Answer:
The length of CD is 4 units
Step-by-step explanation:
Given the triangle ABC and if BC = 6 units and AD = 5 units
we have to find the length of DC.
In ΔABC and ΔBDC
∠ABC=∠BDC (each 90°)
BC=BC (common)
∠C=∠C (Common)
By ASA rule, ΔABC≈ΔBDC
Therefore their corresponding sides are in proportion
Let CD=x units
x=4, -9
Distance can't be negative therefore
The length of CD is 4 units
Ah, yes
if you start with P amount of something and the half life is h units (in years) and the time elapsed is t (in years) then the amount left is A
the equation is
so
given
h=1620
P=150
t=200
so
use your calculator
A≈137.69781917515g
about 138grams left
Rope = 225 cm
Needed rope = 11/2m = (11/2) × 100 cm = 550cm
So, rope needed to be cut
= 550cm - 225cm
= 225cm
=225/100m
=2.25 m
N the slope-intercept form you use the slope of the line and the y-intercept to express the linear function.
y=mx+b
y=mx+b
Where m is the slope and b is the y-intercept.
Example
Graph the equation
y−2x=1
y−2x=1
rewrite in slope-intercept form
y=2x+1
y=2x+1
Identify the slope and the y-intercept
m = 2 and b = 1
Plot the point corresponding to the y-intercept, (0,1)
picture23
The m-value, the slope, tells us that for each step to the right on the x-axis we move 2 steps upwards on the y-axis (since m = 2)
picture24
And once you have your second point you can just draw a line through the two points and extend it in both directions.
picture25
You can check to see that the line you've drawn is the correct one by substituting the coordinates of the second point into the original equation. If the equation holds true than the second point is correct.
Our second point = (1, 3)
y−2x=1
y−2x=1
3−2⋅1=3−2=1
3−2⋅1=3−2=1
Our second point is a solution to the equation i.e. the line we drew is correct.
A line that passes through the origin has a y-intersect of zero, b = 0, and represents a direct variation.
y=mx
y=mx
In a direct variation the nonzero number m is called the constant of variation.
You can name a function, f by using the function notion
f(x)=mx+b
f(x)=mx+b
f(x) is another name for y and is read as "the value of f at x" or "f of x". You can use other letters than f to name functions.
A group of functions that have similar characteristics are called a family of functions. All functions that can be written on the form f(x) = mx + b belong to the family of linear functions.
The most basic function in a family of functions is called the parent function. The parent function of all linear functions is
f(x)=x
