In this case, because both numbers are negative, -5.31 is greater then -5.313 as it is closer to the positive numbers on a number line. I hope that helped! :D
Solution
Step 1:
There are three types of systems of linear equations in two variables, and three types of solutions.
1. An independent system has exactly one solution pair. The point where the two lines intersect is the only solution.
2. An inconsistent system has no solution.
3. A dependent system has infinitely many solutions.
Step 2
Solve the systems of the equations using the substitution method
![\begin{gathered} \text{y = -x + 4} \\ 2x\text{ + 2y = 8} \\ 2x\text{ + 2\lparen-x + 4\rparen = 8} \\ 2x\text{ - 2x + 8 = 8} \\ 8\text{ = 8} \end{gathered}](https://tex.z-dn.net/?f=%5Cbegin%7Bgathered%7D%20%5Ctext%7By%20%3D%20-x%20%2B%204%7D%20%5C%5C%202x%5Ctext%7B%20%2B%202y%20%3D%208%7D%20%5C%5C%202x%5Ctext%7B%20%2B%202%5Clparen-x%20%2B%204%5Crparen%20%3D%208%7D%20%5C%5C%202x%5Ctext%7B%20-%202x%20%2B%208%20%3D%208%7D%20%5C%5C%208%5Ctext%7B%20%3D%208%7D%20%5Cend%7Bgathered%7D)
Final answer
The system is dependent so there are infinite solutions.
Equivalent
Answer:
Dividing by 4 and -4
Step-by-step explanation:
Solving 4x < -16 is different from solving -4x< 16, because for 4x < -16, you are dividing by a positive 4 on both sides, but for -4x< 16, you are dividing by -4 on both sides.
Answer:
<u>True Statements:</u>
"Kaylee's necklace can have 25 pieces of rotelle"
"Kaylee's necklace can have 10 macaroni noodles and 15 pieces of rotelle"
"Kaylee's necklace can have 1 macaroni noodle"
Step-by-step explanation:
First condition:
max pieces is 25
Checking the choices, we eliminate anyone having more than 25 pieces.
choice 1 - 26 piece NO
choice 2 - 25 piece OK
choice 3 - 25 piece OK
choice 4 - 25 piece OK
choice 5 - 1 piece OK
choice 6 - 25 piece OK
So we eliminate first choice. Now, 2nd condition is 15 macaroni or 50 rotelle, so that's 50/15 = 3.33 rotelle = 1 macaroni
We check each choice and convert macaroni to rotelle and make sure they are under 50
choice 2 - 25 rotelle, so OK
choice 3 - 10*3.33 + 15 = 48.3, under 50, so OK
choice 4 - 14*3.33 + 11 = 57.62, NOT OK
choice 5 - 1*3.33 = 3.33 rotelle OK
choice 6 - 16*3.33 + 9 = 62.28 rotelle , NOT OK
So finally, the statements that are TRUE are:
Choice 2, Choice 3, Choice 5
That "|x + 2|" indicates that the vertex of the most basic absolute value function, y=|x|, has been shifted 2 units to the left. That "+4" indicates that the vertex has been shifted 4 units up. Thus, the vertex of f(x)=|x+2|+4 is (-2,4).