Answer:
less than half
Step-by-step explanation:
13/12 - 7/10 = 23/60
The similar circles P and Q can be made equal by dilation and translation
- The horizontal distance between the center of circles P and Q is 11.70 units
- The scale factor of dilation from circle P to Q is 2.5
<h3>The horizontal distance between their centers?</h3>
From the figure, we have the centers to be:
P = (-5,4)
Q = (6,8)
The distance is then calculated using:
d = √(x2 - x1)^2 + (y2 - y1)^2
So, we have:
d = √(6 + 5)^2 + (8 - 4)^2
Evaluate the sum
d = √137
Evaluate the root
d = 11.70
Hence, the horizontal distance between the center of circles P and Q is 11.70 units
<h3>The scale factor of dilation from circle P to Q</h3>
We have their radius to be:
P = 2
Q = 5
Divide the radius of Q by P to determine the scale factor (k)
k = Q/P
k = 5/2
k = 2.5
Hence, the scale factor of dilation from circle P to Q is 2.5
Read more about dilation at:
brainly.com/question/3457976
To solve this we can make it into an equation, which looks like this
y = 2x (for Rebecca)
y = x + 10 (for Alice)
The we subtract one equation from the other to solve
0 = x - 10
10 = x
x = 10
Now we replace x in whichever equation and we get 20
So, each girl will read 20 books for them to be at the same book.
Hope this helps, remember that Jesus loves you
Answer:
This shows that the mean increases by 2.95
Step-by-step explanation:
Assume the given data is 2, 5, 6, 8
Mean = 2 +5+6+8/4
Mean = 21/4
Mean = 5.25
If number 20 is added, the data becomes 2, 5, 6, 8, 20
New mean = 2 +5+6+8+20/4
New mean = 41/5
New mean = 8.2
Taking the difference in the mean:
Difference = 8.2 - 5.25
Difference = 2.95
This shows that the mean increases by 2.95
<em>NB: The data used was assumed since we are not given any data in question</em>
<em></em>
Using the dot product:
For any vector x, we have
||x|| = √(x • x)
This means that
||w|| = √(w • w)
… = √((u + z) • (u + z))
… = √((u • u) + (u • z) + (z • u) + (z • z))
… = √(||u||² + 2 (u • z) + ||z||²)
We have
u = ⟨2, 12⟩ ⇒ ||u|| = √(2² + 12²) = 2√37
z = ⟨-7, 5⟩ ⇒ ||z|| = √((-7)² + 5²) = √74
u • z = ⟨2, 12⟩ • ⟨-7, 5⟩ = -14 + 60 = 46
and so
||w|| = √((2√37)² + 2•46 + (√74)²)
… = √(4•37 + 2•46 + 74)
… = √314 ≈ 17.720
Alternatively, without mentioning the dot product,
w = u + z = ⟨2, 12⟩ + ⟨-7, 5⟩ = ⟨-5, 17⟩
and so
||w|| = √((-5)² + 17²) = √314 ≈ 17.720
