Answer:
1) D: All of the above.
2) A: No solution
3) B: One solution
Step-by-step explanation:
<h3>1. The systems of linear equations can be solved through the following methods: </h3>
Graphing method: Using the slope and y-intercepts of each equation to plot points and graph the lines to see whether the given system has a <u>point of intersection</u> as a solution.
Elimination method: this involves either <u>adding</u> (when the coefficients have opposite signs) or <u>subtracting</u> (when the coefficients have the same sign).
Substitution method: involves solving for one of the variables of either equations, and substituting the values of that expression into the other linear equation in the system.
Therefore, the correct answer is Option D: All of the above.
<h3>2. Graph of Parallel Lines:</h3>
Given the graph of parallel lines, which means that they will never have a point of intersection. Therefore, the given systems of linear equations have no solution. Therefore, the correct answer is Option A: No solution.
<h3>3. Graph of Two Intersecting lines</h3>
Given the graph of two non-perpendicular intersecting lines, it means that they have <u>one point of intersection</u> that represents the <em>solution</em> to the given system.
Therefore, the correct answer is Option B: One solution.
Answer:
3(2x + 3) = 5(x + 1)
Step-by-step explanation:
lets call the number X
She will have to have run for 30 minutes to have run 3 miles.
Answer:
y= -11/144(x-8)^2+6
Step-by-step explanation:
This equation can be represented in vertex form, which is:
y=a(x-h)^2+k
If we plug in 8 as h and 6 as k we get the following equation:
y=a(x-8)^2+6
Now we have to plug in x and y. We can use the other point (-4,-5) and plug it into the equation and get:
-5=a(-4-8)^2+6
Once we solve this we get a= -11/144
Now we have to plug in -11/144 into the original equation to get
y = -11/144 (x-8)^2 + 6
8320 cubes can fit into the prism.
Solution:
Convert mixed fraction into improper fraction.
Length of the prism = 20 in
Width of the prism = 2 in
Height of the prism = 
in
Volume of the prism = length × width × height
= 130 in³
Volume of the prism = 130 in³
Length of the cube = 
in
Volume of the cube = length × length × length
Volume of the cube = 0.015625 in³
= 8320
Number of cubes = 8320
Hence 8320 cubes can fit into the prism.
