equation
(y-(-3)) = 0×(x-(-6))
We have to convert this equation the slope intercept form
Slope intercept form is
y = mx + b
Where m is the slope of the line
b is the y intercept
(y-(-3)) = 0×(x-(-6))
y+3 = 0×(x+6)
y+3 = 0
y = -3
Hence, the equation of the line that passes through the point (-6,-3) and has a slope of 0 is y = -3.
Learn more about slope intercept form here
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The question is incomplete. Here is the complete question.
Find the measurements (the lenght L and the width W) of an inscribed rectangle under the line y = -
x + 3 with the 1st quadrant of the x & y coordinate system such that the area is maximum. Also, find that maximum area. To get full credit, you must draw the picture of the problem and label the length and the width in terms of x and y.
Answer: L = 1; W = 9/4; A = 2.25;
Step-by-step explanation: The rectangle is under a straight line. Area of a rectangle is given by A = L*W. To determine the maximum area:
A = x.y
A = x(-
)
A = -
To maximize, we have to differentiate the equation:
=
(-
)
= -3x + 3
The critical point is:
= 0
-3x + 3 = 0
x = 1
Substituing:
y = -
x + 3
y = -
.1 + 3
y = 9/4
So, the measurements are x = L = 1 and y = W = 9/4
The maximum area is:
A = 1 . 9/4
A = 9/4
A = 2.25
<span>MNO is similar to GHK by AA Similarity Postulate
Let's start by listing each triangle and the measurements of all three angles. For each triangle, we've been given the measurements of 2 of the angles and the 3 angle will simply be 180 minus the other 2 angles. I assume you can do the subtraction, so I'll simply list each triangle with all three angle measurements.
NMO: 79, 22, 79
GHK: 79, 79, 22
PQR: 20, 79, 81
DEF: 82, 22, 76
And the triangles NMO and GHK are similar to each other since they have the same angles. The order really doesn't matter since it's OK for similar triangles to be rotated or reflected. The key thing to remember in a triangle is that if you've been told what 2 of the angles are, you also know what the 3rd angle is since the sum of the angles of a triangle will always be 180.
So the answer is:
MNO is similar to GHK by AA Similarity Postulate"</span>
Answer: there are 10 multiple choice questions and 15 short-answer questions
Step-by-step explanation:
Let x represent the number of multiple choice questions in the test.
Let y represent the number of short-answer questions in the test.
If the test has 25 questions, it means that
x + y = 25
Multiple-choice questions are worth 2 points, and short-answer questions are worth 4 points. The test is worth a total of 80 points. It means that
2x + 4y = 80 - - - - - - - -1
Substituting x = 25 - y into equation 1, it becomes
2(25 - y) + 4y = 80
50 - 2y + 4y = 80
- 2y + 4y = 80 - 50
2y = 30
y = 30/2 = 15
x = 25 - y = 25 - 15 = 10
A. The number of multiple-choice questions plus the number of short-answer questions is 25.