Answer:
15 units
Step-by-step explanation:
The distance between two points can be found using the following formula:
Given points:
(-7, 5) and (2, -7)
<u>where:</u>
- x₁ = -7
- x₂ = 2
- y₁ = 5
- y₂ = -7
Substitute these points into the formula and simplify:
![\sf d=\sqrt{(2-(-7))^2+((-7)-5)^2} \ \textsf{[simplify the radicand]}\\\\ d=\sqrt{(2+7)^2+(-12)^2} \ \textsf{[simplify]}\\\\d=\sqrt{(9)^2+(-12)^2} \ \textsf{[evaluate the power]}\\\\d=\sqrt{81+144} \ \textsf{[add]}\\\\d=\sqrt{225}\ \textsf{[simplify]}\\\\d=15](https://tex.z-dn.net/?f=%5Csf%20d%3D%5Csqrt%7B%282-%28-7%29%29%5E2%2B%28%28-7%29-5%29%5E2%7D%20%5C%20%5Ctextsf%7B%5Bsimplify%20the%20radicand%5D%7D%5C%5C%5C%5C%20d%3D%5Csqrt%7B%282%2B7%29%5E2%2B%28-12%29%5E2%7D%20%5C%20%5Ctextsf%7B%5Bsimplify%5D%7D%5C%5C%5C%5Cd%3D%5Csqrt%7B%289%29%5E2%2B%28-12%29%5E2%7D%20%5C%20%5Ctextsf%7B%5Bevaluate%20the%20power%5D%7D%5C%5C%5C%5Cd%3D%5Csqrt%7B81%2B144%7D%20%5C%20%5Ctextsf%7B%5Badd%5D%7D%5C%5C%5C%5Cd%3D%5Csqrt%7B225%7D%5C%20%5Ctextsf%7B%5Bsimplify%5D%7D%5C%5C%5C%5Cd%3D15)
The distance between the two points is 15 units.
Learn more here:
brainly.com/question/27708708
brainly.com/question/21152362
The circumference of the smaller circle is ![[\frac{2\pi}{3} ]x \ units](https://tex.z-dn.net/?f=%5B%5Cfrac%7B2%5Cpi%7D%7B3%7D%20%5Dx%20%5C%20units)
.
The given parameters:
- Radius of the larger circle = x
- Radius of the smaller circle = ¹/₃ x
The circumference of the smaller circle is calculated as follows;
![C = 2\pi r\\\\C = 2\pi (\frac{x}{3} )\\\\C = [\frac{2\pi}{3} ]x \ units](https://tex.z-dn.net/?f=C%20%3D%202%5Cpi%20r%5C%5C%5C%5CC%20%3D%202%5Cpi%20%28%5Cfrac%7Bx%7D%7B3%7D%20%29%5C%5C%5C%5CC%20%3D%20%5B%5Cfrac%7B2%5Cpi%7D%7B3%7D%20%5Dx%20%5C%20units)
Thus, the circumference of the smaller circle is .
Learn more about circumference of circle here: brainly.com/question/9782777
The area of a square is the square of the length of its side. Here, we're told that the side of each square is equal to the radius (r) of the circle. Then the area of each square is
.. Asquare = r^2
There are 3 of them, so their total area is
.. Aall_squares = 3*r^2
The area of a circle is given by the formula
.. Acircle = π*r^2 . . . . . where r represents the radius of the circle
Fernie wants to compare the area of the 3 squares to that of the circle. We know that the value of π is about 3.1416, a little more than 3, so we have
.. Aall_squares = 3*r^2
.. Acircle ≈ 3.1416*r^2
We notice that 3.1416 is more than 3, so the area of the circle is greater than the area of Fernie's 3 squares.
___
It is not clear to me that Fernie's drawing will explain the formula A = π*r^2, unless it can somehow be used to show that the parts of each square that are outside the circle add up to an amount that is slightly less than the uncovered part of the circle.
Letter D will be your answer. So, the answer is f(x)-4.
Answer:
I. Ella packed 70 books more than Ray.
II. Ray packed 580 books.
III. Ella packed 650 books.
Step-by-step explanation:
Given the following data;
Ray = 29 boxes of 20 books
Ella = 26 boxes with 25 books
To find the total number of books packed by Ray;
Total for Ray (Ray packed) = 29 * 20
Total for Ray = 580 books.
To find the total number of books packed by Ella;
Total for Ella (Ella packed) = 26 * 25
Total for Ella = 650 books.
Next, we find the difference between the books packed by Ella and Ray;
Difference = Ella - Ray
Difference = 650 - 580
Difference = 70 books
