let the numbers are x , x+1 ,x+2
∴ 6 [ x + (x+1) +(x+2) ] = 162
∴ x + (x+1) + (x+2) = 162/6 = 27
∴3x + 3 = 27
∴ 3x = 27 - 3 = 24
∴ x = 24/3 = 8
<u>So, the numbers are 8 , 9 , 10</u>
Answer:
(d) 2x +y = 8
Step-by-step explanation:
The answer choices are shown in "standard form," so the comparison to the given equation is easier if it is written in standard form. Add 2x to both sides:
2x +y = 5 . . . . . . given equation in standard form
The other equation in a system with no solution will look like this, but will have a different constant:
2x +y = 8 . . . . . . does not intersect the given equation
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<em>Additional comment</em>
All of the other equations shown will intersect the given equation. One way to show this is to use the given equation to substitute for y in the answer choices:
a: 2x -(-2x+5) = 8 ⇒ 6x -5 = 8 . . . one solution: x=13/6
b: x +2(-2x+5) = 8 ⇒ -3x +10 = 8 . . . one solution: x=2/3
c: x -2(-2x+5) = 8 ⇒ 5x -10 = 8 . . . one solution: x=18/5
d: 2x +(-2x+5) = 8 ⇒ 5 = 8 . . . no solution
Answer:
B. y > 3x -7
Step-by-step explanation:
We can choose the correct inequality based on the y-intercept and the shading.
<h3>Y-intercept</h3>
The dashed line crosses the y-axis at approximately y=-7. This is the value of y when x=0. This observation eliminates choices D, E, F.
<h3>Shading</h3>
The shading on the graph is seen to be above and to the left of the line. This means the variables in relation to the inequality symbol must be ...
y > ( ) . . . . eliminates choice A
and
x < ( ) or ( ) > x . . . . eliminates choice C, confirms choice B
The inequality that matches the graph is y > 3x -7.
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<em>Additional comment</em>
For looking at shading, we are interested in the relation of the inequality symbol to a variable term with a <em>positive coefficient</em>. If the coefficient is negative, you can do either of ...
- add the opposite of that variable term to both sides of the equation
- reverse the inequality symbol
That is, if you have -3x < ( ), when considering shading, you can consider the relation x > ( ) with the inequality reversed, or you can consider ( ) < x, which has x on the other side of the inequality. Both of these tell you shading is right of the line, where x-values are greater than those on the line.
Your answer is 33 because you do the opposite of -6, so 27+6=33
