It is given that, ABC BC =6.5cm CA=6.3cm AB=4.8cm Steps involved in construction Step 1: First draw a line segment AB = 4.8cm using pencil and ruler And mark one end A and other end B Step 2: From the point A draw an cm Step 3: From the point B draw an arc of length 6.5 cm Step point of intersection of these arc as C. Step 5: Join A and C & B and C. Now the triangle ABC is ready with BC =6.5cm CA=6.3cm AB=4.8cm
X² + 8x +y² - 2y -64 =0
We see that the equation has x² and y² . Also we see that coefficients in front of x² and y² are equal. So this is an equation of the circle.
(x² + 8x) +(y² - 2y) -64 =0
(x² + 8x) +(y² - 2y) = 64
We need to complete square for x and y groups, that means it should be written in form (a+b)² or (a-b)².
Expressions in parenthesis we will write as a²+/-2ab+b², to write it after as (a+/-b)², because a²+/-2ab+b² = (a+/-b)²
(x² + 2*4x) +(y² - 2*1y) = 64
(x² + 2*4x+4²) +(y² - 2*1y+1²) = 64+4²+1²
(x+4)² + (y-1)²= 81 Sometimes this is called a standard form of the circle.
(x+4)² + (y-1)²= 9² Sometimes it is required to write like this.
And if you are studying circles,ellipses and hyperbolas, the standard form should look like
Question 50.
a. Description
You walk 0.5 miles during 10 minutes, stop and wait for the bus during 4 minutes, then ride the bus for 2 miles during 4 minutes.
b. slopes
the slope of each line represents the average speed of every track.
1) first track
slope = 0.5 miles / 10 minutes = 0.05 miles / minutes.
Given that the slope is constant, you walked at a constant speed of 0.05 miles/minute.
2) second track
slope = 0 => you didn,t move (you were waiting the bus)
3) third track
slope = (2.5 - 0.5) miles / (18 min - 14 min) = 2 miles / 4 min = 0.5 miles / min
means the speed of the bus was constant and equal to 0.5 miles / min.
Answer:
The absolute value graph below does not flip.
Step-by-step explanation:
New graphs are made when transformed from their parents graphs. The parent graph for an absolute value graph is f(x) = |x|.
The equation used for a new graph transformed from the parent graph is in the form f(x) = a |k(x - d)| + c.
"a" shows vertical stretch (a>1) or vertical compression (0<a<1), and <u>flip across the x-axis if "a" is negative</u>.
"k" shows horizontal stretch (0<k<1) or horizontal compression (k>1), and <u>flip across the y-axis if "k" is negative</u>.
"d" shows horizontal shifts left (positive number) or right (negative number).
"c" shows vertical shifts up (positive) or down (negative).
The function f(x)=2|x-9|+3 has these transformations from the parent graph:
a = 2; Vertical stretch by a factor of 2
k = 1; No change
d = 9; Horizontal shift right 9 units
c = 3; Vertical shift up 3 units
Since neither "a" nor "k" was negative, there were no flips, <u>also known as reflections</u>.