The goal is to translate the triangle with the given vertices in any which you choose and then prove that the original triangle and the translated triangle are congruent by the side-side-side postulate (i.e., if 3 sides of a triangle are equal to 3 sides of another triangle (in length/distance)...
-2x + 2 + x - 5 = 1 - 2x - x + 5
first, simplify the equation by combining any like terms on either side of the equation:
-2x + 2 + x - 5 = 1
- 2x - x + 5
y + 5 = 2(x + 8)
=> distribute the 2 on the right hand side of the equation into each term inside the parentheses to get:
y + 5 = 2x + 16
=> subtract 5 from both sides of the equation to get:
y = -2x - 8 ; -4x - y = 24
the substitution method requires that you solve one of the given equation for one of the unknown variables in term of the other variable and substitute it into the other given equation and that would leave you with an equation...
(1) Translations: f(x+c) => translates graph c units to the left
(-1/6)t ≥ 9
First, multiply both sides of the inequality by 6:
6·(-1/6)t ≥ 6·9
(-6/6)t ≥ 54
(-1)t ≥ 54
Divide both sides of the inequality by -1, remembering that when you divide...
-4y - (5y + 6) = -7y + 3
Distribute the negative sign into the terms inside the parentheses on the left hand side:
-4y + (-5y - 6) = -7y + 3
-4y + -5y + -6 = -7y + 3
The example states the following: 4 nm ≥ 4x10-9 m
The conversion is from nanometers (nm) to meters (m). Since 1 nm = 1x10-9 m , 4 nm was converted to m by multiplying 4 nm by 1x10-9 m/1 nm , in which the nm in the denominator and numerator cancel...
It would be helpful if you included the original problem for which the final result you are asking about, but since the topic you posted this under is factoring expressions completely then we can find what the original expression should be from the final result you have and work from that.
Recall: i = √(-1) ==> i2 = (√(-1))2 = -1
i6 • i8 = i6+8
Given: ƒ(x) = 0.0316x2 + 0.015x - 0.046
x = time (in years) from 1981 to 2006 ,
where 1981: x = 1 , 1982: x = 2 , ... , 2006: x = 26
(a) the year 2001 corresponds to x = 21
First note that anything to the power of 0 is equal to 1....so since z0=1, then the expression is now as follows:
(4x2y3)(5x-3y-2) = 4·5·x2·x-3·y3·y-2
Recall that the slope, m, of a line given two points, (x1, y1) and (x2, y2), on the line is defined by the following formula:
m = (y2 - y1)/(x2 - x1)
Given: (x1, y1) = (-3, -5)
(3x2 + 2x - 5) + (5x2 - 4x + 6)
Here you have two trinomials being added to one another. To simplify this expression, simply combine like terms:
(3x2 + 5x2) + (2x - 4x) + (-5 + 6)
Given that the distance, h, a body will move in a free fall is expressed by the following formula:
h = (1/2)gt2 ,
where g = 980 cm/sec/sec (or, g = 980 cm/sec2) and
t = 20 sec
Then to solve for h, plug in the given values...
Given that the volume, v, of a pyramid is defined by the following formula: v = bh/3 ...
...then to find the formula that defines the altitude, h, you need to isolate the variable is question (h) to one side of the equation. To do so, first multiply both sides of the equation...
Find the greatest common factor among each expression:
18/24 ==> factors of 18: 1, 2, 3, 6, 9, 18
factors of 24: ...
Given that the area, A, of a circle is defined by the following formula:
A = πr2 , where r is the radius of the circle ....
....then the area of a circle with a radius of 6 ft is as follows:
The altitude of a triangle is equivalent to the height of a triangle.
Recall that the area, A, of a triangle is defined by the following formula:
A = (1/2)bh ,
where b is the base of the triangle and
h is the height of the triangle.
You are given...
Given: (1) 3x + 2y + z = 6
(2) x + y + 3z = -5
(3) 4x + y - z = 10
Since you are only looking...