One triangle on a graph has a vertical side of 5 and a horizontal side of 11. Another triangle on a graph has a vertical side of
15 and a horizontal side of 33.
Could the hypotenuses of these two triangles lie along the same line?
Could the hypotenuses of these two triangles lie along the same line?
1 answer:
Answer:
Yes.
Step-by-step explanation:
The two triangles are <em>similar</em> because they have:
- a common angle (90°)
- corresponding sides with lengths in a 3:1 ratio
All you need to do is to slide the smaller triangle into the larger one so that a small angle and one of its sides coincide.
Then the hypotenuses of each triangle will lie along the same line.
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The ordered pair (6 , 4) is a solution for y - 4 = 7(x - 6)
Step-by-step explanation:
The point-slope form of a linear equation is:
, where
- m is the slope of the line
is a point on the line
Any point on the line is a solution for the equation of the line
The solution of an equation is the values of x and y which make the left hand side is equal to the right hand side
∵ The equation is y - 4 = 7(x - 6)
- Compare the equation by the point-slope form above
∴ m = 7
∴ = 6 and
= 4
- That means point (6 , 6) lies on the line
∴ Point (6 , 4) is a point on the line which represents the
given equation
∵ Any point on a line is a solution of the equation of that line
∴ (6 , 4) is a solution of the equation
The ordered pair (6 , 4) is a solution for y - 4 = 7(x - 6)
Learn more:
You can learn more about the linear equations in brainly.com/question/1284310
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Answer:
The domain of is restricted to
, and the domain of
is restricted to
.
Step-by-step explanation:
From Function Theory we know that domain of a function is the set of values such that an image exist. Let and
the function and its inverse, respectively.
At first glance we notice that function is a second order polynomial and every polinomial is a continuous function and therefore, there exists an image for every element of domain.
But domain of its inverse is restricted to every value of x so that , which means that
.
Finally, we concluded that following answer offers the best approximation to our result:
The domain of is restricted to
, and the domain of
is restricted to
.