Answer:
Look at the equations:
y
=
−
9
x
−
21
and
y
=
5
x
+
7
Because both equations equal (y), they both equal the same.
If an equations says "
y
=
−
9
x
−
21
" , that means we can replace (y) with
−
9
x
−
21
.
Therefore when i take the equation:
y
=
5
x
+
7
, we can replace (y) to get:
−
9
x
−
21
=
5
x
+
7
Now isolate (x):
−
9
x
−
21
=
5
x
+
7
⇔
−
21
=
14
x
+
7
⇔
−
28
=
14
x
⇔
x
=
−
2
9514 1404 393
Answer:
√629 ≈ 25.08
Step-by-step explanation:
The distance formula is useful for this.
d = √((x2 -x1)² +(y2 -y1)²)
d = √((-12 -13)² +(6 -8)²) = √(625 +4) = √629 ≈ 25.08
The distance between the points is about 25.08 units.
Answer:
Option B is correct.
The point which lies on the new graph g(x) is, (-3, 7.5)
Step-by-step explanation:
For a base function f(x), a new function g(x) = cf(x) is vertically stretched by a factor c if c> 1.
Given the parent function: f(x) =|x|
Now, by vertically stretched definition,
A function f(x) is vertically stretched by a factor of 2.5 then; we have the new function or new graph i.e,
g(x) = 2.5 f(x) where c=2.5 > 1
therefore, g(x) =2.5|x|
We have to find which point lies on the new graph;
Option A:
(-4 , -4)
Here x = -4 and g(-4) = -4
![-4=2.5 \cdot 4=10](https://tex.z-dn.net/?f=-4%3D2.5%20%5Ccdot%204%3D10)
-4 = 10 False.
Option B:
(-3 , 7.5)
g(x) = 2.5|x|
![g(-3) = 2.5 |-3|](https://tex.z-dn.net/?f=g%28-3%29%20%3D%202.5%20%7C-3%7C)
![7.5= 2.5 \cdot 3=7.5](https://tex.z-dn.net/?f=7.5%3D%202.5%20%5Ccdot%203%3D7.5)
7.5 = 7.5 True.
Option C:
(-2 , 5.5)
![g(-2) = 2.5 |-2|](https://tex.z-dn.net/?f=g%28-2%29%20%3D%202.5%20%7C-2%7C)
![5.5 = 2.5 \cdot 2=5](https://tex.z-dn.net/?f=5.5%20%3D%202.5%20%5Ccdot%202%3D5)
5.5 = 2 False.
Option D:
(-1 , -2.5)
![-2.5 = 2.5 \cdot 1=2.5](https://tex.z-dn.net/?f=-2.5%20%3D%202.5%20%5Ccdot%201%3D2.5)
-2.5 = 2.5 False
Therefore, from above you can see that the only point which is true for the new graph is, (-3 , 7.5)
Its a formula that helps identify the slope intercept form
Answer:
144 inches
Step-by-step explanation:
There are 12 inches in a foot
multiply 12 x 12 (the ladder)