Answer:
146
General Formulas and Concepts:
<u>Pre-Algebra</u>
Order of Operations: BPEMDAS
- Brackets
- Parenthesis
- Exponents
- Multiplication
- Division
- Addition
- Subtraction
<u>Algebra I</u>
<u>Algebra II</u>
- Distance Formula:
![\displaystyle d = \sqrt{(x_2-x_1)^2+(y_2-y_1)^2}](https://tex.z-dn.net/?f=%5Cdisplaystyle%20d%20%3D%20%5Csqrt%7B%28x_2-x_1%29%5E2%2B%28y_2-y_1%29%5E2%7D)
Step-by-step explanation:
<u>Step 1: Define</u>
Point A(2, 125)
Point B(98, 15)
<u>Step 2: Identify</u>
A(2, 125) → x₁ = 2, y₁ = 125
B(98, 15) → x₂ = 98, y₂ = 15
<u>Step 3: Find distance </u><em><u>d</u></em>
- Substitute in coordinates [Distance Formula]:
![\displaystyle d = \sqrt{(98-2)^2+(15-125)^2}](https://tex.z-dn.net/?f=%5Cdisplaystyle%20d%20%3D%20%5Csqrt%7B%2898-2%29%5E2%2B%2815-125%29%5E2%7D)
- [√Radical] (Parenthesis) Subtract:
![\displaystyle d = \sqrt{(96)^2+(-110)^2}](https://tex.z-dn.net/?f=%5Cdisplaystyle%20d%20%3D%20%5Csqrt%7B%2896%29%5E2%2B%28-110%29%5E2%7D)
- [√Radical] Evaluate exponents:
![\displaystyle d = \sqrt{9216+12100}](https://tex.z-dn.net/?f=%5Cdisplaystyle%20d%20%3D%20%5Csqrt%7B9216%2B12100%7D)
- [√Radical] Add:
![\displaystyle d = \sqrt{21316}](https://tex.z-dn.net/?f=%5Cdisplaystyle%20d%20%3D%20%5Csqrt%7B21316%7D)
- [√Radical] Evaluate:
![\displaystyle d = 146](https://tex.z-dn.net/?f=%5Cdisplaystyle%20d%20%3D%20146)
Answer:
- an = 12 + 7(n -1)
- a250 = 1755
Step-by-step explanation:
The first figure has 12 line segments. The second figure has 19, 7 more than the first. The third figure has 7 more than that. The sequence of line segment counts is an arithmetic sequence with first term 12 and common difference 7. The formula for the general term of an arithmetic sequence can be used.
General term for sequence with first term a1 and common difference d:
an = a1 + d(n -1)
For the numbers in this problem, the equation is ...
an = 12 + 7(n -1)
__
The 250th term of the sequence is ...
a250 = 12 + 7(250 -1) = 1755
Answer:
2,457 mm^2
Step-by-step explanation:
The dimensions of each of the triangles in terms of their bases and heights will be;
26 mm by 27 mm
Mathematically, the area of one of the triangles will be ;
1/2 * base * height
= 1/2 * 26 * 27 = 351 mm^2
So the area of the heptagon is the sum of the areas of all of the triangles
mathematically, that would be;
351 * 7 = 2,457 mm^2
Answer:
A fair six-sized die is rolled. Find the probability of getting at least a 4.
There are 6 outcomes and three of them are 4, 5 or 6, so the probability of greater than or equal to 4 is 3/6=½.