Answer:
<em>-3x+10y</em>
Step-by-step explanation:
Given the expression , we are to simplify by combining the like terms. On simplification we have;
Open the parenthesis:
Collect the like terms:
Sum up the resulting expression
<em>Hence the required expression on simplification is -3x+10y</em>
(a) The slope of the graph is
(b) The equation of the line in point-slope form is y - 1 = (x + 2.5)
(c) The y-intercept of the graph is (0 , 2)
(d) The y-intercept is correct
(e) We substitute x by zero because the line intersects y-axis at a point
its x-coordinate must be zero. Then we calculate the value of
y-coordinate when x = 0. The y-coordinate = 2, so the
y-intercept is (0 , 2)
Step-by-step explanation:
The slope of a line whose endpoints are and
is
The equation of a line in a point-slope form is:
From the graph:
1. The line passes through points (-5 , 0) and (0 , 2)
2. Substitute these points in the rule of the slope to find it
3. Writ the equation of the line in the form of point-slope
(a)
∵ = (-5 , 0)
∵ = (0 , 2)
∴
The slope of the graph is
(b)
∵ Point (-2.5 , 1) lies on the line
∴ = (-2.5 , 1)
∵ The point-slope form is ⇒
∵ m =
- Substitute the coordinates of the point and the slope in the equation
∴ y - 1 = (x - -2.5)
∴ y - 1 = (x + 2.5)
The equation of the line in point-slope form is y - 1 = (x + 2.5)
(c)
When the line intersects the y-axis at point (0 , b), then b is the
y-intercept
∵ The line intersects y-axis at point (0 , 2)
∴ The y-intercept is (0 , 2)
The y-intercept of the graph is (0 , 2)
(d)
Let us substitute x in the equation by zero
∵ x = 0
∵ The point slope form of the equation is y - 1 = (x + 2.5)
∴ y - 1 = (0 + 2.5)
∴ y - 1 = (2.5)
∴ y - 1 = 1
- Add 1 to both sides
∴ y = 2
- When x = 0 then y = 2
∴ Point (0 , 2) is the y-intercept
The y-intercept is correct
(e)
We substitute x by zero because the line intersects y-axis at a point its
x-coordinate must be zero
Then we calculate the value of y-coordinate when x = 0
The y-coordinate = 2, so the y intercept is (0 , 2)
Learn more:
You can learn more about linear equation in brainly.com/question/13168205
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Answer:
5507.79 feet
Step-by-step explanation:
To find the height of the mountain, we can draw triangles as in the image attached.
Let's call the height of the mountain 'h', and the distance from the first point (31 degrees) to the mountain 'x'.
Then, we can use the tangent relation of the angles:
tan(34) = h/x
tan(31) = h/(x+1000)
tan(31) is equal to 0.6009, and tan(34) is equal to 0.6745, so:
h/x = 0.6745 -> x = h/0.6745
using this value of x in the second equation:
h/(x+1000) = 0.6009
h/(h/0.6745 + 1000) = 0.6009
h = 0.6009 * (h/0.6745 + 1000)
h = 0.8909*h + 600.9
0.1091h = 600.9
h = 600.9 / 0.1091 = 5507.79 feet
Answer:
A
Step-by-step explanation:
← divide numerator/ denominator by 4
=
Thus A form a proportion
≠
Thus B is not a proportion
← divide numerator/ denominator by 4
= ≠
Thus C is not a proportion
≠
Thus D is not a proportion