1. 1/2- you count the total (8) and then count the two and all the numbers greater than 5( don’t count 5) that is 4 so it would be 4/8 simplified to 1/2
2. 1/2- count the total (still 8) and how many prime numbers there are (4- 2,3,5, and 7) the answer is 4/8 simplified to 1/2
Answer:
7.5
Step-by-step explanation:
106% of $x = $7.95
In other words,
![\[\frac{106}{100}\]](https://tex.z-dn.net/?f=%5C%5B%5Cfrac%7B106%7D%7B100%7D%5C%5D)
of $x = 7.95
Multiplying both sides of the equation by ![\[\frac{100}{106}\]](https://tex.z-dn.net/?f=%5C%5B%5Cfrac%7B100%7D%7B106%7D%5C%5D)
![\[\frac{106}{100} * \frac{100}{106}\]](https://tex.z-dn.net/?f=%5C%5B%5Cfrac%7B106%7D%7B100%7D%20%2A%20%5Cfrac%7B100%7D%7B106%7D%5C%5D)
of x = 7.95 * ![[\frac{100}{106}]](https://tex.z-dn.net/?f=%5B%5Cfrac%7B100%7D%7B106%7D%5D)
=> x = ![[\frac{750}{100}]](https://tex.z-dn.net/?f=%5B%5Cfrac%7B750%7D%7B100%7D%5D)
=> x = ![[\frac{7.50}{1}]](https://tex.z-dn.net/?f=%5B%5Cfrac%7B7.50%7D%7B1%7D%5D)
=> x = 7.5
Validation: 106% of 7.5 = 7.95
Answer:
The perpendicular line would be y = -2x - 4
Step-by-step explanation:
First we must solve the original equation for y.
x - 2y = 7
-2y = -x + 7
y = 1/2x - 7/2
In order to find the equation of this line, we first have to note that perpendicular lines have opposite and reciprocal slopes. Therefore, since the original line has a slope of 1/2, we know the new line will have a slope of -2. Now we can use that information along with the given point in point-slope form to find the equation.
y - y1 = m(x - x1)
y - 2 = -2(x + 3)
y - 2 = -2x - 6
y = -2x - 4
Answer:
Step-by-step explanation:
a+b+c=0, a+b=-c,a+c=-b, b+c=-a
(a+b+c)^3=(a+b+c)^2*(a+b+c)=(a^2+b^2+c^2+2ab+2ac+2bc)*(a+b+c)=
a^3+ab^2+ac^2+2a^2b+2a^2c+2abc+a^2b+b^3+bc^2+2ab^2+2abc+2b^2c+a^2c+b^2c+c^3+2abc+2ac^2+2bc^2=a^3+b^3+c^3+3a^2b+3a^2c+3ac^2+3ab^2+3bc^2+3b^2c+6abc=
a^3+b^3+c^3+3a^2*(b+c)+3c^2(a+b)+3b^2(a+c)+6abc=
a^3+b^3+c^3+3a^2*(-a)+3c^2*(-c)+3b^2*(-b)+6abc=
a^3+b^3+c^3-3a^3-3c^3-3b^3+6abc=
6abc-2a^3-2b^3-2c^3=2(3abc-a^3-b^3-c^3)=
2*[3abc-(a^3+b^3+c^3)]=0
so 3abc-(a^3+b^3+c^3)=0
so a^3+b^3+c^3=3abc
Answer:
A^k/b^k
Step-by-step explanation:
A/b^k=a^k/b^k
