Lets try substitution5x+2y=21=5x=21-2y=x=(21-2y)/5
sub into second equation
-2(21-2y)/5+6y=-34(-42+4y)/5+6y=-34solve for yy=-64/17plug into equation and solve for x=(97/17)
Answer:
A, B, and B.
Step-by-step explanation:
-2
-5
Right on the number line, -2 > -5
Answer:
<h2>The total number of outcomes is 8.</h2>
Step-by-step explanation:
We know that there are different golf balls, white and pink, orange and purple, yellow and red. There are three jars with two golf balls each.
If Kendall chooses one golf ball from each jar, the total number of balls selected would be 4. Now, there are two different colors per jar, and 8 total golf balls with different colors. But, the sets can't have repetitions, and the order matters.
Having said that, the total number of possible sets is:
- White, Orange, Yellow.
- White, Purple, Red.
- White, Orange Red.
- White, Purple, Yellow.
- Pink, Orange, Yellow.
- Pink, Purple, Red.
- Pink, Purple, Yellow.
- Pink, Orange, Red.
Notice that these eight outcomes includes all possible results.
Therefore, there are 8 possible outcomes.
How To Solve Systems of Inequalities Graphically
1) Write the inequality in slope-intercept form or in the form
y
=
m
x
+
b
y=mx+b
.
For example, if asked to solve
x
+
y
≤
10
x+y≤10
, we first re-write as
y
≤
−
x
+
10
y≤−x+10
.
2) Temporarily exchange the given inequality symbol (in this case
≤
≤
) for just equal symbol. In doing so, you can treat the inequality like an equation. BUT DO NOT forget to replace the equal symbol with the original inequality symbol at the END of the problem!
So,
y
≤
−
x
+
10
y≤−x+10
becomes
y
=
−
x
+
10
y=−x+10
for the moment.
3) Graph the line found in step 2. This will form the "boundary" of the inequality -- on one side of the line the condition will be true, on the other side it will not. Review how to graph a line here.
4) Revisit the inequality we found before as
y
≤
−
x
+
10
y≤−x+10
. Notice that it is true when y is less than or equal to. In step 3 we plotted the line (the equal-to case), so now we need to account for the less-than case. Since y is less than a particular value on the low-side of the axis, we will shade the region below the line to indicate that the inequality is true for all points below the line:
5) Verify. Plug in a point not on the line, like (0,0). Verify that the inequality holds. In this case, that means
0
≤
−
0
+
10
0≤−0+10
, which is clearly true. We have shaded the correct side of the line.
By definition a triangle's third side must be larger than the difference of the other two sides (so in this case 10-10 = 0, so it must be larger than 0) and smaller than the sum (so 10+10 = 20 so it must be smaller than 20). Because this is not a specific type of triangle such as a right triangle, this is really the only rule that applies in this problem, so everything except E and F apply.
