Answer:
Given system of equations:
To solve by substitution, equate the equations and solve for x:
Therefore, the x-values of the solution are 
and 
.
To find the y-values of the solution, substitute the found values of x into the functions:
Therefore, the solutions to the given system of equations are:
and 
Answer:
c = 20 ft
Step-by-step explanation:
The largest square will be 14 sqrt(2) ft long
To figure out the side length of the square
use the pythagorean theorem
a^2 + b^2 =c^2
we are limited by the shortest side of the rectangle
28 ft
each side of the triangle is 1/2 the length of the short side of the rectangle or 14 ft
a^2 + b^2 =c^2
14^2 + 14^2 = c^2 where c is the side of the square
196 + 196 = c^2
392 = c^2
take the square root of each side
sqrt(392) = sqrt(c^2)
c = 14sqrt(2)
c = 19.799ft
to the nearest whole number
c = 20 ft
Answer:
B and E
Step-by-step explanation:
A. 8x = 2
8(4) = 2
32 = 2
B. 19 + x = 23
19 + 4 = 23
23 = 23
C. 40/x = 5
40/4 = 5
10 = 5
D. -3x = 12
-3(4) = 12
-12 = 12
E. x - x - x - x = -8
4 - 4 - 4 - 4 = -8
0 - 4 - 4 = -8
-4 - 4 = -8
-4 + (-4) = -8
-8 = -8
Options
The circle at the new location has _____________ the original circle.
- the same center as
- twice the circumference of
- half the radius of
- the same area as
Answer:
the same area as
Step-by-step explanation:
When a circle is translated and reflected, the center of the circle will change; however, its area, circumference, radius and diameter remain the same.
This is so because, translation and reflection only affect the positioning of the circle not the size.
Considering the above analysis, we can conclude that option d answers the question correctly.
First, we inspect what type of sequence is the order of the coordinates:
a2 = 1
a3 = 2
a4 = 4
Getting the difference,
a3 - a2 = 1
a4 - a3 = 2
The differences are not equal; hence, the sequence is not arithmetic.
Getting the ratio:
a3/a2 = 2
a4/a3 = 2
The common ratio is 2. Using the general form for a geometric series:
an = a1 r^(n-1)
If n = 2
1 = a1 (2)^(2-1)
a1 = 1/2
So,
an = (1/2) (2)^(n-1)
The answer is the first option.
