Answer: 200 minutes have to be used for the costs of both plans to be the same.
Step-by-step explanation:
Let x represent the number of minutes that have to be used for the costs of both plans to be the same.
Package A is $35.00 per month with an additional charge of $0.15 per minute for long distance. This means that the cost of using package A for x minutes in a month would be
35 + 0.15x
Package B is $45.00 per month with an additional charge of $0.10 per minute for long distance. This means that the cost of using package A for x minutes in a month would be
45 + 0.1x
For both costs to be the same, it means that
35 + 0.15x = 45 + 0.1x
0.15x - 0.1x = 45 - 35
0.05x = 10
x = 10/0.05
x = 200
Answer:
x = √47
General Formulas and Concepts:
<u>Pre-Algebra</u>
Order of Operations: BPEMDAS
- Brackets
- Parenthesis
- Exponents
- Multiplication
- Division
- Addition
- Subtraction
Equality Properties
<u>Trigonometry</u>
- [Right Triangles Only] Pythagorean Theorem: a² + b² = c²
Step-by-step explanation:
<u>Step 1: Define</u>
We have a right triangle. We can use PT to solve for the missing side length.
<u>Step 2: Identify Variables</u>
Leg <em>a</em> = 5
Leg <em>b </em>= <em>x</em>
Hypotenuse <em>c</em> = √72
<u>Step 3: Solve for </u><em><u>x</u></em>
- Substitute [PT]: 5² + x² = (√72)²
- Exponents: 25 + x² = 72
- Isolate <em>x</em> term: x² = 47
- Isolate <em>x</em>: x = √47
Hello!
To solve this question, we must first add the exponent into the number 7 before multiplying it by the number 6.
7 to the second power simply means 7x7.
7x7= 49
Now that the exponent is in the equation, we can multiply 49 by 6 to find your final answer.
6 x 49 = 294
I hope this helps answer your question! Have a great day!
-MMMski
Answer:
Part 1) ![m\angle AFE=55^o](https://tex.z-dn.net/?f=m%5Cangle%20AFE%3D55%5Eo)
Part 2) ![m\angle EFB=125^o](https://tex.z-dn.net/?f=m%5Cangle%20EFB%3D125%5Eo)
Step-by-step explanation:
Part 1) what is the measure of angle AFE
we know that
The measure of the interior angle is the semisum of the arches that comprise it and its opposite.
<u>Note:</u> In this problem the correct measure of arc EA is 40 degrees (see the picture)
so
![m\angle AFE=\frac{1}{2}(arc\ EA+arc\ DB)](https://tex.z-dn.net/?f=m%5Cangle%20AFE%3D%5Cfrac%7B1%7D%7B2%7D%28arc%5C%20EA%2Barc%5C%20DB%29)
substitute the given values
![m\angle AFE=\frac{1}{2}(40^o+70^o)=55^o](https://tex.z-dn.net/?f=m%5Cangle%20AFE%3D%5Cfrac%7B1%7D%7B2%7D%2840%5Eo%2B70%5Eo%29%3D55%5Eo)
Part 2) what is the measure of angle EFB?
we know that
---> by supplementary angles (form a linear pair)
so
substitute the given value
![55^o+m\angle EFB=180^o](https://tex.z-dn.net/?f=55%5Eo%2Bm%5Cangle%20EFB%3D180%5Eo)
![m\angle EFB=180^o-55^o=125^o](https://tex.z-dn.net/?f=m%5Cangle%20EFB%3D180%5Eo-55%5Eo%3D125%5Eo)
Answer:
![x=4\\\\y=-1](https://tex.z-dn.net/?f=x%3D4%5C%5C%5C%5Cy%3D-1)
Step-by-step explanation:
Given Equation:
Equation:1
Equation:2
Dividing Equation:2 by '3' both the sides:
or
Equation:3
Putting the vale of 'x' in Equation:1
![x-3y=7](https://tex.z-dn.net/?f=x-3y%3D7)
![(3-y)-3y=7\\\\3-y-3y=7\\\\3-4y=7\\\\](https://tex.z-dn.net/?f=%283-y%29-3y%3D7%5C%5C%5C%5C3-y-3y%3D7%5C%5C%5C%5C3-4y%3D7%5C%5C%5C%5C)
Subtracting '3' both sides
![-4y=7-3\\\\-4y=4](https://tex.z-dn.net/?f=-4y%3D7-3%5C%5C%5C%5C-4y%3D4)
![y=\frac{4}{-4}](https://tex.z-dn.net/?f=y%3D%5Cfrac%7B4%7D%7B-4%7D)
![y=-1](https://tex.z-dn.net/?f=y%3D-1)
Putting value of 'y' in Equation:3
![x=3-y](https://tex.z-dn.net/?f=x%3D3-y)
![x=3-(-1)\\\\x=3+1\\\\x=4](https://tex.z-dn.net/?f=x%3D3-%28-1%29%5C%5C%5C%5Cx%3D3%2B1%5C%5C%5C%5Cx%3D4)
The solution of the equations is :
![x=4\\\\y=-1](https://tex.z-dn.net/?f=x%3D4%5C%5C%5C%5Cy%3D-1)