A jar contains 3 yellow and 7 green marbles. You randomly draw one marble from the jar then REPLACE it and randomly draw a secon
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Since you did not provide a diagram, I made one for easier reference. You are asking what kind of triangle is the one shaded in red. Since a rectangle has two sets of congruent sides, their diagonals are also equal. When two diagonals intersect each other, they make 4 congruent sides. Thus, the triangle is an isosceles triangle, since it has two equal sides ST and TR.
Answer:
See attached graph.
Step-by-step explanation:
We can graph this with relative ease on the calculator or computer (see attachment) but let's make sure we understand it theoretically and algebraically!
y=|x - 4| + 2
First of all, this is an absolute value function, so it'll look like a v where every input equals its positive output (2, 2) (-3,3) etc. You can't get a negative number with a graph of y=|x| unless you translate it.
Next, there's a -4 inside the abs val. According to the formula y = |x - h| + k, where h is the horizontal shift, this means we need to shift the vertex right 4.
There's a +2 outside the abs val. K is the vertical shift, so we need to shift the vertex up 2.
The first equation, 8x - 9y = - 23
Obtain the equation in slope- intercept form
y = mx + c ( m is the slope and c the y-intercept )
to calculate m use the gradient formula
m = ( y₂ - y₁ ) / ( x₂ - x₁ )
with (x₁, y₁ ) = ( , 3) and (x₂, y₂ ) = (- 4, - 1 )
m = = (- 4)/-
=
partial equation is y = x + c
to find c substitute either of the 2 points into the partial equation
using (- 4, - 1 ), then
- 1 = - + c ⇒ c =
y = x +
← in slope- intercept form
the equation of a line in standard form is
Ax + By = C ( A is a positive integer and B, C are integers )
rearrange the slope- intercept equation into this form
multiply through by 9
9y = 8x + 23 ( subtract 9y and 23 from both sides )
8x - 9y = - 23 in standard form